Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+Arg_2,Arg_2-1):|:0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0
1:n_eval___1(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0-1,Arg_1,Arg_2-1):|:0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0
2:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+Arg_2,Arg_2-1):|:0<=1+Arg_0 && 0<=Arg_0
3:n_eval___2(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0-1,Arg_1,Arg_2-1):|:0<=1+Arg_0 && 0<=Arg_0
4:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___1(Arg_0,Arg_1+Arg_2,Arg_2-1):|:0<=Arg_0
5:n_eval___3(Arg_0,Arg_1,Arg_2) -> n_eval___2(Arg_0-1,Arg_1,Arg_2-1):|:0<=Arg_0
6:n_start(Arg_0,Arg_1,Arg_2) -> n_eval___3(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {Arg_1,Arg_2} that do not contribute to the problem

Found invariant 0<=Arg_0 for location n_eval___1

Found invariant 0<=1+Arg_0 for location n_eval___2

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_start
Transitions:
14:n_eval___1(Arg_0) -> n_eval___1(Arg_0):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0
15:n_eval___1(Arg_0) -> n_eval___2(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0
16:n_eval___2(Arg_0) -> n_eval___1(Arg_0):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0
17:n_eval___2(Arg_0) -> n_eval___2(Arg_0-1):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0
18:n_eval___3(Arg_0) -> n_eval___1(Arg_0):|:0<=Arg_0
19:n_eval___3(Arg_0) -> n_eval___2(Arg_0-1):|:0<=Arg_0
20:n_start(Arg_0) -> n_eval___3(Arg_0)

MPRF for transition 15:n_eval___1(Arg_0) -> n_eval___2(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_0+3 {O(n)}

MPRF:

n_eval___1 [Arg_0+1 ]
n_eval___2 [Arg_0+1 ]

MPRF for transition 16:n_eval___2(Arg_0) -> n_eval___1(Arg_0):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_0+2 {O(n)}

MPRF:

n_eval___1 [Arg_0 ]
n_eval___2 [Arg_0+1 ]

MPRF for transition 17:n_eval___2(Arg_0) -> n_eval___2(Arg_0-1):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_0+2 {O(n)}

MPRF:

n_eval___1 [Arg_0 ]
n_eval___2 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
14: n_eval___1->n_eval___1: inf {Infinity}
15: n_eval___1->n_eval___2: 2*Arg_0+3 {O(n)}
16: n_eval___2->n_eval___1: 2*Arg_0+2 {O(n)}
17: n_eval___2->n_eval___2: 2*Arg_0+2 {O(n)}
18: n_eval___3->n_eval___1: 1 {O(1)}
19: n_eval___3->n_eval___2: 1 {O(1)}
20: n_start->n_eval___3: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
14: n_eval___1->n_eval___1: inf {Infinity}
15: n_eval___1->n_eval___2: 2*Arg_0+3 {O(n)}
16: n_eval___2->n_eval___1: 2*Arg_0+2 {O(n)}
17: n_eval___2->n_eval___2: 2*Arg_0+2 {O(n)}
18: n_eval___3->n_eval___1: 1 {O(1)}
19: n_eval___3->n_eval___2: 1 {O(1)}
20: n_start->n_eval___3: 1 {O(1)}

Sizebounds

14: n_eval___1->n_eval___1, Arg_0: 4*Arg_0+3 {O(n)}
15: n_eval___1->n_eval___2, Arg_0: 4*Arg_0+3 {O(n)}
16: n_eval___2->n_eval___1, Arg_0: 4*Arg_0+3 {O(n)}
17: n_eval___2->n_eval___2, Arg_0: 4*Arg_0+3 {O(n)}
18: n_eval___3->n_eval___1, Arg_0: Arg_0 {O(n)}
19: n_eval___3->n_eval___2, Arg_0: Arg_0+1 {O(n)}
20: n_start->n_eval___3, Arg_0: Arg_0 {O(n)}