Initial Problem

Start: eval_textbook_ex3_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_textbook_ex3_bb0_in, eval_textbook_ex3_bb1_in, eval_textbook_ex3_bb2_in, eval_textbook_ex3_bb3_in, eval_textbook_ex3_bb4_in, eval_textbook_ex3_bb5_in, eval_textbook_ex3_bb6_in, eval_textbook_ex3_bb7_in, eval_textbook_ex3_bb8_in, eval_textbook_ex3_start, eval_textbook_ex3_stop
Transitions:
1:eval_textbook_ex3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb1_in(Arg_0,1,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_textbook_ex3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,1,Arg_4,Arg_5):|:Arg_1<=Arg_5
3:eval_textbook_ex3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb8_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<Arg_1
4:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_3<=Arg_1
5:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<Arg_3
6:eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb4_in(Arg_2+1,Arg_1,Arg_2,Arg_3,1,Arg_5):|:Arg_2+1<=Arg_5
7:eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb6_in(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<Arg_2+1
9:eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4,Arg_5):|:Arg_0<Arg_4
8:eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4<=Arg_0
10:eval_textbook_ex3_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5)
11:eval_textbook_ex3_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5)
12:eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5)
13:eval_textbook_ex3_bb8_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
0:eval_textbook_ex3_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Found invariant 2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_textbook_ex3_bb5_in

Found invariant 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 for location eval_textbook_ex3_bb2_in

Found invariant Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_textbook_ex3_bb6_in

Found invariant 1<=Arg_1 for location eval_textbook_ex3_bb1_in

Found invariant 2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2+Arg_2 && Arg_4<=1+Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_textbook_ex3_bb4_in

Found invariant 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 for location eval_textbook_ex3_bb3_in

Found invariant 1+Arg_5<=Arg_1 && 1<=Arg_1 for location eval_textbook_ex3_bb8_in

Found invariant 1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_1 for location eval_textbook_ex3_bb7_in

Found invariant 1+Arg_5<=Arg_1 && 1<=Arg_1 for location eval_textbook_ex3_stop

Problem after Preprocessing

Start: eval_textbook_ex3_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: eval_textbook_ex3_bb0_in, eval_textbook_ex3_bb1_in, eval_textbook_ex3_bb2_in, eval_textbook_ex3_bb3_in, eval_textbook_ex3_bb4_in, eval_textbook_ex3_bb5_in, eval_textbook_ex3_bb6_in, eval_textbook_ex3_bb7_in, eval_textbook_ex3_bb8_in, eval_textbook_ex3_start, eval_textbook_ex3_stop
Transitions:
1:eval_textbook_ex3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb1_in(Arg_0,1,Arg_2,Arg_3,Arg_4,Arg_5)
2:eval_textbook_ex3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,1,Arg_4,Arg_5):|:1<=Arg_1 && Arg_1<=Arg_5
3:eval_textbook_ex3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb8_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_1 && Arg_5<Arg_1
4:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_3<=Arg_1
5:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_1<Arg_3
6:eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb4_in(Arg_2+1,Arg_1,Arg_2,Arg_3,1,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_2+1<=Arg_5
7:eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb6_in(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<Arg_2+1
9:eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4,Arg_5):|:2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2+Arg_2 && Arg_4<=1+Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<Arg_4
8:eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2+Arg_2 && Arg_4<=1+Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_4<=Arg_0
10:eval_textbook_ex3_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5):|:2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
11:eval_textbook_ex3_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5):|:Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0
12:eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_1
13:eval_textbook_ex3_bb8_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1+Arg_5<=Arg_1 && 1<=Arg_1
0:eval_textbook_ex3_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

MPRF for transition 2:eval_textbook_ex3_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,1,Arg_4,Arg_5):|:1<=Arg_1 && Arg_1<=Arg_5 of depth 1:

new bound:

Arg_5+2 {O(n)}

MPRF:

eval_textbook_ex3_bb3_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb5_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb4_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb6_in [Arg_2-Arg_1 ]
eval_textbook_ex3_bb2_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb7_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [Arg_5+1-Arg_1 ]

MPRF for transition 5:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_1<Arg_3 of depth 1:

new bound:

Arg_5+2 {O(n)}

MPRF:

eval_textbook_ex3_bb3_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb5_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb4_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb6_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb2_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb7_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [Arg_5+1-Arg_1 ]

MPRF for transition 12:eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb1_in(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_5+1 {O(n)}

MPRF:

eval_textbook_ex3_bb3_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb5_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb4_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb6_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb2_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb7_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [2*Arg_5-Arg_1 ]

MPRF for transition 4:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_3<=Arg_1 of depth 1:

new bound:

