Initial Problem

Start: n_eval_easy2_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval_easy2_bb0_in___9, n_eval_easy2_bb1_in___5, n_eval_easy2_bb1_in___8, n_eval_easy2_bb2_in___4, n_eval_easy2_bb2_in___7, n_eval_easy2_bb3_in___3, n_eval_easy2_bb3_in___6, n_eval_easy2_start, n_eval_easy2_stop___1, n_eval_easy2_stop___2
Transitions:
0:n_eval_easy2_bb0_in___9(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___8(Arg_1,Arg_1)
1:n_eval_easy2_bb1_in___5(Arg_0,Arg_1) -> n_eval_easy2_bb2_in___4(Arg_0,Arg_1):|:0<Arg_0
2:n_eval_easy2_bb1_in___5(Arg_0,Arg_1) -> n_eval_easy2_bb3_in___3(Arg_0,Arg_1):|:Arg_0<=0
3:n_eval_easy2_bb1_in___8(Arg_0,Arg_1) -> n_eval_easy2_bb2_in___7(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
4:n_eval_easy2_bb1_in___8(Arg_0,Arg_1) -> n_eval_easy2_bb3_in___6(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0
5:n_eval_easy2_bb2_in___4(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___5(Arg_0-1,Arg_1):|:0<Arg_0
6:n_eval_easy2_bb2_in___7(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___5(Arg_0-1,Arg_1):|:0<Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
7:n_eval_easy2_bb3_in___3(Arg_0,Arg_1) -> n_eval_easy2_stop___2(Arg_0,Arg_1):|:Arg_0<=0
8:n_eval_easy2_bb3_in___6(Arg_0,Arg_1) -> n_eval_easy2_stop___1(Arg_0,Arg_1):|:Arg_0<=0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
9:n_eval_easy2_start(Arg_0,Arg_1) -> n_eval_easy2_bb0_in___9(Arg_0,Arg_1)

Preprocessing

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval_easy2_stop___1

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval_easy2_bb1_in___5

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_easy2_bb3_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_easy2_bb2_in___7

Found invariant Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_eval_easy2_bb1_in___8

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_eval_easy2_bb2_in___4

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval_easy2_bb3_in___6

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_easy2_stop___2

Problem after Preprocessing

Start: n_eval_easy2_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval_easy2_bb0_in___9, n_eval_easy2_bb1_in___5, n_eval_easy2_bb1_in___8, n_eval_easy2_bb2_in___4, n_eval_easy2_bb2_in___7, n_eval_easy2_bb3_in___3, n_eval_easy2_bb3_in___6, n_eval_easy2_start, n_eval_easy2_stop___1, n_eval_easy2_stop___2
Transitions:
0:n_eval_easy2_bb0_in___9(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___8(Arg_1,Arg_1)
1:n_eval_easy2_bb1_in___5(Arg_0,Arg_1) -> n_eval_easy2_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
2:n_eval_easy2_bb1_in___5(Arg_0,Arg_1) -> n_eval_easy2_bb3_in___3(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=0
3:n_eval_easy2_bb1_in___8(Arg_0,Arg_1) -> n_eval_easy2_bb2_in___7(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<Arg_0
4:n_eval_easy2_bb1_in___8(Arg_0,Arg_1) -> n_eval_easy2_bb3_in___6(Arg_0,Arg_1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=0
5:n_eval_easy2_bb2_in___4(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___5(Arg_0-1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 0<Arg_0
6:n_eval_easy2_bb2_in___7(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___5(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
7:n_eval_easy2_bb3_in___3(Arg_0,Arg_1) -> n_eval_easy2_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
8:n_eval_easy2_bb3_in___6(Arg_0,Arg_1) -> n_eval_easy2_stop___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 && Arg_0<=0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
9:n_eval_easy2_start(Arg_0,Arg_1) -> n_eval_easy2_bb0_in___9(Arg_0,Arg_1)

MPRF for transition 1:n_eval_easy2_bb1_in___5(Arg_0,Arg_1) -> n_eval_easy2_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_easy2_bb2_in___4 [Arg_0 ]
n_eval_easy2_bb1_in___5 [Arg_0+1 ]

