Initial Problem
Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval_foo_bb0_in___13, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___3, n_eval_foo_bb1_in___8, n_eval_foo_bb2_in___10, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___2, n_eval_foo_bb2_in___6, n_eval_foo_bb2_in___7, n_eval_foo_bb3_in___5, n_eval_foo_bb3_in___9, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___4
Transitions:
0:n_eval_foo_bb0_in___13(Arg_0,Arg_1) -> n_eval_foo_bb1_in___12(Arg_1,Arg_1)
1:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb2_in___10(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
2:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb2_in___11(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<0
3:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb3_in___9(0,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0 && 0<=Arg_0
4:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1):|:0<Arg_0
5:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:Arg_0<0
6:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb3_in___5(0,Arg_1):|:Arg_0<=0 && 0<=Arg_0
7:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1):|:Arg_0<=1 && 0<Arg_0
8:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:Arg_0<=1 && Arg_0<0
9:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb3_in___5(0,Arg_1):|:Arg_0<=1 && Arg_0<=0 && 0<=Arg_0
10:n_eval_foo_bb2_in___10(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1):|:0<Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
11:n_eval_foo_bb2_in___11(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1):|:Arg_0<0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0
12:n_eval_foo_bb2_in___2(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1):|:0<Arg_0 && 0<Arg_0
13:n_eval_foo_bb2_in___6(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0-1,Arg_1):|:Arg_0<=1 && 0<Arg_0 && 0<Arg_0
14:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1):|:Arg_0<0 && Arg_0<=0
15:n_eval_foo_bb3_in___5(Arg_0,Arg_1) -> n_eval_foo_stop___4(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0
16:n_eval_foo_bb3_in___9(Arg_0,Arg_1) -> n_eval_foo_stop___1(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1
17:n_eval_foo_start(Arg_0,Arg_1) -> n_eval_foo_bb0_in___13(Arg_0,Arg_1)
Preprocessing
Cut unsatisfiable transition 5: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___7
Cut unsatisfiable transition 7: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___6
Cut unreachable locations [n_eval_foo_bb2_in___6] from the program graph
Found invariant 2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___7
Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb3_in___9
Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_foo_bb2_in___2
Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval_foo_bb1_in___3
Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_foo_bb2_in___10
Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb3_in___5
Found invariant 1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 1+Arg_0<=0 for location n_eval_foo_bb2_in___11
Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_stop___1
Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_stop___4
Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 for location n_eval_foo_bb1_in___8
Found invariant Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_eval_foo_bb1_in___12
Problem after Preprocessing
Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval_foo_bb0_in___13, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___3, n_eval_foo_bb1_in___8, n_eval_foo_bb2_in___10, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___2, n_eval_foo_bb2_in___7, n_eval_foo_bb3_in___5, n_eval_foo_bb3_in___9, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___4
Transitions:
0:n_eval_foo_bb0_in___13(Arg_0,Arg_1) -> n_eval_foo_bb1_in___12(Arg_1,Arg_1)
1:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb2_in___10(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
2:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb2_in___11(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<0
3:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb3_in___9(0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0 && 0<=Arg_0
4:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<Arg_0
6:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb3_in___5(0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
8:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=1 && Arg_0<0
9:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb3_in___5(0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=1 && Arg_0<=0 && 0<=Arg_0
10:n_eval_foo_bb2_in___10(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
11:n_eval_foo_bb2_in___11(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && 1+Arg_0<=0 && Arg_0<0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0
12:n_eval_foo_bb2_in___2(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 && 0<Arg_0
14:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1):|:2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && Arg_0<0 && Arg_0<=0
15:n_eval_foo_bb3_in___5(Arg_0,Arg_1) -> n_eval_foo_stop___4(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
16:n_eval_foo_bb3_in___9(Arg_0,Arg_1) -> n_eval_foo_stop___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1
