Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0___2, n_f0___3, n_f3, n_f4___1
Transitions:
0:n_f0___2(Arg_0,Arg_1) -> n_f0___2(Arg_0,Arg_1-1):|:Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_1
1:n_f0___2(Arg_0,Arg_1) -> n_f4___1(-1,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_1<=0
2:n_f0___3(Arg_0,Arg_1) -> n_f0___2(Arg_0,Arg_1-1):|:Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1
3:n_f0___3(Arg_0,Arg_1) -> n_f4___1(-1,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0
4:n_f3(Arg_0,Arg_1) -> n_f0___3(0,Arg_1)
5:n_f4___1(Arg_0,Arg_1) -> n_f4___1(Arg_0,Arg_1):|:1+Arg_0<=0 && 0<=1+Arg_0 && Arg_1<=0

Preprocessing

Found invariant Arg_1<=0 && Arg_1<=1+Arg_0 && 1+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && 0<=1+Arg_0 for location n_f4___1

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_f0___3

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f0___2

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0___2, n_f0___3, n_f3, n_f4___1
Transitions:
0:n_f0___2(Arg_0,Arg_1) -> n_f0___2(Arg_0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_1
1:n_f0___2(Arg_0,Arg_1) -> n_f4___1(-1,Arg_1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_1<=0
2:n_f0___3(Arg_0,Arg_1) -> n_f0___2(Arg_0,Arg_1-1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1
3:n_f0___3(Arg_0,Arg_1) -> n_f4___1(-1,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0
4:n_f3(Arg_0,Arg_1) -> n_f0___3(0,Arg_1)
5:n_f4___1(Arg_0,Arg_1) -> n_f4___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=1+Arg_0 && 1+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && 0<=1+Arg_0 && 1+Arg_0<=0 && 0<=1+Arg_0 && Arg_1<=0

MPRF for transition 0:n_f0___2(Arg_0,Arg_1) -> n_f0___2(Arg_0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f0___2 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0___2->n_f0___2: Arg_1+1 {O(n)}
1: n_f0___2->n_f4___1: 1 {O(1)}
2: n_f0___3->n_f0___2: 1 {O(1)}
3: n_f0___3->n_f4___1: 1 {O(1)}
4: n_f3->n_f0___3: 1 {O(1)}
5: n_f4___1->n_f4___1: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0___2->n_f0___2: Arg_1+1 {O(n)}
1: n_f0___2->n_f4___1: 1 {O(1)}
2: n_f0___3->n_f0___2: 1 {O(1)}
3: n_f0___3->n_f4___1: 1 {O(1)}
4: n_f3->n_f0___3: 1 {O(1)}
5: n_f4___1->n_f4___1: inf {Infinity}

Sizebounds

0: n_f0___2->n_f0___2, Arg_0: 0 {O(1)}
0: n_f0___2->n_f0___2, Arg_1: Arg_1 {O(n)}
1: n_f0___2->n_f4___1, Arg_0: 1 {O(1)}
1: n_f0___2->n_f4___1, Arg_1: 0 {O(1)}
2: n_f0___3->n_f0___2, Arg_0: 0 {O(1)}
2: n_f0___3->n_f0___2, Arg_1: Arg_1 {O(n)}
3: n_f0___3->n_f4___1, Arg_0: 1 {O(1)}
3: n_f0___3->n_f4___1, Arg_1: Arg_1 {O(n)}
4: n_f3->n_f0___3, Arg_0: 0 {O(1)}
4: n_f3->n_f0___3, Arg_1: Arg_1 {O(n)}
5: n_f4___1->n_f4___1, Arg_0: 1 {O(1)}
5: n_f4___1->n_f4___1, Arg_1: Arg_1 {O(n)}