Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval1___3, n_eval1___5, n_eval2___1, n_eval2___2, n_eval2___4, n_start
Transitions:
0:n_eval1___3(Arg_0,Arg_1) -> n_eval2___1(Arg_0,Arg_1):|:Arg_1<=0 && 0<=Arg_0 && Arg_1<=0 && 1<=Arg_0
1:n_eval1___5(Arg_0,Arg_1) -> n_eval2___4(Arg_0,Arg_1):|:1<=Arg_0
2:n_eval2___1(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:Arg_1<=0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && Arg_1<=0
3:n_eval2___2(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && Arg_1<=0
4:n_eval2___2(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
5:n_eval2___4(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0
6:n_eval2___4(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
7:n_start(Arg_0,Arg_1) -> n_eval1___5(Arg_0,Arg_1)

Preprocessing

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_eval2___2

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 for location n_eval1___3

Found invariant 1<=Arg_0 for location n_eval2___4

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 for location n_eval2___1

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval1___3, n_eval1___5, n_eval2___1, n_eval2___2, n_eval2___4, n_start
Transitions:
0:n_eval1___3(Arg_0,Arg_1) -> n_eval2___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_0 && Arg_1<=0 && 1<=Arg_0
1:n_eval1___5(Arg_0,Arg_1) -> n_eval2___4(Arg_0,Arg_1):|:1<=Arg_0
2:n_eval2___1(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && Arg_1<=0
3:n_eval2___2(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && Arg_1<=0
4:n_eval2___2(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
5:n_eval2___4(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0
6:n_eval2___4(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
7:n_start(Arg_0,Arg_1) -> n_eval1___5(Arg_0,Arg_1)

MPRF for transition 4:n_eval2___2(Arg_0,Arg_1) -> n_eval2___2(Arg_0,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_eval2___2 [Arg_1+1 ]

MPRF for transition 0:n_eval1___3(Arg_0,Arg_1) -> n_eval2___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_0 && Arg_1<=0 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+2 {O(n)}

MPRF:

n_eval2___1 [Arg_0 ]
n_eval1___3 [Arg_0+1 ]

MPRF for transition 2:n_eval2___1(Arg_0,Arg_1) -> n_eval1___3(Arg_0-1,Arg_1):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && Arg_1<=0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_eval2___1 [Arg_0 ]
n_eval1___3 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:6*Arg_0+Arg_1+8 {O(n)}
0: n_eval1___3->n_eval2___1: 3*Arg_0+2 {O(n)}
1: n_eval1___5->n_eval2___4: 1 {O(1)}
2: n_eval2___1->n_eval1___3: 3*Arg_0 {O(n)}
3: n_eval2___2->n_eval1___3: 1 {O(1)}
4: n_eval2___2->n_eval2___2: Arg_1+1 {O(n)}
5: n_eval2___4->n_eval1___3: 1 {O(1)}
6: n_eval2___4->n_eval2___2: 1 {O(1)}
7: n_start->n_eval1___5: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_0+Arg_1+8 {O(n)}
0: n_eval1___3->n_eval2___1: 3*Arg_0+2 {O(n)}
1: n_eval1___5->n_eval2___4: 1 {O(1)}
2: n_eval2___1->n_eval1___3: 3*Arg_0 {O(n)}
3: n_eval2___2->n_eval1___3: 1 {O(1)}
4: n_eval2___2->n_eval2___2: Arg_1+1 {O(n)}
5: n_eval2___4->n_eval1___3: 1 {O(1)}
6: n_eval2___4->n_eval2___2: 1 {O(1)}
7: n_start->n_eval1___5: 1 {O(1)}

Sizebounds

0: n_eval1___3->n_eval2___1, Arg_0: 3*Arg_0 {O(n)}
0: n_eval1___3->n_eval2___1, Arg_1: Arg_1 {O(n)}
1: n_eval1___5->n_eval2___4, Arg_0: Arg_0 {O(n)}
1: n_eval1___5->n_eval2___4, Arg_1: Arg_1 {O(n)}
2: n_eval2___1->n_eval1___3, Arg_0: 3*Arg_0 {O(n)}
2: n_eval2___1->n_eval1___3, Arg_1: Arg_1 {O(n)}
3: n_eval2___2->n_eval1___3, Arg_0: 2*Arg_0 {O(n)}
3: n_eval2___2->n_eval1___3, Arg_1: 0 {O(1)}
4: n_eval2___2->n_eval2___2, Arg_0: Arg_0 {O(n)}
4: n_eval2___2->n_eval2___2, Arg_1: Arg_1 {O(n)}
5: n_eval2___4->n_eval1___3, Arg_0: Arg_0 {O(n)}
5: n_eval2___4->n_eval1___3, Arg_1: Arg_1 {O(n)}
6: n_eval2___4->n_eval2___2, Arg_0: Arg_0 {O(n)}
6: n_eval2___4->n_eval2___2, Arg_1: Arg_1 {O(n)}
7: n_start->n_eval1___5, Arg_0: Arg_0 {O(n)}
7: n_start->n_eval1___5, Arg_1: Arg_1 {O(n)}