Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_eval_foo_bb0_in___8, n_eval_foo_bb1_in___1, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___7, n_eval_foo_bb2_in___3, n_eval_foo_bb2_in___6, n_eval_foo_bb3_in___2, n_eval_foo_bb3_in___5, n_eval_foo_start
Transitions:
0:n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___7(Arg_3,Arg_2,Arg_2,Arg_3)
1:n_eval_foo_bb1_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1
2:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<Arg_0
3:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_1
4:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_1<Arg_0
5:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_0<=Arg_1
6:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+4,Arg_2,Arg_3):|:Arg_1<Arg_0
7:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+4,Arg_2,Arg_3):|:Arg_1<Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_0<=Arg_3 && Arg_3<=Arg_0
8:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___1(Arg_0+1,Arg_1+2,Arg_2,Arg_3):|:Arg_0<=Arg_1
9:n_eval_foo_bb3_in___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___1(Arg_0+1,Arg_1+2,Arg_2,Arg_3):|:Arg_0<=Arg_1 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1
10:n_eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_1 for location n_eval_foo_bb3_in___2

Found invariant Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 for location n_eval_foo_bb1_in___7

Found invariant 2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1+Arg_0<=Arg_1 for location n_eval_foo_bb1_in___1

Found invariant Arg_3<=Arg_0 && 1+Arg_2<=Arg_3 && Arg_1<=3+Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=3+Arg_0 for location n_eval_foo_bb1_in___4

Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=Arg_1 for location n_eval_foo_bb3_in___5

Found invariant Arg_3<=Arg_0 && 5+Arg_2<=Arg_3 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 5+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_eval_foo_bb2_in___3

Found invariant Arg_3<=Arg_0 && 1+Arg_2<=Arg_3 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 for location n_eval_foo_bb2_in___6

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_eval_foo_bb0_in___8, n_eval_foo_bb1_in___1, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___7, n_eval_foo_bb2_in___3, n_eval_foo_bb2_in___6, n_eval_foo_bb3_in___2, n_eval_foo_bb3_in___5, n_eval_foo_start
Transitions:
0:n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___7(Arg_3,Arg_2,Arg_2,Arg_3)
1:n_eval_foo_bb1_in___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:2+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1+Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1
2:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 1+Arg_2<=Arg_3 && Arg_1<=3+Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=3+Arg_0 && Arg_1<Arg_0
3:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 1+Arg_2<=Arg_3 && Arg_1<=3+Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=3+Arg_0 && Arg_0<=Arg_1
4:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_1<Arg_0
5:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_0<=Arg_1
6:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+4,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 5+Arg_2<=Arg_3 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 5+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<Arg_0
7:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+4,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 1+Arg_2<=Arg_3 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_1<Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_0<=Arg_3 && Arg_3<=Arg_0
8:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___1(Arg_0+1,Arg_1+2,Arg_2,Arg_3):|:Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1
9:n_eval_foo_bb3_in___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___1(Arg_0+1,Arg_1+2,Arg_2,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1
10:n_eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 2:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 1+Arg_2<=Arg_3 && Arg_1<=3+Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=3+Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_2+Arg_3+8 {O(n)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_0-Arg_1 ]
n_eval_foo_bb1_in___4 [Arg_3+4-Arg_1 ]

MPRF for transition 6:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+4,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 5+Arg_2<=Arg_3 && 1+Arg_1<=Arg_3 && Arg_0<=Arg_3 && 4+Arg_2<=Arg_1 && 5+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_1<Arg_0 of depth 1:

new bound:

