Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: NoDet0
Locations: n_f0, n_f2___1, n_f2___2
Transitions:
0:n_f0(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:1<=Arg_1
1:n_f2___1(Arg_0,Arg_1) -> n_f2___1(Arg_0-1,Arg_1):|:0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
2:n_f2___1(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1
3:n_f2___2(Arg_0,Arg_1) -> n_f2___1(Arg_0-1,Arg_1):|:0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
4:n_f2___2(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1

Preprocessing

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

Found invariant 0<=Arg_1 for location n_f2___2

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: NoDet0
Locations: n_f0, n_f2___1, n_f2___2
Transitions:
0:n_f0(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:1<=Arg_1
1:n_f2___1(Arg_0,Arg_1) -> n_f2___1(Arg_0-1,Arg_1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
2:n_f2___1(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1
3:n_f2___2(Arg_0,Arg_1) -> n_f2___1(Arg_0-1,Arg_1):|:0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
4:n_f2___2(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1

MPRF for transition 2:n_f2___1(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f2___1 [Arg_1+1 ]
n_f2___2 [Arg_1+1 ]

MPRF for transition 3:n_f2___2(Arg_0,Arg_1) -> n_f2___1(Arg_0-1,Arg_1):|:0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f2___1 [Arg_1 ]
n_f2___2 [Arg_1+1 ]

MPRF for transition 4:n_f2___2(Arg_0,Arg_1) -> n_f2___2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f2___1 [Arg_1 ]
n_f2___2 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0->n_f2___2: 1 {O(1)}
1: n_f2___1->n_f2___1: inf {Infinity}
2: n_f2___1->n_f2___2: Arg_1+1 {O(n)}
3: n_f2___2->n_f2___1: Arg_1+1 {O(n)}
4: n_f2___2->n_f2___2: Arg_1+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0->n_f2___2: 1 {O(1)}
1: n_f2___1->n_f2___1: inf {Infinity}
2: n_f2___1->n_f2___2: Arg_1+1 {O(n)}
3: n_f2___2->n_f2___1: Arg_1+1 {O(n)}
4: n_f2___2->n_f2___2: Arg_1+1 {O(n)}

Sizebounds

0: n_f0->n_f2___2, Arg_1: Arg_1 {O(n)}
1: n_f2___1->n_f2___1, Arg_1: 2*Arg_1 {O(n)}
2: n_f2___1->n_f2___2, Arg_1: 2*Arg_1 {O(n)}
3: n_f2___2->n_f2___1, Arg_1: 2*Arg_1 {O(n)}
4: n_f2___2->n_f2___2, Arg_1: 2*Arg_1 {O(n)}