Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f2___1
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_2<=Arg_1
1:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=1+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=1+Arg_1
2:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0,Arg_1+Arg_2-1,Arg_2-1):|:Arg_2<=1+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_1

Preprocessing

Found invariant Arg_2<=Arg_1 && 0<=Arg_0 for location n_f2___1

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f2___1
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_2<=Arg_1
1:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=1+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=1+Arg_1
2:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0,Arg_1+Arg_2-1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=1+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_1

MPRF for transition 1:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=1+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=1+Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_f2___1 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0->n_f2___1: 1 {O(1)}
1: n_f2___1->n_f2___1: Arg_0+1 {O(n)}
2: n_f2___1->n_f2___1: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0->n_f2___1: 1 {O(1)}
1: n_f2___1->n_f2___1: Arg_0+1 {O(n)}
2: n_f2___1->n_f2___1: inf {Infinity}

Sizebounds

0: n_f0->n_f2___1, Arg_0: Arg_0 {O(n)}
0: n_f0->n_f2___1, Arg_1: Arg_1 {O(n)}
0: n_f0->n_f2___1, Arg_2: Arg_2 {O(n)}
1: n_f2___1->n_f2___1, Arg_0: 2*Arg_0 {O(n)}
2: n_f2___1->n_f2___1, Arg_0: 2*Arg_0 {O(n)}