Initial Problem

Start: eval_perfect_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_perfect_bb0_in, eval_perfect_bb1_in, eval_perfect_bb2_in, eval_perfect_bb3_in, eval_perfect_bb4_in, eval_perfect_bb5_in, eval_perfect_bb6_in, eval_perfect_start, eval_perfect_stop
Transitions:
2:eval_perfect_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_1,Arg_3,Arg_1):|:1<Arg_1
1:eval_perfect_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=1
3:eval_perfect_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb2_in(Arg_2-1,Arg_1,Arg_2,Arg_1,Arg_4):|:1<Arg_2
4:eval_perfect_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_2<=1
5:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_3
6:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<Arg_0
7:eval_perfect_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3-Arg_0,Arg_4)
8:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4-Arg_0):|:Arg_3<=0 && 0<=Arg_3
9:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:Arg_3<0
10:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:0<Arg_3
11:eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<0
12:eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:0<Arg_4
13:eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=0 && 0<=Arg_4
14:eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_perfect_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Found invariant Arg_4<=Arg_1 && Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 for location eval_perfect_bb1_in

Found invariant Arg_4<=Arg_1 && Arg_2<=1 && 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 for location eval_perfect_bb5_in

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_perfect_bb2_in

Found invariant Arg_4<=Arg_1 && Arg_3<=Arg_1 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_perfect_bb3_in

Found invariant Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_perfect_bb4_in

Problem after Preprocessing

Start: eval_perfect_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval_perfect_bb0_in, eval_perfect_bb1_in, eval_perfect_bb2_in, eval_perfect_bb3_in, eval_perfect_bb4_in, eval_perfect_bb5_in, eval_perfect_bb6_in, eval_perfect_start, eval_perfect_stop
Transitions:
2:eval_perfect_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_1,Arg_3,Arg_1):|:1<Arg_1
1:eval_perfect_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=1
3:eval_perfect_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb2_in(Arg_2-1,Arg_1,Arg_2,Arg_1,Arg_4):|:Arg_4<=Arg_1 && Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 && 1<Arg_2
4:eval_perfect_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 && Arg_2<=1
5:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3
6:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<Arg_0
7:eval_perfect_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3-Arg_0,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_1 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0
8:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4-Arg_0):|:Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=0 && 0<=Arg_3
9:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<0
10:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_3
11:eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_2<=1 && 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 && Arg_4<0
12:eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_2<=1 && 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 && 0<Arg_4
13:eval_perfect_bb5_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_2<=1 && 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 && Arg_4<=0 && 0<=Arg_4
14:eval_perfect_bb6_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
0:eval_perfect_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb0_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 3:eval_perfect_bb1_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb2_in(Arg_2-1,Arg_1,Arg_2,Arg_1,Arg_4):|:Arg_4<=Arg_1 && Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 && 1<Arg_2 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

eval_perfect_bb3_in [Arg_0-1 ]
eval_perfect_bb2_in [Arg_2-2 ]
eval_perfect_bb4_in [Arg_0-1 ]
eval_perfect_bb1_in [Arg_2-1 ]

MPRF for transition 6:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

eval_perfect_bb3_in [2*Arg_0+1-Arg_2 ]
eval_perfect_bb2_in [Arg_0 ]
eval_perfect_bb4_in [Arg_0-1 ]
eval_perfect_bb1_in [Arg_2-1 ]

MPRF for transition 8:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4-Arg_0):|:Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=0 && 0<=Arg_3 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval_perfect_bb3_in [Arg_2 ]
eval_perfect_bb2_in [Arg_2 ]
eval_perfect_bb4_in [Arg_0+1 ]
eval_perfect_bb1_in [Arg_2 ]

MPRF for transition 9:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<0 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

eval_perfect_bb3_in [Arg_0+Arg_1 ]
eval_perfect_bb2_in [Arg_0+Arg_1 ]
eval_perfect_bb4_in [Arg_0+Arg_1 ]
eval_perfect_bb1_in [Arg_1+Arg_2-1 ]