17:n_eval_foo_start(Arg_0,Arg_1) -> n_eval_foo_bb0_in___13(Arg_0,Arg_1)
MPRF for transition 4:n_eval_foo_bb1_in___3(Arg_0,Arg_1) -> n_eval_foo_bb2_in___2(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<Arg_0 of depth 1:
new bound:
Arg_1+1 {O(n)}
MPRF:
n_eval_foo_bb2_in___2 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0+1 ]
MPRF for transition 12:n_eval_foo_bb2_in___2(Arg_0,Arg_1) -> n_eval_foo_bb1_in___3(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 && 0<Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
n_eval_foo_bb2_in___2 [Arg_0 ]
n_eval_foo_bb1_in___3 [Arg_0 ]
MPRF for transition 8:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=1 && Arg_0<0 of depth 1:
new bound:
Arg_1+1 {O(n)}
MPRF:
n_eval_foo_bb2_in___7 [-Arg_0 ]
n_eval_foo_bb1_in___8 [1-Arg_0 ]
MPRF for transition 14:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1):|:2+Arg_1<=0 && 1+Arg_1<=Arg_0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && Arg_0<0 && Arg_0<=0 of depth 1:
new bound:
Arg_1+1 {O(n)}
MPRF:
n_eval_foo_bb2_in___7 [1-Arg_0 ]
n_eval_foo_bb1_in___8 [1-Arg_0 ]
All Bounds
Timebounds
Overall timebound:4*Arg_1+14 {O(n)}
0: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
1: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10: 1 {O(1)}
2: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
3: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9: 1 {O(1)}
4: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___2: Arg_1+1 {O(n)}
6: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___5: 1 {O(1)}
8: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: Arg_1+1 {O(n)}
9: n_eval_foo_bb1_in___8->n_eval_foo_bb3_in___5: 1 {O(1)}
10: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___3: 1 {O(1)}
11: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8: 1 {O(1)}
12: n_eval_foo_bb2_in___2->n_eval_foo_bb1_in___3: Arg_1 {O(n)}
14: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8: Arg_1+1 {O(n)}
15: n_eval_foo_bb3_in___5->n_eval_foo_stop___4: 1 {O(1)}
16: n_eval_foo_bb3_in___9->n_eval_foo_stop___1: 1 {O(1)}
17: n_eval_foo_start->n_eval_foo_bb0_in___13: 1 {O(1)}
Costbounds
Overall costbound: 4*Arg_1+14 {O(n)}
0: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
1: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10: 1 {O(1)}
2: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
3: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9: 1 {O(1)}
4: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___2: Arg_1+1 {O(n)}
6: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___5: 1 {O(1)}
8: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: Arg_1+1 {O(n)}
9: n_eval_foo_bb1_in___8->n_eval_foo_bb3_in___5: 1 {O(1)}
10: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___3: 1 {O(1)}
11: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8: 1 {O(1)}
12: n_eval_foo_bb2_in___2->n_eval_foo_bb1_in___3: Arg_1 {O(n)}
14: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8: Arg_1+1 {O(n)}
15: n_eval_foo_bb3_in___5->n_eval_foo_stop___4: 1 {O(1)}
16: n_eval_foo_bb3_in___9->n_eval_foo_stop___1: 1 {O(1)}
17: n_eval_foo_start->n_eval_foo_bb0_in___13: 1 {O(1)}
Sizebounds
0: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12, Arg_0: Arg_1 {O(n)}
0: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12, Arg_1: Arg_1 {O(n)}
1: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10, Arg_0: Arg_1 {O(n)}
1: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10, Arg_1: Arg_1 {O(n)}
2: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_0: Arg_1 {O(n)}
2: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_1: Arg_1 {O(n)}
3: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9, Arg_0: 0 {O(1)}
3: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9, Arg_1: 0 {O(1)}
4: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___2, Arg_0: Arg_1 {O(n)}
4: n_eval_foo_bb1_in___3->n_eval_foo_bb2_in___2, Arg_1: Arg_1 {O(n)}
6: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___5, Arg_0: 0 {O(1)}
6: n_eval_foo_bb1_in___3->n_eval_foo_bb3_in___5, Arg_1: 2*Arg_1 {O(n)}
8: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7, Arg_0: Arg_1 {O(n)}
8: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7, Arg_1: Arg_1 {O(n)}
9: n_eval_foo_bb1_in___8->n_eval_foo_bb3_in___5, Arg_0: 0 {O(1)}
9: n_eval_foo_bb1_in___8->n_eval_foo_bb3_in___5, Arg_1: 2*Arg_1 {O(n)}
10: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___3, Arg_0: Arg_1 {O(n)}
10: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___3, Arg_1: Arg_1 {O(n)}
11: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8, Arg_0: Arg_1 {O(n)}
11: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8, Arg_1: Arg_1 {O(n)}
12: n_eval_foo_bb2_in___2->n_eval_foo_bb1_in___3, Arg_0: Arg_1 {O(n)}
12: n_eval_foo_bb2_in___2->n_eval_foo_bb1_in___3, Arg_1: Arg_1 {O(n)}
14: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8, Arg_0: Arg_1 {O(n)}
14: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8, Arg_1: Arg_1 {O(n)}
15: n_eval_foo_bb3_in___5->n_eval_foo_stop___4, Arg_0: 0 {O(1)}
15: n_eval_foo_bb3_in___5->n_eval_foo_stop___4, Arg_1: 4*Arg_1 {O(n)}
16: n_eval_foo_bb3_in___9->n_eval_foo_stop___1, Arg_0: 0 {O(1)}
16: n_eval_foo_bb3_in___9->n_eval_foo_stop___1, Arg_1: 0 {O(1)}
17: n_eval_foo_start->n_eval_foo_bb0_in___13, Arg_0: Arg_0 {O(n)}
17: n_eval_foo_start->n_eval_foo_bb0_in___13, Arg_1: Arg_1 {O(n)}