Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && Arg_0<=0 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && Arg_0<=0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && Arg_0<=0 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
2:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 1+Arg_2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2
4:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2
6:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval___1

Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval___2

Found invariant 0<=Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_0 for location n_eval___3

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && Arg_0<=0 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_2 && Arg_0<=0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && Arg_0<=0 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
2:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_0 && 0<=Arg_2 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_0 && 0<=Arg_2 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 1+Arg_2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2
4:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0
5:n_eval___4(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:1+Arg_2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2
6:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___4(Arg_0,Arg_1,Arg_2)

MPRF for transition 3:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0-1,Arg_1,Arg_2):|:0<=Arg_2 && 0<=Arg_0+Arg_2 && 0<=Arg_0 && 0<=Arg_2 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 1+Arg_2<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_eval___3 [Arg_0+1 ]

MPRF for transition 1:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_2 && Arg_0<=0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && Arg_0<=0 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval___2 [Arg_1+1 ]

MPRF for transition 0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_2<=Arg_0+Arg_1 && Arg_0<=0 && 1+Arg_2<=Arg_0+Arg_1 && 0<=Arg_2 && Arg_0<=0 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

n_eval___1 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:3*Arg_1+Arg_0+7 {O(n)}
0: n_eval___1->n_eval___1: 2*Arg_1+1 {O(n)}
1: n_eval___2->n_eval___2: Arg_1+1 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___3: Arg_0+1 {O(n)}
4: n_eval___4->n_eval___2: 1 {O(1)}
5: n_eval___4->n_eval___3: 1 {O(1)}
6: n_start->n_eval___4: 1 {O(1)}

Costbounds

Overall costbound: 3*Arg_1+Arg_0+7 {O(n)}
0: n_eval___1->n_eval___1: 2*Arg_1+1 {O(n)}
1: n_eval___2->n_eval___2: Arg_1+1 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___3: Arg_0+1 {O(n)}
4: n_eval___4->n_eval___2: 1 {O(1)}
5: n_eval___4->n_eval___3: 1 {O(1)}
6: n_start->n_eval___4: 1 {O(1)}

Sizebounds

0: n_eval___1->n_eval___1, Arg_0: 0 {O(1)}
0: n_eval___1->n_eval___1, Arg_1: 2*Arg_1 {O(n)}
0: n_eval___1->n_eval___1, Arg_2: 2*Arg_2 {O(n)}
1: n_eval___2->n_eval___2, Arg_0: Arg_0 {O(n)}
1: n_eval___2->n_eval___2, Arg_1: Arg_1 {O(n)}
1: n_eval___2->n_eval___2, Arg_2: Arg_2 {O(n)}
2: n_eval___3->n_eval___1, Arg_0: 0 {O(1)}
2: n_eval___3->n_eval___1, Arg_1: 2*Arg_1 {O(n)}
2: n_eval___3->n_eval___1, Arg_2: 2*Arg_2 {O(n)}
3: n_eval___3->n_eval___3, Arg_0: Arg_0 {O(n)}
3: n_eval___3->n_eval___3, Arg_1: Arg_1 {O(n)}
3: n_eval___3->n_eval___3, Arg_2: Arg_2 {O(n)}
4: n_eval___4->n_eval___2, Arg_0: Arg_0 {O(n)}
4: n_eval___4->n_eval___2, Arg_1: Arg_1 {O(n)}
4: n_eval___4->n_eval___2, Arg_2: Arg_2 {O(n)}
5: n_eval___4->n_eval___3, Arg_0: Arg_0 {O(n)}
5: n_eval___4->n_eval___3, Arg_1: Arg_1 {O(n)}
5: n_eval___4->n_eval___3, Arg_2: Arg_2 {O(n)}
6: n_start->n_eval___4, Arg_0: Arg_0 {O(n)}
6: n_start->n_eval___4, Arg_1: Arg_1 {O(n)}
6: n_start->n_eval___4, Arg_2: Arg_2 {O(n)}