MPRF for transition 10:eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb1_in(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_3 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

eval_perfect_bb3_in [Arg_0 ]
eval_perfect_bb2_in [Arg_0 ]
eval_perfect_bb4_in [Arg_2-1 ]
eval_perfect_bb1_in [Arg_2-1 ]

MPRF for transition 5:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_3 of depth 1:

new bound:

8*Arg_1*Arg_1+14*Arg_1+6 {O(n^2)}

MPRF:

eval_perfect_bb1_in [Arg_1+2-Arg_2 ]
eval_perfect_bb4_in [Arg_3-Arg_0 ]
eval_perfect_bb3_in [Arg_3-Arg_0 ]
eval_perfect_bb2_in [Arg_3+1-Arg_0 ]

MPRF for transition 7:eval_perfect_bb3_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3-Arg_0,Arg_4):|:Arg_4<=Arg_1 && Arg_3<=Arg_1 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

8*Arg_1*Arg_1+6*Arg_1 {O(n^2)}

MPRF:

eval_perfect_bb1_in [Arg_1+Arg_2 ]
eval_perfect_bb4_in [Arg_0+Arg_3-1 ]
eval_perfect_bb3_in [Arg_3 ]
eval_perfect_bb2_in [Arg_0+Arg_3-1 ]

Analysing control-flow refined program

Cut unsatisfiable transition 6: eval_perfect_bb2_in->eval_perfect_bb4_in

Found invariant Arg_4<=Arg_1 && Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 for location eval_perfect_bb1_in

Found invariant Arg_4<=Arg_1 && 1+Arg_3<=Arg_1 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_perfect_bb3_in___1

Found invariant Arg_4<=Arg_1 && Arg_2<=1 && 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 2<=Arg_1 for location eval_perfect_bb5_in

Found invariant Arg_4<=Arg_3 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_perfect_bb3_in___3

Found invariant Arg_4<=Arg_3 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_perfect_bb2_in

Found invariant Arg_4<=Arg_1 && 1+Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_perfect_bb2_in___2

Found invariant Arg_4<=Arg_1 && 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location eval_perfect_bb4_in

knowledge_propagation leads to new time bound Arg_1+1 {O(n)} for transition 101:eval_perfect_bb2_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval_perfect_bb3_in___3(Arg_0,Arg_1,Arg_0+1,Arg_3,Arg_4):|:Arg_4<=Arg_3 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=Arg_1 && Arg_0<=Arg_3 && 1+Arg_0<=Arg_1 && Arg_4<=Arg_1 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && Arg_3<=Arg_1 && Arg_4<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0

knowledge_propagation leads to new time bound Arg_1+1 {O(n)} for transition 103:n_eval_perfect_bb3_in___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval_perfect_bb2_in___2(Arg_0,Arg_1,Arg_0+1,Arg_3-Arg_0,Arg_4):|:Arg_4<=Arg_3 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_3 && 4<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 3<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=Arg_1 && Arg_0<=Arg_3 && 1+Arg_0<=Arg_1 && Arg_4<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_0 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0

MPRF for transition 100:n_eval_perfect_bb2_in___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval_perfect_bb3_in___1(Arg_0,Arg_1,Arg_0+1,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_4<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1+Arg_0<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_0 && Arg_4<=Arg_1 && 0<=Arg_3 && Arg_0+Arg_3<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_3<=Arg_1 && Arg_4<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 of depth 1:

new bound:

6*Arg_1*Arg_1+7*Arg_1 {O(n^2)}

MPRF:

eval_perfect_bb2_in [Arg_1 ]
n_eval_perfect_bb3_in___3 [Arg_1 ]
eval_perfect_bb1_in [Arg_1 ]
eval_perfect_bb4_in [Arg_1 ]
n_eval_perfect_bb3_in___1 [Arg_0+Arg_1+Arg_3-1 ]
n_eval_perfect_bb2_in___2 [Arg_0+Arg_1+Arg_3 ]

MPRF for transition 108:n_eval_perfect_bb2_in___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval_perfect_bb4_in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 2<=Arg_2+Arg_3 && 2<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_3<Arg_0 of depth 1:

new bound:

