Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_foo_bb0_in___13, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___6, n_eval_foo_bb1_in___8, n_eval_foo_bb2_in___10, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___4, n_eval_foo_bb2_in___5, n_eval_foo_bb2_in___7, n_eval_foo_bb3_in___3, n_eval_foo_bb3_in___9, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___2
Transitions:
0:n_eval_foo_bb0_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___12(Arg_1,Arg_1,Arg_2)
1:n_eval_foo_bb1_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___10(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
2:n_eval_foo_bb1_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___11(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<0
3:n_eval_foo_bb1_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb3_in___9(0,Arg_1,Arg_2):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0 && 0<=Arg_0
4:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2):|:0<Arg_0
5:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2):|:Arg_0<0
6:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb3_in___3(0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0
7:n_eval_foo_bb1_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2):|:Arg_0<0 && 1+Arg_0<=0 && Arg_0<0
8:n_eval_foo_bb2_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___6(Arg_0-1,Arg_1,Arg_2):|:0<Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
9:n_eval_foo_bb2_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___8(Arg_0-1,Arg_1,Arg_2):|:Arg_0<0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
10:n_eval_foo_bb2_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___6(Arg_0-1,Arg_1,Arg_2):|:0<Arg_0
11:n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___8(Arg_0-1,Arg_1,Arg_2):|:Arg_0<0
12:n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___8(Arg_0-1,Arg_1,Arg_2):|:1+Arg_0<=0
13:n_eval_foo_bb3_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_stop___2(Arg_0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0
14:n_eval_foo_bb3_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1
15:n_eval_foo_start(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb0_in___13(Arg_0,Arg_1,Arg_2)

Preprocessing

Cut unsatisfiable transition 5: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5

Cut unreachable locations [n_eval_foo_bb2_in___5] from the program graph

Eliminate variables {Arg_2} that do not contribute to the problem

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___4

Found invariant 1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+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 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 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_stop___2

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 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb3_in___3

Found invariant 1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+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

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___6

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___6, n_eval_foo_bb1_in___8, n_eval_foo_bb2_in___10, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___4, n_eval_foo_bb2_in___7, n_eval_foo_bb3_in___3, n_eval_foo_bb3_in___9, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___2
Transitions:
33:n_eval_foo_bb0_in___13(Arg_0,Arg_1) -> n_eval_foo_bb1_in___12(Arg_1,Arg_1)
34: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
35: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
36: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
37:n_eval_foo_bb1_in___6(Arg_0,Arg_1) -> n_eval_foo_bb2_in___4(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && 0<Arg_0
38:n_eval_foo_bb1_in___6(Arg_0,Arg_1) -> n_eval_foo_bb3_in___3(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
39:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+Arg_0<=0 && Arg_0<0 && 1+Arg_0<=0 && Arg_0<0
40:n_eval_foo_bb2_in___10(Arg_0,Arg_1) -> n_eval_foo_bb1_in___6(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
41: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
42:n_eval_foo_bb2_in___4(Arg_0,Arg_1) -> n_eval_foo_bb1_in___6(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0
43:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0-1,Arg_1):|:1+Arg_1<=0 && 3+Arg_0+Arg_1<=0 && 1+Arg_0<=Arg_1 && 2+Arg_0<=0 && 1+Arg_0<=0
44:n_eval_foo_bb3_in___3(Arg_0,Arg_1) -> n_eval_foo_stop___2(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
45: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
46:n_eval_foo_start(Arg_0,Arg_1) -> n_eval_foo_bb0_in___13(Arg_0,Arg_1)

MPRF for transition 37:n_eval_foo_bb1_in___6(Arg_0,Arg_1) -> n_eval_foo_bb2_in___4(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___4 [Arg_0 ]
n_eval_foo_bb1_in___6 [Arg_0+1 ]

