Initial Problem

Start: eval_ex2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_ex2_0, eval_ex2_1, eval_ex2_10, eval_ex2_2, eval_ex2_3, eval_ex2_4, eval_ex2_5, eval_ex2_6, eval_ex2_9, eval_ex2_bb0_in, eval_ex2_bb1_in, eval_ex2_bb2_in, eval_ex2_bb3_in, eval_ex2_bb4_in, eval_ex2_bb5_in, eval_ex2_start, eval_ex2_stop
Transitions:
2:eval_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_2(Arg_0,Arg_1,Arg_2,Arg_3)
16:eval_ex2_10(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3)
4:eval_ex2_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_3(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_ex2_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_4(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_ex2_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb1_in(Arg_0,Arg_1,1,Arg_3)
12:eval_ex2_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_6(Arg_0,Arg_1,Arg_2,Arg_3)
13:eval_ex2_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3+1)
15:eval_ex2_9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_10(Arg_0,Arg_1,Arg_2,Arg_3)
1:eval_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_2<=Arg_1
8:eval_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_2
9:eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1
10:eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_3
11:eval_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_5(Arg_0,Arg_1,Arg_2,Arg_3)
14:eval_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_9(Arg_2+1,Arg_1,Arg_2,Arg_3)
17:eval_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_stop(Arg_0,Arg_1,Arg_2,Arg_3)
0:eval_ex2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 for location eval_ex2_10

Found invariant Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_ex2_bb3_in

Found invariant 1<=Arg_2 && 1+Arg_1<=Arg_2 for location eval_ex2_bb5_in

Found invariant Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_ex2_bb4_in

Found invariant Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_ex2_5

Found invariant 1<=Arg_2 for location eval_ex2_bb1_in

Found invariant Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 for location eval_ex2_9

Found invariant Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_ex2_bb2_in

Found invariant 1<=Arg_2 && 1+Arg_1<=Arg_2 for location eval_ex2_stop

Found invariant Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 for location eval_ex2_6

Problem after Preprocessing

Start: eval_ex2_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval_ex2_0, eval_ex2_1, eval_ex2_10, eval_ex2_2, eval_ex2_3, eval_ex2_4, eval_ex2_5, eval_ex2_6, eval_ex2_9, eval_ex2_bb0_in, eval_ex2_bb1_in, eval_ex2_bb2_in, eval_ex2_bb3_in, eval_ex2_bb4_in, eval_ex2_bb5_in, eval_ex2_start, eval_ex2_stop
Transitions:
2:eval_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3)
3:eval_ex2_1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_2(Arg_0,Arg_1,Arg_2,Arg_3)
16:eval_ex2_10(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0
4:eval_ex2_2(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_3(Arg_0,Arg_1,Arg_2,Arg_3)
5:eval_ex2_3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_4(Arg_0,Arg_1,Arg_2,Arg_3)
6:eval_ex2_4(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb1_in(Arg_0,Arg_1,1,Arg_3)
12:eval_ex2_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_6(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1
13:eval_ex2_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1
15:eval_ex2_9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_10(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0
1:eval_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_0(Arg_0,Arg_1,Arg_2,Arg_3)
7:eval_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_2):|:1<=Arg_2 && Arg_2<=Arg_1
8:eval_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && Arg_1<Arg_2
9:eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_3<=Arg_1
10:eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_1<Arg_3
11:eval_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1
14:eval_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_9(Arg_2+1,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1
17:eval_ex2_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_stop(Arg_0,Arg_1,Arg_2,Arg_3):|:1<=Arg_2 && 1+Arg_1<=Arg_2
0:eval_ex2_start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 16:eval_ex2_10(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval_ex2_6 [2*Arg_1-Arg_2 ]
eval_ex2_10 [2*Arg_1-Arg_2 ]
eval_ex2_bb1_in [2*Arg_1-Arg_2 ]
eval_ex2_bb2_in [2*Arg_1-Arg_2 ]
eval_ex2_bb3_in [2*Arg_1-Arg_2 ]
eval_ex2_5 [2*Arg_1-Arg_2 ]
eval_ex2_bb4_in [2*Arg_1-Arg_2 ]
eval_ex2_9 [2*Arg_1-Arg_2 ]