4*Arg_5*Arg_5+6*Arg_5+3 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [Arg_1 ]
eval_textbook_ex3_bb7_in [Arg_1-Arg_3 ]
eval_textbook_ex3_bb3_in [Arg_1-Arg_3 ]
eval_textbook_ex3_bb5_in [Arg_1-Arg_3 ]
eval_textbook_ex3_bb4_in [Arg_1-Arg_3 ]
eval_textbook_ex3_bb6_in [Arg_1-Arg_3 ]
eval_textbook_ex3_bb2_in [Arg_1+1-Arg_3 ]

MPRF for transition 7:eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb6_in(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<Arg_2+1 of depth 1:

new bound:

2*Arg_5*Arg_5+2*Arg_5 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [Arg_5 ]
eval_textbook_ex3_bb7_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb3_in [Arg_5+1-Arg_3 ]
eval_textbook_ex3_bb5_in [Arg_5+1-Arg_3 ]
eval_textbook_ex3_bb4_in [Arg_5+1-Arg_3 ]
eval_textbook_ex3_bb6_in [Arg_2-Arg_3 ]
eval_textbook_ex3_bb2_in [Arg_5+1-Arg_3 ]

MPRF for transition 11:eval_textbook_ex3_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5):|:Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

8*Arg_5*Arg_5+12*Arg_5+6 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [2*Arg_1 ]
eval_textbook_ex3_bb7_in [2*Arg_1-Arg_3 ]
eval_textbook_ex3_bb3_in [2*Arg_1-Arg_3 ]
eval_textbook_ex3_bb5_in [2*Arg_1-Arg_3 ]
eval_textbook_ex3_bb4_in [2*Arg_1-Arg_3 ]
eval_textbook_ex3_bb6_in [2*Arg_1-Arg_3 ]
eval_textbook_ex3_bb2_in [2*Arg_1-Arg_3 ]

MPRF for transition 6:eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb4_in(Arg_2+1,Arg_1,Arg_2,Arg_3,1,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_2+1<=Arg_5 of depth 1:

new bound:

24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+43*Arg_5+13 {O(n^3)}

MPRF:

eval_textbook_ex3_bb2_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb6_in [Arg_5-Arg_2 ]
eval_textbook_ex3_bb3_in [Arg_5-Arg_2 ]
eval_textbook_ex3_bb5_in [Arg_5-Arg_2-1 ]
eval_textbook_ex3_bb4_in [Arg_5-Arg_2-1 ]
eval_textbook_ex3_bb7_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [Arg_5-Arg_1 ]

MPRF for transition 9:eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb3_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4,Arg_5):|:2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2+Arg_2 && Arg_4<=1+Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_0<Arg_4 of depth 1:

new bound:

24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+43*Arg_5+13 {O(n^3)}

MPRF:

eval_textbook_ex3_bb2_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb6_in [Arg_3+Arg_5-Arg_1-Arg_2 ]
eval_textbook_ex3_bb3_in [Arg_5-Arg_2 ]
eval_textbook_ex3_bb5_in [Arg_5+1-Arg_0 ]
eval_textbook_ex3_bb4_in [Arg_5+1-Arg_0 ]
eval_textbook_ex3_bb7_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [Arg_5-Arg_1 ]

MPRF for transition 8:eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2+Arg_2 && Arg_4<=1+Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_4<=Arg_0 of depth 1:

new bound:

1152*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+4992*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+9920*Arg_5*Arg_5*Arg_5*Arg_5+11360*Arg_5*Arg_5*Arg_5+7818*Arg_5*Arg_5+3048*Arg_5+521 {O(n^6)}

MPRF:

eval_textbook_ex3_bb3_in [2*Arg_2+2*Arg_5-3*Arg_1 ]
eval_textbook_ex3_bb5_in [Arg_0+2*Arg_2-2*Arg_1-Arg_4 ]
eval_textbook_ex3_bb4_in [Arg_0+2*Arg_2+1-2*Arg_1-Arg_4 ]
eval_textbook_ex3_bb6_in [2*Arg_0+2*Arg_5-3*Arg_1-2 ]
eval_textbook_ex3_bb2_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb7_in [2*Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [2*Arg_5-Arg_1 ]

MPRF for transition 10:eval_textbook_ex3_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5):|:2<=Arg_5 && 3<=Arg_4+Arg_5 && Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+741 {O(n^6)}

