Initial Problem

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

Preprocessing

Found invariant Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_eval___1

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 for location n_eval___2

Problem after Preprocessing

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

MPRF for transition 1:n_eval___2(Arg_0,Arg_1) -> n_eval___2(Arg_0-1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && 0<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+2 {O(n)}

MPRF:

n_eval___2 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+6 {O(n)}
0: n_eval___1->n_eval___2: 1 {O(1)}
1: n_eval___2->n_eval___2: Arg_0+Arg_1+2 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___2: 1 {O(1)}
4: n_start->n_eval___3: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+Arg_1+6 {O(n)}
0: n_eval___1->n_eval___2: 1 {O(1)}
1: n_eval___2->n_eval___2: Arg_0+Arg_1+2 {O(n)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___2: 1 {O(1)}
4: n_start->n_eval___3: 1 {O(1)}

Sizebounds

0: n_eval___1->n_eval___2, Arg_0: Arg_1 {O(n)}
0: n_eval___1->n_eval___2, Arg_1: Arg_1 {O(n)}
1: n_eval___2->n_eval___2, Arg_0: Arg_0+Arg_1 {O(n)}
1: n_eval___2->n_eval___2, Arg_1: 2*Arg_1 {O(n)}
2: n_eval___3->n_eval___1, Arg_0: Arg_1 {O(n)}
2: n_eval___3->n_eval___1, Arg_1: Arg_1 {O(n)}
3: n_eval___3->n_eval___2, Arg_0: Arg_0 {O(n)}
3: n_eval___3->n_eval___2, Arg_1: Arg_1 {O(n)}
4: n_start->n_eval___3, Arg_0: Arg_0 {O(n)}
4: n_start->n_eval___3, Arg_1: Arg_1 {O(n)}