MPRF for transition 15:eval_ex2_9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_10(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 4<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 2<=Arg_0 of depth 1:

new bound:

3*Arg_1+1 {O(n)}

MPRF:

eval_ex2_6 [3*Arg_1-Arg_2 ]
eval_ex2_10 [3*Arg_1-Arg_2-1 ]
eval_ex2_bb1_in [3*Arg_1-Arg_2 ]
eval_ex2_bb2_in [3*Arg_1-Arg_2 ]
eval_ex2_bb3_in [3*Arg_1-Arg_2 ]
eval_ex2_5 [3*Arg_1-Arg_2 ]
eval_ex2_bb4_in [3*Arg_1-Arg_2 ]
eval_ex2_9 [3*Arg_1-Arg_2 ]

MPRF for transition 7:eval_ex2_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_2):|:1<=Arg_2 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_ex2_6 [Arg_1-Arg_2 ]
eval_ex2_10 [Arg_1+1-Arg_0 ]
eval_ex2_bb1_in [Arg_1+1-Arg_2 ]
eval_ex2_bb2_in [Arg_1-Arg_2 ]
eval_ex2_bb3_in [Arg_1-Arg_2 ]
eval_ex2_5 [Arg_1-Arg_2 ]
eval_ex2_bb4_in [Arg_1-Arg_2 ]
eval_ex2_9 [Arg_1+1-Arg_0 ]

MPRF for transition 10:eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_1<Arg_3 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_ex2_6 [Arg_1+1-Arg_2 ]
eval_ex2_10 [Arg_1+1-Arg_0 ]
eval_ex2_bb1_in [Arg_1+1-Arg_2 ]
eval_ex2_bb2_in [Arg_1+1-Arg_2 ]
eval_ex2_bb3_in [Arg_1+1-Arg_2 ]
eval_ex2_5 [Arg_1+1-Arg_2 ]
eval_ex2_bb4_in [Arg_1-Arg_2 ]
eval_ex2_9 [Arg_1+1-Arg_0 ]

MPRF for transition 14:eval_ex2_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_9(Arg_2+1,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

eval_ex2_6 [Arg_1+1-Arg_2 ]
eval_ex2_10 [Arg_1-Arg_2 ]
eval_ex2_bb1_in [Arg_1+1-Arg_2 ]
eval_ex2_bb2_in [Arg_1+1-Arg_2 ]
eval_ex2_bb3_in [Arg_1+1-Arg_2 ]
eval_ex2_5 [Arg_1+1-Arg_2 ]
eval_ex2_bb4_in [Arg_1+1-Arg_2 ]
eval_ex2_9 [Arg_1-Arg_2 ]

MPRF for transition 12:eval_ex2_5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_6(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}

MPRF:

eval_ex2_6 [Arg_1-Arg_3 ]
eval_ex2_9 [Arg_1 ]
eval_ex2_10 [Arg_1 ]
eval_ex2_bb1_in [Arg_1+1-Arg_2 ]
eval_ex2_bb2_in [Arg_1+1-Arg_3 ]
eval_ex2_bb4_in [Arg_1-Arg_3 ]
eval_ex2_bb3_in [Arg_1+1-Arg_3 ]
eval_ex2_5 [Arg_1+1-Arg_3 ]

MPRF for transition 13:eval_ex2_6(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_1*Arg_1+3*Arg_1 {O(n^2)}

MPRF:

eval_ex2_6 [Arg_1+1-Arg_3 ]
eval_ex2_9 [Arg_1 ]
eval_ex2_10 [Arg_1 ]
eval_ex2_bb1_in [Arg_1 ]
eval_ex2_bb2_in [Arg_1+1-Arg_3 ]
eval_ex2_bb4_in [Arg_1-Arg_3 ]
eval_ex2_bb3_in [Arg_1+1-Arg_3 ]
eval_ex2_5 [Arg_1+1-Arg_3 ]

MPRF for transition 9:eval_ex2_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_3<=Arg_1 of depth 1:

new bound:

Arg_1*Arg_1+3*Arg_1 {O(n^2)}

MPRF:

eval_ex2_6 [Arg_1-Arg_3 ]
eval_ex2_9 [Arg_1 ]
eval_ex2_10 [Arg_1 ]
eval_ex2_bb1_in [Arg_1 ]
eval_ex2_bb2_in [Arg_1+1-Arg_3 ]
eval_ex2_bb4_in [Arg_1-Arg_3 ]
eval_ex2_bb3_in [Arg_1-Arg_3 ]
eval_ex2_5 [Arg_1-Arg_3 ]

MPRF for transition 11:eval_ex2_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3) -> eval_ex2_5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_1 of depth 1:

new bound:

Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}

MPRF:

eval_ex2_6 [Arg_1-Arg_3 ]
eval_ex2_9 [Arg_1 ]
eval_ex2_10 [Arg_1 ]
eval_ex2_bb1_in [Arg_1+1-Arg_2 ]
eval_ex2_bb2_in [Arg_1+1-Arg_3 ]
eval_ex2_bb4_in [Arg_1-Arg_3 ]
eval_ex2_bb3_in [Arg_1+1-Arg_3 ]
eval_ex2_5 [Arg_1-Arg_3 ]

All Bounds

Timebounds

Overall timebound:4*Arg_1*Arg_1+20*Arg_1+21 {O(n^2)}
2: eval_ex2_0->eval_ex2_1: 1 {O(1)}
3: eval_ex2_1->eval_ex2_2: 1 {O(1)}
16: eval_ex2_10->eval_ex2_bb1_in: 2*Arg_1+1 {O(n)}
4: eval_ex2_2->eval_ex2_3: 1 {O(1)}
5: eval_ex2_3->eval_ex2_4: 1 {O(1)}
6: eval_ex2_4->eval_ex2_bb1_in: 1 {O(1)}
12: eval_ex2_5->eval_ex2_6: Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}
13: eval_ex2_6->eval_ex2_bb2_in: Arg_1*Arg_1+3*Arg_1 {O(n^2)}
15: eval_ex2_9->eval_ex2_10: 3*Arg_1+1 {O(n)}
1: eval_ex2_bb0_in->eval_ex2_0: 1 {O(1)}
7: eval_ex2_bb1_in->eval_ex2_bb2_in: Arg_1+2 {O(n)}
8: eval_ex2_bb1_in->eval_ex2_bb5_in: 1 {O(1)}
9: eval_ex2_bb2_in->eval_ex2_bb3_in: Arg_1*Arg_1+3*Arg_1 {O(n^2)}
10: eval_ex2_bb2_in->eval_ex2_bb4_in: Arg_1+2 {O(n)}
11: eval_ex2_bb3_in->eval_ex2_5: Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}
14: eval_ex2_bb4_in->eval_ex2_9: Arg_1+2 {O(n)}
17: eval_ex2_bb5_in->eval_ex2_stop: 1 {O(1)}
0: eval_ex2_start->eval_ex2_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_1*Arg_1+20*Arg_1+21 {O(n^2)}
2: eval_ex2_0->eval_ex2_1: 1 {O(1)}
3: eval_ex2_1->eval_ex2_2: 1 {O(1)}
16: eval_ex2_10->eval_ex2_bb1_in: 2*Arg_1+1 {O(n)}
4: eval_ex2_2->eval_ex2_3: 1 {O(1)}
5: eval_ex2_3->eval_ex2_4: 1 {O(1)}
6: eval_ex2_4->eval_ex2_bb1_in: 1 {O(1)}
12: eval_ex2_5->eval_ex2_6: Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}
13: eval_ex2_6->eval_ex2_bb2_in: Arg_1*Arg_1+3*Arg_1 {O(n^2)}
15: eval_ex2_9->eval_ex2_10: 3*Arg_1+1 {O(n)}
1: eval_ex2_bb0_in->eval_ex2_0: 1 {O(1)}
7: eval_ex2_bb1_in->eval_ex2_bb2_in: Arg_1+2 {O(n)}
8: eval_ex2_bb1_in->eval_ex2_bb5_in: 1 {O(1)}
9: eval_ex2_bb2_in->eval_ex2_bb3_in: Arg_1*Arg_1+3*Arg_1 {O(n^2)}
10: eval_ex2_bb2_in->eval_ex2_bb4_in: Arg_1+2 {O(n)}
11: eval_ex2_bb3_in->eval_ex2_5: Arg_1*Arg_1+3*Arg_1+2 {O(n^2)}
14: eval_ex2_bb4_in->eval_ex2_9: Arg_1+2 {O(n)}
17: eval_ex2_bb5_in->eval_ex2_stop: 1 {O(1)}
0: eval_ex2_start->eval_ex2_bb0_in: 1 {O(1)}