2*Arg_1 {O(n)}

MPRF:

eval_perfect_bb2_in [Arg_0+Arg_1+1 ]
eval_perfect_bb1_in [Arg_1+Arg_2 ]
eval_perfect_bb4_in [Arg_0+Arg_1 ]
n_eval_perfect_bb3_in___1 [Arg_1+Arg_2 ]
n_eval_perfect_bb3_in___3 [Arg_0+Arg_1+1 ]
n_eval_perfect_bb2_in___2 [Arg_0+Arg_1+1 ]

MPRF for transition 102:n_eval_perfect_bb3_in___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_eval_perfect_bb2_in___2(Arg_0,Arg_1,Arg_0+1,Arg_3-Arg_0,Arg_4):|:Arg_4<=Arg_1 && 1+Arg_3<=Arg_1 && 1<=Arg_3 && 3<=Arg_2+Arg_3 && Arg_2<=1+Arg_3 && 3<=Arg_1+Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_4<=Arg_1 && Arg_0+Arg_3<=Arg_1 && Arg_0<=Arg_3 && 1<=Arg_0 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 && 1<=Arg_0 && Arg_4<=Arg_1 && Arg_3<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=Arg_3 && Arg_0+1<=Arg_2 && Arg_2<=1+Arg_0 of depth 1:

new bound:

5*Arg_1*Arg_1+6*Arg_1+1 {O(n^2)}

MPRF:

eval_perfect_bb2_in [0 ]
n_eval_perfect_bb3_in___3 [0 ]
eval_perfect_bb1_in [0 ]
eval_perfect_bb4_in [0 ]
n_eval_perfect_bb3_in___1 [Arg_3 ]
n_eval_perfect_bb2_in___2 [Arg_0+Arg_3-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:16*Arg_1*Arg_1+26*Arg_1+18 {O(n^2)}
1: eval_perfect_bb0_in->eval_perfect_bb6_in: 1 {O(1)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in: 1 {O(1)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in: Arg_1+1 {O(n)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in: 1 {O(1)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in: 8*Arg_1*Arg_1+14*Arg_1+6 {O(n^2)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in: Arg_1+1 {O(n)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in: 8*Arg_1*Arg_1+6*Arg_1 {O(n^2)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in: Arg_1 {O(n)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in: 2*Arg_1+1 {O(n)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in: Arg_1+1 {O(n)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in: 1 {O(1)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in: 1 {O(1)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in: 1 {O(1)}
14: eval_perfect_bb6_in->eval_perfect_stop: 1 {O(1)}
0: eval_perfect_start->eval_perfect_bb0_in: 1 {O(1)}

Costbounds

Overall costbound: 16*Arg_1*Arg_1+26*Arg_1+18 {O(n^2)}
1: eval_perfect_bb0_in->eval_perfect_bb6_in: 1 {O(1)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in: 1 {O(1)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in: Arg_1+1 {O(n)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in: 1 {O(1)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in: 8*Arg_1*Arg_1+14*Arg_1+6 {O(n^2)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in: Arg_1+1 {O(n)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in: 8*Arg_1*Arg_1+6*Arg_1 {O(n^2)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in: Arg_1 {O(n)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in: 2*Arg_1+1 {O(n)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in: Arg_1+1 {O(n)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in: 1 {O(1)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in: 1 {O(1)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in: 1 {O(1)}
14: eval_perfect_bb6_in->eval_perfect_stop: 1 {O(1)}
0: eval_perfect_start->eval_perfect_bb0_in: 1 {O(1)}