Arg_2+Arg_3+4 {O(n)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_3-Arg_1 ]
n_eval_foo_bb1_in___4 [Arg_3-Arg_1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7: 1 {O(1)}
1: n_eval_foo_bb1_in___1->n_eval_foo_bb3_in___2: inf {Infinity}
2: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3: Arg_2+Arg_3+8 {O(n)}
3: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2: 1 {O(1)}
4: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6: 1 {O(1)}
5: n_eval_foo_bb1_in___7->n_eval_foo_bb3_in___5: 1 {O(1)}
6: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4: Arg_2+Arg_3+4 {O(n)}
7: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4: 1 {O(1)}
8: n_eval_foo_bb3_in___2->n_eval_foo_bb1_in___1: inf {Infinity}
9: n_eval_foo_bb3_in___5->n_eval_foo_bb1_in___1: 1 {O(1)}
10: n_eval_foo_start->n_eval_foo_bb0_in___8: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7: 1 {O(1)}
1: n_eval_foo_bb1_in___1->n_eval_foo_bb3_in___2: inf {Infinity}
2: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3: Arg_2+Arg_3+8 {O(n)}
3: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2: 1 {O(1)}
4: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6: 1 {O(1)}
5: n_eval_foo_bb1_in___7->n_eval_foo_bb3_in___5: 1 {O(1)}
6: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4: Arg_2+Arg_3+4 {O(n)}
7: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4: 1 {O(1)}
8: n_eval_foo_bb3_in___2->n_eval_foo_bb1_in___1: inf {Infinity}
9: n_eval_foo_bb3_in___5->n_eval_foo_bb1_in___1: 1 {O(1)}
10: n_eval_foo_start->n_eval_foo_bb0_in___8: 1 {O(1)}

Sizebounds

0: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_0: Arg_3 {O(n)}
0: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_1: Arg_2 {O(n)}
0: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_2: Arg_2 {O(n)}
0: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_3: Arg_3 {O(n)}
1: n_eval_foo_bb1_in___1->n_eval_foo_bb3_in___2, Arg_2: 3*Arg_2 {O(n)}
1: n_eval_foo_bb1_in___1->n_eval_foo_bb3_in___2, Arg_3: 3*Arg_3 {O(n)}
2: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_0: Arg_3 {O(n)}
2: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_1: 4*Arg_3+5*Arg_2+20 {O(n)}
2: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_2: Arg_2 {O(n)}
2: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_3: Arg_3 {O(n)}
3: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_0: 2*Arg_3 {O(n)}
3: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_1: 4*Arg_3+6*Arg_2+24 {O(n)}
3: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_2: 2*Arg_2 {O(n)}
3: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_3: 2*Arg_3 {O(n)}
4: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_0: Arg_3 {O(n)}
4: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_1: Arg_2 {O(n)}
4: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_2: Arg_2 {O(n)}
4: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_3: Arg_3 {O(n)}
5: n_eval_foo_bb1_in___7->n_eval_foo_bb3_in___5, Arg_0: Arg_3 {O(n)}
5: n_eval_foo_bb1_in___7->n_eval_foo_bb3_in___5, Arg_1: Arg_2 {O(n)}
5: n_eval_foo_bb1_in___7->n_eval_foo_bb3_in___5, Arg_2: Arg_2 {O(n)}
5: n_eval_foo_bb1_in___7->n_eval_foo_bb3_in___5, Arg_3: Arg_3 {O(n)}
6: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_0: Arg_3 {O(n)}
6: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_1: 4*Arg_3+5*Arg_2+20 {O(n)}
6: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_2: Arg_2 {O(n)}
6: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_3: Arg_3 {O(n)}
7: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_0: Arg_3 {O(n)}
7: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_1: Arg_2+4 {O(n)}
7: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_2: Arg_2 {O(n)}
7: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_3: Arg_3 {O(n)}
8: n_eval_foo_bb3_in___2->n_eval_foo_bb1_in___1, Arg_2: 3*Arg_2 {O(n)}
8: n_eval_foo_bb3_in___2->n_eval_foo_bb1_in___1, Arg_3: 3*Arg_3 {O(n)}
9: n_eval_foo_bb3_in___5->n_eval_foo_bb1_in___1, Arg_0: Arg_3+1 {O(n)}
9: n_eval_foo_bb3_in___5->n_eval_foo_bb1_in___1, Arg_1: Arg_2+2 {O(n)}
9: n_eval_foo_bb3_in___5->n_eval_foo_bb1_in___1, Arg_2: Arg_2 {O(n)}
9: n_eval_foo_bb3_in___5->n_eval_foo_bb1_in___1, Arg_3: Arg_3 {O(n)}
10: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_0: Arg_0 {O(n)}
10: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_1: Arg_1 {O(n)}
10: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_2: Arg_2 {O(n)}
10: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_3: Arg_3 {O(n)}