Sizebounds

2: eval_ex2_0->eval_ex2_1, Arg_0: Arg_0 {O(n)}
2: eval_ex2_0->eval_ex2_1, Arg_1: Arg_1 {O(n)}
2: eval_ex2_0->eval_ex2_1, Arg_2: Arg_2 {O(n)}
2: eval_ex2_0->eval_ex2_1, Arg_3: Arg_3 {O(n)}
3: eval_ex2_1->eval_ex2_2, Arg_0: Arg_0 {O(n)}
3: eval_ex2_1->eval_ex2_2, Arg_1: Arg_1 {O(n)}
3: eval_ex2_1->eval_ex2_2, Arg_2: Arg_2 {O(n)}
3: eval_ex2_1->eval_ex2_2, Arg_3: Arg_3 {O(n)}
16: eval_ex2_10->eval_ex2_bb1_in, Arg_0: Arg_1+3 {O(n)}
16: eval_ex2_10->eval_ex2_bb1_in, Arg_1: Arg_1 {O(n)}
16: eval_ex2_10->eval_ex2_bb1_in, Arg_2: Arg_1+3 {O(n)}
16: eval_ex2_10->eval_ex2_bb1_in, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
4: eval_ex2_2->eval_ex2_3, Arg_0: Arg_0 {O(n)}
4: eval_ex2_2->eval_ex2_3, Arg_1: Arg_1 {O(n)}
4: eval_ex2_2->eval_ex2_3, Arg_2: Arg_2 {O(n)}
4: eval_ex2_2->eval_ex2_3, Arg_3: Arg_3 {O(n)}
5: eval_ex2_3->eval_ex2_4, Arg_0: Arg_0 {O(n)}
5: eval_ex2_3->eval_ex2_4, Arg_1: Arg_1 {O(n)}
5: eval_ex2_3->eval_ex2_4, Arg_2: Arg_2 {O(n)}
5: eval_ex2_3->eval_ex2_4, Arg_3: Arg_3 {O(n)}
6: eval_ex2_4->eval_ex2_bb1_in, Arg_0: Arg_0 {O(n)}
6: eval_ex2_4->eval_ex2_bb1_in, Arg_1: Arg_1 {O(n)}
6: eval_ex2_4->eval_ex2_bb1_in, Arg_2: 1 {O(1)}
6: eval_ex2_4->eval_ex2_bb1_in, Arg_3: Arg_3 {O(n)}
12: eval_ex2_5->eval_ex2_6, Arg_0: Arg_0+Arg_1+3 {O(n)}
12: eval_ex2_5->eval_ex2_6, Arg_1: Arg_1 {O(n)}
12: eval_ex2_5->eval_ex2_6, Arg_2: Arg_1+3 {O(n)}
12: eval_ex2_5->eval_ex2_6, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
13: eval_ex2_6->eval_ex2_bb2_in, Arg_0: Arg_0+Arg_1+3 {O(n)}
13: eval_ex2_6->eval_ex2_bb2_in, Arg_1: Arg_1 {O(n)}
13: eval_ex2_6->eval_ex2_bb2_in, Arg_2: Arg_1+3 {O(n)}
13: eval_ex2_6->eval_ex2_bb2_in, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
15: eval_ex2_9->eval_ex2_10, Arg_0: Arg_1+3 {O(n)}
15: eval_ex2_9->eval_ex2_10, Arg_1: Arg_1 {O(n)}
15: eval_ex2_9->eval_ex2_10, Arg_2: Arg_1+3 {O(n)}
15: eval_ex2_9->eval_ex2_10, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
1: eval_ex2_bb0_in->eval_ex2_0, Arg_0: Arg_0 {O(n)}
1: eval_ex2_bb0_in->eval_ex2_0, Arg_1: Arg_1 {O(n)}
1: eval_ex2_bb0_in->eval_ex2_0, Arg_2: Arg_2 {O(n)}