Sizebounds

1: eval_perfect_bb0_in->eval_perfect_bb6_in, Arg_0: Arg_0 {O(n)}
1: eval_perfect_bb0_in->eval_perfect_bb6_in, Arg_1: Arg_1 {O(n)}
1: eval_perfect_bb0_in->eval_perfect_bb6_in, Arg_2: Arg_2 {O(n)}
1: eval_perfect_bb0_in->eval_perfect_bb6_in, Arg_3: Arg_3 {O(n)}
1: eval_perfect_bb0_in->eval_perfect_bb6_in, Arg_4: Arg_4 {O(n)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in, Arg_0: Arg_0 {O(n)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in, Arg_1: Arg_1 {O(n)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in, Arg_2: Arg_1 {O(n)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in, Arg_3: Arg_3 {O(n)}
2: eval_perfect_bb0_in->eval_perfect_bb1_in, Arg_4: Arg_1 {O(n)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in, Arg_0: Arg_1 {O(n)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in, Arg_1: Arg_1 {O(n)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in, Arg_2: 4*Arg_1 {O(n)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in, Arg_3: 4*Arg_1 {O(n)}
3: eval_perfect_bb1_in->eval_perfect_bb2_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in, Arg_0: Arg_1 {O(n)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in, Arg_1: Arg_1 {O(n)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in, Arg_2: 1 {O(1)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in, Arg_3: 0 {O(1)}
4: eval_perfect_bb1_in->eval_perfect_bb5_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in, Arg_0: Arg_1 {O(n)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in, Arg_1: Arg_1 {O(n)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in, Arg_2: 4*Arg_1 {O(n)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in, Arg_3: 4*Arg_1 {O(n)}
5: eval_perfect_bb2_in->eval_perfect_bb3_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in, Arg_0: Arg_1 {O(n)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in, Arg_1: Arg_1 {O(n)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in, Arg_2: 4*Arg_1 {O(n)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in, Arg_3: 4*Arg_1 {O(n)}
6: eval_perfect_bb2_in->eval_perfect_bb4_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in, Arg_0: Arg_1 {O(n)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in, Arg_1: Arg_1 {O(n)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in, Arg_2: 4*Arg_1 {O(n)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in, Arg_3: 4*Arg_1 {O(n)}
7: eval_perfect_bb3_in->eval_perfect_bb2_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_0: Arg_1 {O(n)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_1: Arg_1 {O(n)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_2: Arg_1 {O(n)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_3: 0 {O(1)}
8: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_0: Arg_1 {O(n)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_1: Arg_1 {O(n)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_2: Arg_1 {O(n)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_3: 4*Arg_1 {O(n)}
9: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_0: Arg_1 {O(n)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_1: Arg_1 {O(n)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_2: Arg_1 {O(n)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_3: 4*Arg_1 {O(n)}
10: eval_perfect_bb4_in->eval_perfect_bb1_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_0: Arg_1 {O(n)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_1: Arg_1 {O(n)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_2: 1 {O(1)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_3: 0 {O(1)}
11: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_0: Arg_1 {O(n)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_1: Arg_1 {O(n)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_2: 1 {O(1)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_3: 0 {O(1)}
12: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_4: Arg_1*Arg_1+2*Arg_1 {O(n^2)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_0: Arg_1 {O(n)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_1: Arg_1 {O(n)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_2: 1 {O(1)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_3: 0 {O(1)}
13: eval_perfect_bb5_in->eval_perfect_bb6_in, Arg_4: 0 {O(1)}
14: eval_perfect_bb6_in->eval_perfect_stop, Arg_0: 3*Arg_1+Arg_0 {O(n)}
14: eval_perfect_bb6_in->eval_perfect_stop, Arg_1: 4*Arg_1 {O(n)}
14: eval_perfect_bb6_in->eval_perfect_stop, Arg_2: Arg_2+3 {O(n)}
14: eval_perfect_bb6_in->eval_perfect_stop, Arg_3: Arg_3 {O(n)}
14: eval_perfect_bb6_in->eval_perfect_stop, Arg_4: 2*Arg_1*Arg_1+4*Arg_1+Arg_4 {O(n^2)}
0: eval_perfect_start->eval_perfect_bb0_in, Arg_0: Arg_0 {O(n)}
0: eval_perfect_start->eval_perfect_bb0_in, Arg_1: Arg_1 {O(n)}
0: eval_perfect_start->eval_perfect_bb0_in, Arg_2: Arg_2 {O(n)}
0: eval_perfect_start->eval_perfect_bb0_in, Arg_3: Arg_3 {O(n)}
0: eval_perfect_start->eval_perfect_bb0_in, Arg_4: Arg_4 {O(n)}