Initial Problem

Start: n_f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0___1, n_f0___2, n_f0___3, n_f1
Transitions:
0:n_f0___1(Arg_0,Arg_1) -> n_f0___1(Arg_0+Arg_1,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1+Arg_1<=0
1:n_f0___2(Arg_0,Arg_1) -> n_f0___2(Arg_0+Arg_1,Arg_1):|:1<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_1 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
2:n_f0___3(Arg_0,Arg_1) -> n_f0___1(Arg_0+Arg_1,Arg_1):|:1<=Arg_0 && 1+Arg_1<=0
3:n_f0___3(Arg_0,Arg_1) -> n_f0___2(Arg_0+Arg_1,Arg_1):|:1<=Arg_0 && 1<=Arg_1
4:n_f1(Arg_0,Arg_1) -> n_f0___3(Arg_0,Arg_1)

Preprocessing

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_f0___2

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 for location n_f0___1

Problem after Preprocessing

Start: n_f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0___1, n_f0___2, n_f0___3, n_f1
Transitions:
0:n_f0___1(Arg_0,Arg_1) -> n_f0___1(Arg_0+Arg_1,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1+Arg_1<=0
1:n_f0___2(Arg_0,Arg_1) -> n_f0___2(Arg_0+Arg_1,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_1 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
2:n_f0___3(Arg_0,Arg_1) -> n_f0___1(Arg_0+Arg_1,Arg_1):|:1<=Arg_0 && 1+Arg_1<=0
3:n_f0___3(Arg_0,Arg_1) -> n_f0___2(Arg_0+Arg_1,Arg_1):|:1<=Arg_0 && 1<=Arg_1
4:n_f1(Arg_0,Arg_1) -> n_f0___3(Arg_0,Arg_1)

MPRF for transition 0:n_f0___1(Arg_0,Arg_1) -> n_f0___1(Arg_0+Arg_1,Arg_1):|:1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1+Arg_1<=0 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

n_f0___1 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0___1->n_f0___1: Arg_0+Arg_1 {O(n)}
1: n_f0___2->n_f0___2: inf {Infinity}
2: n_f0___3->n_f0___1: 1 {O(1)}
3: n_f0___3->n_f0___2: 1 {O(1)}
4: n_f1->n_f0___3: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0___1->n_f0___1: Arg_0+Arg_1 {O(n)}
1: n_f0___2->n_f0___2: inf {Infinity}
2: n_f0___3->n_f0___1: 1 {O(1)}
3: n_f0___3->n_f0___2: 1 {O(1)}
4: n_f1->n_f0___3: 1 {O(1)}

Sizebounds

0: n_f0___1->n_f0___1, Arg_0: 3*Arg_1+Arg_0 {O(n)}
0: n_f0___1->n_f0___1, Arg_1: Arg_1 {O(n)}
1: n_f0___2->n_f0___2, Arg_1: Arg_1 {O(n)}
2: n_f0___3->n_f0___1, Arg_0: Arg_0+Arg_1 {O(n)}
2: n_f0___3->n_f0___1, Arg_1: Arg_1 {O(n)}
3: n_f0___3->n_f0___2, Arg_0: Arg_0+Arg_1 {O(n)}
3: n_f0___3->n_f0___2, Arg_1: Arg_1 {O(n)}
4: n_f1->n_f0___3, Arg_0: Arg_0 {O(n)}
4: n_f1->n_f0___3, Arg_1: Arg_1 {O(n)}