MPRF:

eval_textbook_ex3_bb3_in [3*Arg_2+3*Arg_5-3*Arg_1 ]
eval_textbook_ex3_bb5_in [3*Arg_0-Arg_4-3 ]
eval_textbook_ex3_bb4_in [3*Arg_0-Arg_4-3 ]
eval_textbook_ex3_bb6_in [3*Arg_2+3*Arg_5-3*Arg_1 ]
eval_textbook_ex3_bb2_in [3*Arg_5 ]
eval_textbook_ex3_bb7_in [3*Arg_5 ]
eval_textbook_ex3_bb1_in [3*Arg_5 ]

Analysing control-flow refined program

Cut unsatisfiable transition 5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in

Found invariant 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 for location eval_textbook_ex3_bb2_in

Found invariant Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb6_in___11

Found invariant 1+Arg_5<=Arg_4 && Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 3<=Arg_4 && 4<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 6<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 2+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 for location n_eval_textbook_ex3_bb6_in___5

Found invariant 2<=Arg_5 && 4<=Arg_4+Arg_5 && Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2 && Arg_4<=1+Arg_3 && Arg_4<=1+Arg_2 && Arg_4<=1+Arg_1 && Arg_4<=Arg_0 && 2<=Arg_4 && 3<=Arg_3+Arg_4 && 3<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 4<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb4_in___9

Found invariant 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 for location n_eval_textbook_ex3_bb3_in___13

Found invariant 1<=Arg_1 for location eval_textbook_ex3_bb1_in

Found invariant 1+Arg_5<=Arg_4 && Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 3<=Arg_4 && 5<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 6<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 for location n_eval_textbook_ex3_bb2_in___4

Found invariant 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=1+Arg_0 && 3<=Arg_4 && 4<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 5<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb3_in___6

Found invariant Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 4<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 2<=Arg_1 && 5<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 3<=Arg_0 for location n_eval_textbook_ex3_bb3_in___2

Found invariant 2<=Arg_5 && 3<=Arg_4+Arg_5 && 1+Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1 && Arg_4<=Arg_3 && Arg_4<=Arg_2 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb4_in___12

Found invariant 2<=Arg_5 && 4<=Arg_4+Arg_5 && Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 2<=Arg_4 && 3<=Arg_3+Arg_4 && 3<=Arg_2+Arg_4 && 3<=Arg_1+Arg_4 && 4<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb5_in___8

Found invariant 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=2+Arg_2 && Arg_4<=1+Arg_0 && 3<=Arg_4 && 4<=Arg_3+Arg_4 && 4<=Arg_2+Arg_4 && 4<=Arg_1+Arg_4 && 5<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb4_in___7

Found invariant 2<=Arg_5 && 3<=Arg_4+Arg_5 && 1+Arg_4<=Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 3<=Arg_2+Arg_5 && 1+Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1 && Arg_4<=Arg_3 && Arg_4<=Arg_2 && Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1<=Arg_4 && 2<=Arg_3+Arg_4 && 2<=Arg_2+Arg_4 && 2<=Arg_1+Arg_4 && 3<=Arg_0+Arg_4 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb5_in___10

Found invariant 1+Arg_5<=Arg_1 && 1<=Arg_1 for location eval_textbook_ex3_bb8_in

Found invariant Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=1+Arg_2 && Arg_3<=1+Arg_1 && Arg_3<=Arg_0 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 for location n_eval_textbook_ex3_bb2_in___3

Found invariant Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=1+Arg_2 && Arg_3<=1+Arg_1 && Arg_3<=Arg_0 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location eval_textbook_ex3_bb7_in

Found invariant Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 4<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 2<=Arg_1 && 5<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 3<=Arg_0 for location n_eval_textbook_ex3_bb6_in___1

Found invariant 1+Arg_5<=Arg_1 && 1<=Arg_1 for location eval_textbook_ex3_stop

knowledge_propagation leads to new time bound Arg_5+2 {O(n)} for transition 111:eval_textbook_ex3_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb3_in___13(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_3<=Arg_1 && 1<=Arg_3 && Arg_1<=Arg_5 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 && Arg_3<=1 && 1<=Arg_3 && 1<=Arg_1 && Arg_1<=Arg_5 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5

knowledge_propagation leads to new time bound Arg_5+2 {O(n)} for transition 115:n_eval_textbook_ex3_bb3_in___13(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb6_in___11(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_1<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 && 1<=Arg_3 && Arg_5<1+Arg_2 && Arg_2<=Arg_5 && Arg_1<=Arg_2 && Arg_3<=Arg_1

knowledge_propagation leads to new time bound Arg_5+2 {O(n)} for transition 126:n_eval_textbook_ex3_bb6_in___11(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb2_in___3(Arg_0,Arg_1,Arg_0-1,Arg_3+1,Arg_4,Arg_0-1):|:Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && Arg_5<Arg_0 && Arg_0<=1+Arg_5 && Arg_0<=Arg_1+1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && Arg_3<=Arg_1 && 1<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && Arg_0<=Arg_5+1 && 1+Arg_5<=Arg_0