MPRF for transition 5:n_eval_easy2_bb2_in___4(Arg_0,Arg_1) -> n_eval_easy2_bb1_in___5(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_easy2_bb2_in___4 [Arg_0 ]
n_eval_easy2_bb1_in___5 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+9 {O(n)}
0: n_eval_easy2_bb0_in___9->n_eval_easy2_bb1_in___8: 1 {O(1)}
1: n_eval_easy2_bb1_in___5->n_eval_easy2_bb2_in___4: Arg_1+1 {O(n)}
2: n_eval_easy2_bb1_in___5->n_eval_easy2_bb3_in___3: 1 {O(1)}
3: n_eval_easy2_bb1_in___8->n_eval_easy2_bb2_in___7: 1 {O(1)}
4: n_eval_easy2_bb1_in___8->n_eval_easy2_bb3_in___6: 1 {O(1)}
5: n_eval_easy2_bb2_in___4->n_eval_easy2_bb1_in___5: Arg_1 {O(n)}
6: n_eval_easy2_bb2_in___7->n_eval_easy2_bb1_in___5: 1 {O(1)}
7: n_eval_easy2_bb3_in___3->n_eval_easy2_stop___2: 1 {O(1)}
8: n_eval_easy2_bb3_in___6->n_eval_easy2_stop___1: 1 {O(1)}
9: n_eval_easy2_start->n_eval_easy2_bb0_in___9: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+9 {O(n)}
0: n_eval_easy2_bb0_in___9->n_eval_easy2_bb1_in___8: 1 {O(1)}
1: n_eval_easy2_bb1_in___5->n_eval_easy2_bb2_in___4: Arg_1+1 {O(n)}
2: n_eval_easy2_bb1_in___5->n_eval_easy2_bb3_in___3: 1 {O(1)}
3: n_eval_easy2_bb1_in___8->n_eval_easy2_bb2_in___7: 1 {O(1)}
4: n_eval_easy2_bb1_in___8->n_eval_easy2_bb3_in___6: 1 {O(1)}
5: n_eval_easy2_bb2_in___4->n_eval_easy2_bb1_in___5: Arg_1 {O(n)}
6: n_eval_easy2_bb2_in___7->n_eval_easy2_bb1_in___5: 1 {O(1)}
7: n_eval_easy2_bb3_in___3->n_eval_easy2_stop___2: 1 {O(1)}
8: n_eval_easy2_bb3_in___6->n_eval_easy2_stop___1: 1 {O(1)}
9: n_eval_easy2_start->n_eval_easy2_bb0_in___9: 1 {O(1)}

Sizebounds

0: n_eval_easy2_bb0_in___9->n_eval_easy2_bb1_in___8, Arg_0: Arg_1 {O(n)}
0: n_eval_easy2_bb0_in___9->n_eval_easy2_bb1_in___8, Arg_1: Arg_1 {O(n)}
1: n_eval_easy2_bb1_in___5->n_eval_easy2_bb2_in___4, Arg_0: Arg_1 {O(n)}
1: n_eval_easy2_bb1_in___5->n_eval_easy2_bb2_in___4, Arg_1: Arg_1 {O(n)}
2: n_eval_easy2_bb1_in___5->n_eval_easy2_bb3_in___3, Arg_0: 0 {O(1)}
2: n_eval_easy2_bb1_in___5->n_eval_easy2_bb3_in___3, Arg_1: 2*Arg_1 {O(n)}
3: n_eval_easy2_bb1_in___8->n_eval_easy2_bb2_in___7, Arg_0: Arg_1 {O(n)}
3: n_eval_easy2_bb1_in___8->n_eval_easy2_bb2_in___7, Arg_1: Arg_1 {O(n)}
4: n_eval_easy2_bb1_in___8->n_eval_easy2_bb3_in___6, Arg_0: Arg_1 {O(n)}
4: n_eval_easy2_bb1_in___8->n_eval_easy2_bb3_in___6, Arg_1: Arg_1 {O(n)}
5: n_eval_easy2_bb2_in___4->n_eval_easy2_bb1_in___5, Arg_0: Arg_1 {O(n)}
5: n_eval_easy2_bb2_in___4->n_eval_easy2_bb1_in___5, Arg_1: Arg_1 {O(n)}
6: n_eval_easy2_bb2_in___7->n_eval_easy2_bb1_in___5, Arg_0: Arg_1 {O(n)}
6: n_eval_easy2_bb2_in___7->n_eval_easy2_bb1_in___5, Arg_1: Arg_1 {O(n)}
7: n_eval_easy2_bb3_in___3->n_eval_easy2_stop___2, Arg_0: 0 {O(1)}
7: n_eval_easy2_bb3_in___3->n_eval_easy2_stop___2, Arg_1: 2*Arg_1 {O(n)}
8: n_eval_easy2_bb3_in___6->n_eval_easy2_stop___1, Arg_0: Arg_1 {O(n)}
8: n_eval_easy2_bb3_in___6->n_eval_easy2_stop___1, Arg_1: Arg_1 {O(n)}
9: n_eval_easy2_start->n_eval_easy2_bb0_in___9, Arg_0: Arg_0 {O(n)}
9: n_eval_easy2_start->n_eval_easy2_bb0_in___9, Arg_1: Arg_1 {O(n)}