Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval___1, n_eval___2, n_eval___3, n_eval___4, n_eval___5, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1<=Arg_1
1:n_eval___1(Arg_0,Arg_1) -> n_eval___2(Arg_0,0):|:1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
2:n_eval___3(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1<=Arg_1
3:n_eval___3(Arg_0,Arg_1) -> n_eval___2(Arg_0,0):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
4:n_eval___5(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 1<=Arg_1
5:n_eval___5(Arg_0,Arg_1) -> n_eval___2(Arg_0,0):|:1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
6:n_eval___5(Arg_0,Arg_1) -> n_eval___3(Arg_0,Arg_0):|:1<=Arg_1 && 1+Arg_0<=Arg_1
7:n_eval___5(Arg_0,Arg_1) -> n_eval___4(Arg_0,Arg_0):|:Arg_0<=0 && Arg_1<=1 && 1<=Arg_1
8:n_start(Arg_0,Arg_1) -> n_eval___5(Arg_0,Arg_1)

Preprocessing

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval___1

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

Found invariant Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_eval___3

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=Arg_1 && Arg_0<=0 for location n_eval___4

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_eval___4, n_eval___5, n_start
Transitions:
0:n_eval___1(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1<=Arg_1
1:n_eval___1(Arg_0,Arg_1) -> n_eval___2(Arg_0,0):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
2:n_eval___3(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1<=Arg_1
3:n_eval___3(Arg_0,Arg_1) -> n_eval___2(Arg_0,0):|:Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
4:n_eval___5(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 1<=Arg_1
5:n_eval___5(Arg_0,Arg_1) -> n_eval___2(Arg_0,0):|:1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
6:n_eval___5(Arg_0,Arg_1) -> n_eval___3(Arg_0,Arg_0):|:1<=Arg_1 && 1+Arg_0<=Arg_1
7:n_eval___5(Arg_0,Arg_1) -> n_eval___4(Arg_0,Arg_0):|:Arg_0<=0 && Arg_1<=1 && 1<=Arg_1
8:n_start(Arg_0,Arg_1) -> n_eval___5(Arg_0,Arg_1)

MPRF for transition 0:n_eval___1(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && Arg_1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+2 {O(n)}

MPRF:

n_eval___1 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+10 {O(n)}
0: n_eval___1->n_eval___1: Arg_0+Arg_1+2 {O(n)}
1: n_eval___1->n_eval___2: 1 {O(1)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___2: 1 {O(1)}
4: n_eval___5->n_eval___1: 1 {O(1)}
5: n_eval___5->n_eval___2: 1 {O(1)}
6: n_eval___5->n_eval___3: 1 {O(1)}
7: n_eval___5->n_eval___4: 1 {O(1)}
8: n_start->n_eval___5: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+Arg_1+10 {O(n)}
0: n_eval___1->n_eval___1: Arg_0+Arg_1+2 {O(n)}
1: n_eval___1->n_eval___2: 1 {O(1)}
2: n_eval___3->n_eval___1: 1 {O(1)}
3: n_eval___3->n_eval___2: 1 {O(1)}
4: n_eval___5->n_eval___1: 1 {O(1)}
5: n_eval___5->n_eval___2: 1 {O(1)}
6: n_eval___5->n_eval___3: 1 {O(1)}
7: n_eval___5->n_eval___4: 1 {O(1)}
8: n_start->n_eval___5: 1 {O(1)}

Sizebounds

0: n_eval___1->n_eval___1, Arg_0: 2*Arg_0 {O(n)}
0: n_eval___1->n_eval___1, Arg_1: Arg_0+Arg_1 {O(n)}
1: n_eval___1->n_eval___2, Arg_0: 4*Arg_0 {O(n)}
1: n_eval___1->n_eval___2, Arg_1: 0 {O(1)}
2: n_eval___3->n_eval___1, Arg_0: Arg_0 {O(n)}
2: n_eval___3->n_eval___1, Arg_1: Arg_0 {O(n)}
3: n_eval___3->n_eval___2, Arg_0: 1 {O(1)}
3: n_eval___3->n_eval___2, Arg_1: 0 {O(1)}
4: n_eval___5->n_eval___1, Arg_0: Arg_0 {O(n)}
4: n_eval___5->n_eval___1, Arg_1: Arg_1 {O(n)}
5: n_eval___5->n_eval___2, Arg_0: Arg_0 {O(n)}
5: n_eval___5->n_eval___2, Arg_1: 0 {O(1)}
6: n_eval___5->n_eval___3, Arg_0: Arg_0 {O(n)}
6: n_eval___5->n_eval___3, Arg_1: Arg_0 {O(n)}
7: n_eval___5->n_eval___4, Arg_0: Arg_0 {O(n)}
7: n_eval___5->n_eval___4, Arg_1: Arg_0 {O(n)}
8: n_start->n_eval___5, Arg_0: Arg_0 {O(n)}
8: n_start->n_eval___5, Arg_1: Arg_1 {O(n)}