MPRF for transition 112:n_eval_textbook_ex3_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb3_in___2(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=1+Arg_2 && Arg_3<=1+Arg_1 && Arg_3<=Arg_0 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 && 1<=Arg_3 && Arg_1<=Arg_5 && Arg_5<1+Arg_1 && Arg_1<=Arg_5 && Arg_5<=Arg_1 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=1+Arg_5 && 1+Arg_5<=Arg_0 && 2<=Arg_3 && Arg_3<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 of depth 1:

new bound:

2*Arg_5*Arg_5+13*Arg_5+15 {O(n^2)}

MPRF:

eval_textbook_ex3_bb2_in [3*Arg_5-3*Arg_1 ]
eval_textbook_ex3_bb1_in [3*Arg_5-3*Arg_1 ]
eval_textbook_ex3_bb7_in [3*Arg_0+Arg_5-3*Arg_1-Arg_2-3 ]
n_eval_textbook_ex3_bb3_in___13 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb6_in___11 [Arg_5-Arg_0 ]
n_eval_textbook_ex3_bb3_in___2 [Arg_5+1-Arg_3 ]
n_eval_textbook_ex3_bb4_in___12 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb3_in___6 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb5_in___10 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb4_in___9 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb5_in___8 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb4_in___7 [3*Arg_5-3*Arg_1 ]
n_eval_textbook_ex3_bb6_in___1 [Arg_0-Arg_3 ]
n_eval_textbook_ex3_bb2_in___3 [Arg_1+2-Arg_3 ]
n_eval_textbook_ex3_bb6_in___5 [3*Arg_4-3*Arg_1-3 ]
n_eval_textbook_ex3_bb2_in___4 [2*Arg_4+Arg_5-3*Arg_1-2 ]

MPRF for transition 141:n_eval_textbook_ex3_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 1<=Arg_5 && 3<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 3<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=1+Arg_2 && Arg_3<=1+Arg_1 && Arg_3<=Arg_0 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_1<Arg_3 of depth 1:

new bound:

Arg_5+2 {O(n)}

MPRF:

eval_textbook_ex3_bb2_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb1_in [Arg_5+1-Arg_1 ]
eval_textbook_ex3_bb7_in [Arg_2-Arg_1 ]
n_eval_textbook_ex3_bb3_in___13 [Arg_5+1-Arg_2 ]
n_eval_textbook_ex3_bb3_in___2 [1 ]
n_eval_textbook_ex3_bb4_in___12 [Arg_4+Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb3_in___6 [Arg_4+Arg_5-Arg_1-Arg_2 ]
n_eval_textbook_ex3_bb5_in___10 [Arg_5+1-Arg_1 ]
n_eval_textbook_ex3_bb4_in___9 [Arg_5+1-Arg_1 ]
n_eval_textbook_ex3_bb5_in___8 [Arg_5+1-Arg_1 ]
n_eval_textbook_ex3_bb4_in___7 [Arg_5+1-Arg_1 ]
n_eval_textbook_ex3_bb6_in___1 [1 ]
n_eval_textbook_ex3_bb6_in___11 [1 ]
n_eval_textbook_ex3_bb2_in___3 [1 ]
n_eval_textbook_ex3_bb6_in___5 [Arg_4-Arg_1 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_2+1-Arg_1 ]

MPRF for transition 113:n_eval_textbook_ex3_bb2_in___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb3_in___13(Arg_0,Arg_1,Arg_1,Arg_3,Arg_4,Arg_5):|:1+Arg_5<=Arg_4 && Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 3<=Arg_4 && 5<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 6<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 && 1<=Arg_3 && Arg_1<=Arg_5 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=1+Arg_5 && 1+Arg_5<=Arg_0 && 2<=Arg_3 && Arg_3<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 of depth 1:

new bound:

8*Arg_5*Arg_5+12*Arg_5+5 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [2*Arg_5-Arg_1-1 ]
eval_textbook_ex3_bb2_in [2*Arg_5-Arg_1-1 ]
eval_textbook_ex3_bb7_in [-2*Arg_1 ]
n_eval_textbook_ex3_bb3_in___13 [2*Arg_5-Arg_1-Arg_3-2 ]
n_eval_textbook_ex3_bb3_in___2 [-2*Arg_1 ]
n_eval_textbook_ex3_bb4_in___12 [2*Arg_5-Arg_1-Arg_3-2*Arg_4 ]
n_eval_textbook_ex3_bb3_in___6 [2*Arg_5-Arg_1-Arg_3-2 ]
n_eval_textbook_ex3_bb5_in___10 [2*Arg_5-Arg_1-Arg_3-2*Arg_4 ]
n_eval_textbook_ex3_bb4_in___9 [2*Arg_5-Arg_1-Arg_3-2 ]
n_eval_textbook_ex3_bb5_in___8 [2*Arg_5-Arg_1-Arg_3-2 ]
n_eval_textbook_ex3_bb4_in___7 [2*Arg_5-Arg_1-Arg_3-2 ]
n_eval_textbook_ex3_bb6_in___1 [-2*Arg_1 ]
n_eval_textbook_ex3_bb6_in___11 [2*Arg_5-2*Arg_1-2 ]
n_eval_textbook_ex3_bb2_in___3 [-2*Arg_1 ]
n_eval_textbook_ex3_bb6_in___5 [Arg_0+Arg_4-Arg_1-Arg_3-4 ]
n_eval_textbook_ex3_bb2_in___4 [2*Arg_5-Arg_1-Arg_3-1 ]

MPRF for transition 142:n_eval_textbook_ex3_bb2_in___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> eval_textbook_ex3_bb7_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1+Arg_5<=Arg_4 && Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 3<=Arg_4 && 5<=Arg_3+Arg_4 && 1+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 6<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_3<=Arg_2 && Arg_3<=1+Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 3<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 && 1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=1+Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_1 && Arg_1<Arg_3 of depth 1:

new bound:

Arg_5+1 {O(n)}

MPRF:

eval_textbook_ex3_bb2_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb1_in [Arg_5-Arg_1 ]
eval_textbook_ex3_bb7_in [Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb3_in___13 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb3_in___2 [Arg_2-Arg_5 ]
n_eval_textbook_ex3_bb4_in___12 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb3_in___6 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb5_in___10 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb4_in___9 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb5_in___8 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb4_in___7 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb6_in___1 [Arg_1-Arg_5 ]
n_eval_textbook_ex3_bb6_in___11 [Arg_5-Arg_1 ]
n_eval_textbook_ex3_bb2_in___3 [Arg_2-Arg_5 ]
n_eval_textbook_ex3_bb6_in___5 [Arg_2-Arg_1 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_5-Arg_1 ]

MPRF for transition 114:n_eval_textbook_ex3_bb3_in___13(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb4_in___12(Arg_2+1,Arg_1,Arg_2,Arg_3,1,Arg_5):|:1<=Arg_5 && 2<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 2<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 2<=Arg_1+Arg_5 && Arg_1<=Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_1 && Arg_1<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 && 1<=Arg_3 && 1+Arg_2<=Arg_5 && Arg_1<=Arg_2 && Arg_3<=Arg_1 of depth 1:

new bound:

4*Arg_5*Arg_5+6*Arg_5+3 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [Arg_1 ]
eval_textbook_ex3_bb2_in [Arg_1 ]
eval_textbook_ex3_bb7_in [-Arg_2 ]
n_eval_textbook_ex3_bb3_in___13 [Arg_2+1-Arg_3 ]
n_eval_textbook_ex3_bb3_in___2 [0 ]
n_eval_textbook_ex3_bb4_in___12 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb3_in___6 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb5_in___10 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb4_in___9 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb5_in___8 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb4_in___7 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb6_in___1 [0 ]
n_eval_textbook_ex3_bb6_in___11 [0 ]
n_eval_textbook_ex3_bb2_in___3 [0 ]
n_eval_textbook_ex3_bb6_in___5 [Arg_1-Arg_3 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_1+1-Arg_3 ]

MPRF for transition 116:n_eval_textbook_ex3_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb6_in___1(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 4<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 2<=Arg_1 && 5<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 3<=Arg_0 && Arg_1<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && Arg_5<1+Arg_2 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && Arg_2<=Arg_5 && Arg_5<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 && Arg_2<=Arg_5 && Arg_5<=Arg_2 && 1<=Arg_3 && Arg_3<=Arg_1 && Arg_1<=Arg_5 && 1<=Arg_3 && Arg_5<1+Arg_2 && Arg_2<=Arg_5 && Arg_1<=Arg_2 && Arg_3<=Arg_1 of depth 1:

new bound:

6*Arg_5*Arg_5+24*Arg_5+21 {O(n^2)}

MPRF:

eval_textbook_ex3_bb2_in [2*Arg_5+1 ]
eval_textbook_ex3_bb1_in [2*Arg_5+1 ]
eval_textbook_ex3_bb7_in [Arg_0+Arg_2 ]
n_eval_textbook_ex3_bb3_in___13 [2*Arg_5+1 ]
n_eval_textbook_ex3_bb6_in___11 [Arg_1+Arg_2+1 ]
n_eval_textbook_ex3_bb3_in___2 [3*Arg_1+2-Arg_3 ]
n_eval_textbook_ex3_bb4_in___12 [Arg_4+2*Arg_5 ]
n_eval_textbook_ex3_bb3_in___6 [2*Arg_5+1 ]
n_eval_textbook_ex3_bb5_in___10 [Arg_4+2*Arg_5 ]
n_eval_textbook_ex3_bb4_in___9 [2*Arg_5+1 ]
n_eval_textbook_ex3_bb5_in___8 [2*Arg_5+1 ]
n_eval_textbook_ex3_bb4_in___7 [2*Arg_5+1 ]
n_eval_textbook_ex3_bb6_in___1 [3*Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb2_in___3 [3*Arg_1+2-Arg_3 ]
n_eval_textbook_ex3_bb6_in___5 [2*Arg_4-1 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_2+Arg_5+1 ]

MPRF for transition 118:n_eval_textbook_ex3_bb3_in___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb6_in___5(Arg_2+1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=1+Arg_0 && 3<=Arg_4 && 4<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 5<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 4<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=Arg_2 && Arg_3<=Arg_1 && 1<=Arg_3 && Arg_2<=Arg_5 && Arg_1<=Arg_5 && 1<=Arg_3 && Arg_5<1+Arg_2 && Arg_2<=Arg_5 && Arg_1<=Arg_2 && Arg_3<=Arg_1 of depth 1:

new bound:

6*Arg_5*Arg_5+10*Arg_5+5 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [Arg_1+Arg_5+1 ]
eval_textbook_ex3_bb2_in [Arg_1+Arg_5-Arg_3 ]
eval_textbook_ex3_bb7_in [Arg_2-Arg_3 ]
n_eval_textbook_ex3_bb3_in___13 [Arg_2+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb3_in___2 [Arg_0-1 ]
n_eval_textbook_ex3_bb4_in___12 [Arg_1+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb3_in___6 [Arg_1+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb5_in___10 [Arg_1+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb4_in___9 [Arg_1+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb5_in___8 [Arg_1+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb4_in___7 [Arg_1+Arg_5-Arg_3 ]
n_eval_textbook_ex3_bb6_in___1 [Arg_5 ]
n_eval_textbook_ex3_bb6_in___11 [Arg_5 ]
n_eval_textbook_ex3_bb2_in___3 [Arg_2 ]
n_eval_textbook_ex3_bb6_in___5 [Arg_1+Arg_5-Arg_3-1 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_1+Arg_5-Arg_3 ]

MPRF for transition 125:n_eval_textbook_ex3_bb6_in___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb2_in___3(Arg_0,Arg_1,Arg_0-1,Arg_3+1,Arg_4,Arg_0-1):|:Arg_5<=Arg_2 && Arg_5<=Arg_1 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 4<=Arg_1+Arg_5 && Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 5<=Arg_0+Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1+Arg_1<=Arg_0 && 2<=Arg_1 && 5<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 3<=Arg_0 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && Arg_0<=Arg_1+1 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_5+1 && 1+Arg_5<=Arg_0 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && Arg_3<=Arg_1 && 1<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && Arg_0<=Arg_5+1 && 1+Arg_5<=Arg_0 of depth 1:

new bound:

2*Arg_5*Arg_5+9*Arg_5+10 {O(n^2)}

MPRF:

eval_textbook_ex3_bb2_in [0 ]
eval_textbook_ex3_bb1_in [0 ]
eval_textbook_ex3_bb7_in [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb3_in___13 [0 ]
n_eval_textbook_ex3_bb6_in___11 [0 ]
n_eval_textbook_ex3_bb3_in___2 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb4_in___12 [0 ]
n_eval_textbook_ex3_bb3_in___6 [0 ]
n_eval_textbook_ex3_bb5_in___10 [0 ]
n_eval_textbook_ex3_bb4_in___9 [0 ]
n_eval_textbook_ex3_bb5_in___8 [0 ]
n_eval_textbook_ex3_bb4_in___7 [0 ]
n_eval_textbook_ex3_bb6_in___1 [Arg_0-Arg_3 ]
n_eval_textbook_ex3_bb2_in___3 [Arg_0-Arg_3 ]
n_eval_textbook_ex3_bb6_in___5 [0 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_2+1-Arg_4 ]