1: eval_ex2_bb0_in->eval_ex2_0, Arg_3: Arg_3 {O(n)}
7: eval_ex2_bb1_in->eval_ex2_bb2_in, Arg_0: Arg_0+Arg_1+3 {O(n)}
7: eval_ex2_bb1_in->eval_ex2_bb2_in, Arg_1: Arg_1 {O(n)}
7: eval_ex2_bb1_in->eval_ex2_bb2_in, Arg_2: Arg_1+3 {O(n)}
7: eval_ex2_bb1_in->eval_ex2_bb2_in, Arg_3: Arg_1+4 {O(n)}
8: eval_ex2_bb1_in->eval_ex2_bb5_in, Arg_0: Arg_0+Arg_1+3 {O(n)}
8: eval_ex2_bb1_in->eval_ex2_bb5_in, Arg_1: 2*Arg_1 {O(n)}
8: eval_ex2_bb1_in->eval_ex2_bb5_in, Arg_2: Arg_1+4 {O(n)}
8: eval_ex2_bb1_in->eval_ex2_bb5_in, Arg_3: Arg_1*Arg_1+4*Arg_1+Arg_3+4 {O(n^2)}
9: eval_ex2_bb2_in->eval_ex2_bb3_in, Arg_0: Arg_0+Arg_1+3 {O(n)}
9: eval_ex2_bb2_in->eval_ex2_bb3_in, Arg_1: Arg_1 {O(n)}
9: eval_ex2_bb2_in->eval_ex2_bb3_in, Arg_2: Arg_1+3 {O(n)}
9: eval_ex2_bb2_in->eval_ex2_bb3_in, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
10: eval_ex2_bb2_in->eval_ex2_bb4_in, Arg_0: Arg_0+Arg_1+3 {O(n)}
10: eval_ex2_bb2_in->eval_ex2_bb4_in, Arg_1: Arg_1 {O(n)}
10: eval_ex2_bb2_in->eval_ex2_bb4_in, Arg_2: Arg_1+3 {O(n)}
10: eval_ex2_bb2_in->eval_ex2_bb4_in, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
11: eval_ex2_bb3_in->eval_ex2_5, Arg_0: Arg_0+Arg_1+3 {O(n)}
11: eval_ex2_bb3_in->eval_ex2_5, Arg_1: Arg_1 {O(n)}
11: eval_ex2_bb3_in->eval_ex2_5, Arg_2: Arg_1+3 {O(n)}
11: eval_ex2_bb3_in->eval_ex2_5, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
14: eval_ex2_bb4_in->eval_ex2_9, Arg_0: Arg_1+3 {O(n)}
14: eval_ex2_bb4_in->eval_ex2_9, Arg_1: Arg_1 {O(n)}
14: eval_ex2_bb4_in->eval_ex2_9, Arg_2: Arg_1+3 {O(n)}
14: eval_ex2_bb4_in->eval_ex2_9, Arg_3: Arg_1*Arg_1+4*Arg_1+4 {O(n^2)}
17: eval_ex2_bb5_in->eval_ex2_stop, Arg_0: Arg_0+Arg_1+3 {O(n)}
17: eval_ex2_bb5_in->eval_ex2_stop, Arg_1: 2*Arg_1 {O(n)}
17: eval_ex2_bb5_in->eval_ex2_stop, Arg_2: Arg_1+4 {O(n)}
17: eval_ex2_bb5_in->eval_ex2_stop, Arg_3: Arg_1*Arg_1+4*Arg_1+Arg_3+4 {O(n^2)}
0: eval_ex2_start->eval_ex2_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_ex2_start->eval_ex2_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_ex2_start->eval_ex2_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_ex2_start->eval_ex2_bb0_in, Arg_3: Arg_3 {O(n)}