MPRF for transition 42:n_eval_foo_bb2_in___4(Arg_0,Arg_1) -> n_eval_foo_bb1_in___6(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_eval_foo_bb2_in___4 [Arg_0 ]
n_eval_foo_bb1_in___6 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
33: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
34: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10: 1 {O(1)}
35: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
36: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9: 1 {O(1)}
37: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4: Arg_1+1 {O(n)}
38: n_eval_foo_bb1_in___6->n_eval_foo_bb3_in___3: 1 {O(1)}
39: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: inf {Infinity}
40: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___6: 1 {O(1)}
41: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8: 1 {O(1)}
42: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___6: Arg_1 {O(n)}
43: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8: inf {Infinity}
44: n_eval_foo_bb3_in___3->n_eval_foo_stop___2: 1 {O(1)}
45: n_eval_foo_bb3_in___9->n_eval_foo_stop___1: 1 {O(1)}
46: n_eval_foo_start->n_eval_foo_bb0_in___13: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
33: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
34: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10: 1 {O(1)}
35: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
36: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9: 1 {O(1)}
37: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4: Arg_1+1 {O(n)}
38: n_eval_foo_bb1_in___6->n_eval_foo_bb3_in___3: 1 {O(1)}
39: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: inf {Infinity}
40: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___6: 1 {O(1)}
41: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8: 1 {O(1)}
42: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___6: Arg_1 {O(n)}
43: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8: inf {Infinity}
44: n_eval_foo_bb3_in___3->n_eval_foo_stop___2: 1 {O(1)}
45: n_eval_foo_bb3_in___9->n_eval_foo_stop___1: 1 {O(1)}
46: n_eval_foo_start->n_eval_foo_bb0_in___13: 1 {O(1)}

Sizebounds

33: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12, Arg_0: Arg_1 {O(n)}
33: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12, Arg_1: Arg_1 {O(n)}
34: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10, Arg_0: Arg_1 {O(n)}
34: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___10, Arg_1: Arg_1 {O(n)}
35: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_0: Arg_1 {O(n)}
35: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_1: Arg_1 {O(n)}
36: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9, Arg_0: 0 {O(1)}
36: n_eval_foo_bb1_in___12->n_eval_foo_bb3_in___9, Arg_1: 0 {O(1)}
37: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4, Arg_0: Arg_1 {O(n)}
37: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___4, Arg_1: Arg_1 {O(n)}
38: n_eval_foo_bb1_in___6->n_eval_foo_bb3_in___3, Arg_0: 0 {O(1)}
38: n_eval_foo_bb1_in___6->n_eval_foo_bb3_in___3, Arg_1: 2*Arg_1 {O(n)}
39: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7, Arg_1: Arg_1 {O(n)}
40: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___6, Arg_0: Arg_1 {O(n)}
40: n_eval_foo_bb2_in___10->n_eval_foo_bb1_in___6, Arg_1: Arg_1 {O(n)}
41: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8, Arg_0: Arg_1+1 {O(n)}
41: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___8, Arg_1: Arg_1 {O(n)}
42: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___6, Arg_0: Arg_1 {O(n)}
42: n_eval_foo_bb2_in___4->n_eval_foo_bb1_in___6, Arg_1: Arg_1 {O(n)}
43: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8, Arg_1: Arg_1 {O(n)}
44: n_eval_foo_bb3_in___3->n_eval_foo_stop___2, Arg_0: 0 {O(1)}
44: n_eval_foo_bb3_in___3->n_eval_foo_stop___2, Arg_1: 2*Arg_1 {O(n)}
45: n_eval_foo_bb3_in___9->n_eval_foo_stop___1, Arg_0: 0 {O(1)}
45: n_eval_foo_bb3_in___9->n_eval_foo_stop___1, Arg_1: 0 {O(1)}
46: n_eval_foo_start->n_eval_foo_bb0_in___13, Arg_0: Arg_0 {O(n)}
46: n_eval_foo_start->n_eval_foo_bb0_in___13, Arg_1: Arg_1 {O(n)}