MPRF for transition 127:n_eval_textbook_ex3_bb6_in___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_textbook_ex3_bb2_in___4(Arg_0,Arg_1,Arg_0-1,Arg_3+1,Arg_4,Arg_0-1):|:1+Arg_5<=Arg_4 && Arg_5<=Arg_2 && 1+Arg_5<=Arg_0 && 2<=Arg_5 && 5<=Arg_4+Arg_5 && Arg_4<=1+Arg_5 && 3<=Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 4<=Arg_2+Arg_5 && Arg_2<=Arg_5 && 3<=Arg_1+Arg_5 && 1+Arg_1<=Arg_5 && 5<=Arg_0+Arg_5 && Arg_0<=1+Arg_5 && Arg_4<=1+Arg_2 && Arg_4<=Arg_0 && 3<=Arg_4 && 4<=Arg_3+Arg_4 && 2+Arg_3<=Arg_4 && 5<=Arg_2+Arg_4 && 1+Arg_2<=Arg_4 && 4<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 6<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 2+Arg_3<=Arg_0 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_1 && 1<=Arg_3 && Arg_5<Arg_0 && Arg_0<=1+Arg_5 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && Arg_3<=Arg_1 && 1<=Arg_3 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2+1 && 1+Arg_2<=Arg_0 && Arg_0<=Arg_5+1 && 1+Arg_5<=Arg_0 of depth 1:

new bound:

20*Arg_5*Arg_5+26*Arg_5+9 {O(n^2)}

MPRF:

eval_textbook_ex3_bb1_in [4*Arg_5-3*Arg_1 ]
eval_textbook_ex3_bb2_in [Arg_1 ]
eval_textbook_ex3_bb7_in [Arg_1-Arg_5 ]
n_eval_textbook_ex3_bb3_in___13 [Arg_2+1-Arg_3 ]
n_eval_textbook_ex3_bb3_in___2 [0 ]
n_eval_textbook_ex3_bb4_in___12 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb3_in___6 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb5_in___10 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb4_in___9 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb5_in___8 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb4_in___7 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb6_in___1 [0 ]
n_eval_textbook_ex3_bb6_in___11 [Arg_2-Arg_3 ]
n_eval_textbook_ex3_bb2_in___3 [0 ]
n_eval_textbook_ex3_bb6_in___5 [Arg_1+1-Arg_3 ]
n_eval_textbook_ex3_bb2_in___4 [Arg_1+1-Arg_3 ]

All Bounds

Timebounds

Overall timebound:2880*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+12480*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+24728*Arg_5*Arg_5*Arg_5*Arg_5+28220*Arg_5*Arg_5*Arg_5+19378*Arg_5*Arg_5+7562*Arg_5+1306 {O(n^6)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in: 1 {O(1)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in: Arg_5+2 {O(n)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in: 1 {O(1)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in: 4*Arg_5*Arg_5+6*Arg_5+3 {O(n^2)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in: Arg_5+2 {O(n)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+43*Arg_5+13 {O(n^3)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in: 2*Arg_5*Arg_5+2*Arg_5 {O(n^2)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in: 1152*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+4992*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+9920*Arg_5*Arg_5*Arg_5*Arg_5+11360*Arg_5*Arg_5*Arg_5+7818*Arg_5*Arg_5+3048*Arg_5+521 {O(n^6)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+43*Arg_5+13 {O(n^3)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+741 {O(n^6)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in: 8*Arg_5*Arg_5+12*Arg_5+6 {O(n^2)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in: 2*Arg_5+1 {O(n)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop: 1 {O(1)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 2880*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+12480*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+24728*Arg_5*Arg_5*Arg_5*Arg_5+28220*Arg_5*Arg_5*Arg_5+19378*Arg_5*Arg_5+7562*Arg_5+1306 {O(n^6)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in: 1 {O(1)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in: Arg_5+2 {O(n)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in: 1 {O(1)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in: 4*Arg_5*Arg_5+6*Arg_5+3 {O(n^2)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in: Arg_5+2 {O(n)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+43*Arg_5+13 {O(n^3)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in: 2*Arg_5*Arg_5+2*Arg_5 {O(n^2)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in: 1152*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+4992*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+9920*Arg_5*Arg_5*Arg_5*Arg_5+11360*Arg_5*Arg_5*Arg_5+7818*Arg_5*Arg_5+3048*Arg_5+521 {O(n^6)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+43*Arg_5+13 {O(n^3)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+741 {O(n^6)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in: 8*Arg_5*Arg_5+12*Arg_5+6 {O(n^2)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in: 2*Arg_5+1 {O(n)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop: 1 {O(1)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in: 1 {O(1)}

