Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0, n_f2___3, n_f2___4, n_f3___1, n_f3___2
Transitions:
0:n_f0(Arg_0,Arg_1) -> n_f2___4(Arg_0,0)
1:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1<=Arg_0
2:n_f2___3(Arg_0,Arg_1) -> n_f3___1(Arg_0,1):|:Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && Arg_0<=0
3:n_f2___4(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0
4:n_f2___4(Arg_0,Arg_1) -> n_f3___2(Arg_0,1):|:Arg_1<=0 && 0<=Arg_1 && Arg_0<=0

Preprocessing

Found invariant Arg_1<=1 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_f3___2

Found invariant Arg_1<=0 && 0<=Arg_1 for location n_f2___4

Found invariant Arg_1<=1 && Arg_1<=1+Arg_0 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f3___1

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_f2___3

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0, n_f2___3, n_f2___4, n_f3___1, n_f3___2
Transitions:
0:n_f0(Arg_0,Arg_1) -> n_f2___4(Arg_0,0)
1:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1<=Arg_0
2:n_f2___3(Arg_0,Arg_1) -> n_f3___1(Arg_0,1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && Arg_0<=0
3:n_f2___4(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:Arg_1<=0 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0
4:n_f2___4(Arg_0,Arg_1) -> n_f3___2(Arg_0,1):|:Arg_1<=0 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && Arg_0<=0

MPRF for transition 1:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_f2___3 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+5 {O(n)}
0: n_f0->n_f2___4: 1 {O(1)}
1: n_f2___3->n_f2___3: Arg_0+1 {O(n)}
2: n_f2___3->n_f3___1: 1 {O(1)}
3: n_f2___4->n_f2___3: 1 {O(1)}
4: n_f2___4->n_f3___2: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+5 {O(n)}
0: n_f0->n_f2___4: 1 {O(1)}
1: n_f2___3->n_f2___3: Arg_0+1 {O(n)}
2: n_f2___3->n_f3___1: 1 {O(1)}
3: n_f2___4->n_f2___3: 1 {O(1)}
4: n_f2___4->n_f3___2: 1 {O(1)}

Sizebounds

0: n_f0->n_f2___4, Arg_0: Arg_0 {O(n)}
0: n_f0->n_f2___4, Arg_1: 0 {O(1)}
1: n_f2___3->n_f2___3, Arg_0: Arg_0 {O(n)}
1: n_f2___3->n_f2___3, Arg_1: 0 {O(1)}
2: n_f2___3->n_f3___1, Arg_0: 0 {O(1)}
2: n_f2___3->n_f3___1, Arg_1: 1 {O(1)}
3: n_f2___4->n_f2___3, Arg_0: Arg_0 {O(n)}
3: n_f2___4->n_f2___3, Arg_1: 0 {O(1)}
4: n_f2___4->n_f3___2, Arg_0: Arg_0 {O(n)}
4: n_f2___4->n_f3___2, Arg_1: 1 {O(1)}