Initial Problem

Start: n_evaleasy2start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_evaleasy2bb1in___4, n_evaleasy2bbin___3, n_evaleasy2entryin___5, n_evaleasy2returnin___2, n_evaleasy2start, n_evaleasy2stop___1
Transitions:
0:n_evaleasy2bb1in___4(Arg_0) -> n_evaleasy2bbin___3(Arg_0):|:1<=Arg_0
1:n_evaleasy2bb1in___4(Arg_0) -> n_evaleasy2returnin___2(Arg_0):|:Arg_0<=0
2:n_evaleasy2bbin___3(Arg_0) -> n_evaleasy2bb1in___4(Arg_0-1):|:1<=Arg_0
3:n_evaleasy2entryin___5(Arg_0) -> n_evaleasy2bb1in___4(Arg_0)
4:n_evaleasy2returnin___2(Arg_0) -> n_evaleasy2stop___1(Arg_0):|:Arg_0<=0
5:n_evaleasy2start(Arg_0) -> n_evaleasy2entryin___5(Arg_0)

Preprocessing

Found invariant Arg_0<=0 for location n_evaleasy2returnin___2

Found invariant Arg_0<=0 for location n_evaleasy2stop___1

Found invariant 1<=Arg_0 for location n_evaleasy2bbin___3

Problem after Preprocessing

Start: n_evaleasy2start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_evaleasy2bb1in___4, n_evaleasy2bbin___3, n_evaleasy2entryin___5, n_evaleasy2returnin___2, n_evaleasy2start, n_evaleasy2stop___1
Transitions:
0:n_evaleasy2bb1in___4(Arg_0) -> n_evaleasy2bbin___3(Arg_0):|:1<=Arg_0
1:n_evaleasy2bb1in___4(Arg_0) -> n_evaleasy2returnin___2(Arg_0):|:Arg_0<=0
2:n_evaleasy2bbin___3(Arg_0) -> n_evaleasy2bb1in___4(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0
3:n_evaleasy2entryin___5(Arg_0) -> n_evaleasy2bb1in___4(Arg_0)
4:n_evaleasy2returnin___2(Arg_0) -> n_evaleasy2stop___1(Arg_0):|:Arg_0<=0 && Arg_0<=0
5:n_evaleasy2start(Arg_0) -> n_evaleasy2entryin___5(Arg_0)

MPRF for transition 0:n_evaleasy2bb1in___4(Arg_0) -> n_evaleasy2bbin___3(Arg_0):|:1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evaleasy2bbin___3 [Arg_0-1 ]
n_evaleasy2bb1in___4 [Arg_0 ]

MPRF for transition 2:n_evaleasy2bbin___3(Arg_0) -> n_evaleasy2bb1in___4(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evaleasy2bbin___3 [Arg_0 ]
n_evaleasy2bb1in___4 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+4 {O(n)}
0: n_evaleasy2bb1in___4->n_evaleasy2bbin___3: Arg_0 {O(n)}
1: n_evaleasy2bb1in___4->n_evaleasy2returnin___2: 1 {O(1)}
2: n_evaleasy2bbin___3->n_evaleasy2bb1in___4: Arg_0 {O(n)}
3: n_evaleasy2entryin___5->n_evaleasy2bb1in___4: 1 {O(1)}
4: n_evaleasy2returnin___2->n_evaleasy2stop___1: 1 {O(1)}
5: n_evaleasy2start->n_evaleasy2entryin___5: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+4 {O(n)}
0: n_evaleasy2bb1in___4->n_evaleasy2bbin___3: Arg_0 {O(n)}
1: n_evaleasy2bb1in___4->n_evaleasy2returnin___2: 1 {O(1)}
2: n_evaleasy2bbin___3->n_evaleasy2bb1in___4: Arg_0 {O(n)}
3: n_evaleasy2entryin___5->n_evaleasy2bb1in___4: 1 {O(1)}
4: n_evaleasy2returnin___2->n_evaleasy2stop___1: 1 {O(1)}
5: n_evaleasy2start->n_evaleasy2entryin___5: 1 {O(1)}

Sizebounds

0: n_evaleasy2bb1in___4->n_evaleasy2bbin___3, Arg_0: Arg_0 {O(n)}
1: n_evaleasy2bb1in___4->n_evaleasy2returnin___2, Arg_0: 2*Arg_0 {O(n)}
2: n_evaleasy2bbin___3->n_evaleasy2bb1in___4, Arg_0: Arg_0 {O(n)}
3: n_evaleasy2entryin___5->n_evaleasy2bb1in___4, Arg_0: Arg_0 {O(n)}
4: n_evaleasy2returnin___2->n_evaleasy2stop___1, Arg_0: 2*Arg_0 {O(n)}
5: n_evaleasy2start->n_evaleasy2entryin___5, Arg_0: Arg_0 {O(n)}