Sizebounds

1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in, Arg_0: Arg_0 {O(n)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in, Arg_1: 1 {O(1)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in, Arg_2: Arg_2 {O(n)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in, Arg_3: Arg_3 {O(n)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in, Arg_4: Arg_4 {O(n)}
1: eval_textbook_ex3_bb0_in->eval_textbook_ex3_bb1_in, Arg_5: Arg_5 {O(n)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+Arg_0+23 {O(n^3)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in, Arg_1: 2*Arg_5+2 {O(n)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+Arg_2+21 {O(n^3)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in, Arg_3: 1 {O(1)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+Arg_4+742 {O(n^6)}
2: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb2_in, Arg_5: Arg_5 {O(n)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+Arg_0+23 {O(n^3)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in, Arg_1: 2*Arg_5+3 {O(n)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+Arg_2+21 {O(n^3)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+Arg_3+7 {O(n^2)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+2*Arg_4+4404*Arg_5+742 {O(n^6)}
3: eval_textbook_ex3_bb1_in->eval_textbook_ex3_bb8_in, Arg_5: 2*Arg_5 {O(n)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in, Arg_0: 48*Arg_5*Arg_5*Arg_5+104*Arg_5*Arg_5+102*Arg_5+Arg_0+46 {O(n^3)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in, Arg_1: 2*Arg_5+2 {O(n)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in, Arg_2: 4*Arg_5+4 {O(n)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+Arg_4+742 {O(n^6)}
4: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb3_in, Arg_5: Arg_5 {O(n)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+23 {O(n^3)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in, Arg_1: 2*Arg_5+2 {O(n)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+Arg_4+742 {O(n^6)}
5: eval_textbook_ex3_bb2_in->eval_textbook_ex3_bb7_in, Arg_5: Arg_5 {O(n)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+47*Arg_5+17 {O(n^3)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in, Arg_1: 2*Arg_5+2 {O(n)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in, Arg_4: 1 {O(1)}
6: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb4_in, Arg_5: Arg_5 {O(n)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+23 {O(n^3)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in, Arg_1: 2*Arg_5+2 {O(n)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+Arg_4+742 {O(n^6)}
7: eval_textbook_ex3_bb3_in->eval_textbook_ex3_bb6_in, Arg_5: Arg_5 {O(n)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+47*Arg_5+17 {O(n^3)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in, Arg_1: 2*Arg_5+2 {O(n)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+742 {O(n^6)}
8: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb5_in, Arg_5: Arg_5 {O(n)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+47*Arg_5+17 {O(n^3)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in, Arg_1: 2*Arg_5+2 {O(n)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+47*Arg_5+17 {O(n^3)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+742 {O(n^6)}
9: eval_textbook_ex3_bb4_in->eval_textbook_ex3_bb3_in, Arg_5: Arg_5 {O(n)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+47*Arg_5+17 {O(n^3)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in, Arg_1: 2*Arg_5+2 {O(n)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+742 {O(n^6)}
10: eval_textbook_ex3_bb5_in->eval_textbook_ex3_bb4_in, Arg_5: Arg_5 {O(n)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+23 {O(n^3)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in, Arg_1: 2*Arg_5+2 {O(n)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+Arg_4+742 {O(n^6)}
11: eval_textbook_ex3_bb6_in->eval_textbook_ex3_bb2_in, Arg_5: Arg_5 {O(n)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+23 {O(n^3)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in, Arg_1: 2*Arg_5+2 {O(n)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+21 {O(n^3)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+7 {O(n^2)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+4404*Arg_5+Arg_4+742 {O(n^6)}
12: eval_textbook_ex3_bb7_in->eval_textbook_ex3_bb1_in, Arg_5: Arg_5 {O(n)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop, Arg_0: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+Arg_0+23 {O(n^3)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop, Arg_1: 2*Arg_5+3 {O(n)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop, Arg_2: 24*Arg_5*Arg_5*Arg_5+52*Arg_5*Arg_5+51*Arg_5+Arg_2+21 {O(n^3)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop, Arg_3: 8*Arg_5*Arg_5+12*Arg_5+Arg_3+7 {O(n^2)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop, Arg_4: 1728*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+7488*Arg_5*Arg_5*Arg_5*Arg_5*Arg_5+14808*Arg_5*Arg_5*Arg_5*Arg_5+16812*Arg_5*Arg_5*Arg_5+11442*Arg_5*Arg_5+2*Arg_4+4404*Arg_5+742 {O(n^6)}
13: eval_textbook_ex3_bb8_in->eval_textbook_ex3_stop, Arg_5: 2*Arg_5 {O(n)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in, Arg_4: Arg_4 {O(n)}
0: eval_textbook_ex3_start->eval_textbook_ex3_bb0_in, Arg_5: Arg_5 {O(n)}