Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_merge___1, n_merge___2, n_merge___3, n_start
Transitions:
0:n_merge___1(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
1:n_merge___1(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
2:n_merge___2(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
3:n_merge___2(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
4:n_merge___3(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
5:n_merge___3(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_1
6:n_start(Arg_0,Arg_1) -> n_merge___3(Arg_0,Arg_1)

Preprocessing

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_merge___1

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_merge___2

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_merge___1, n_merge___2, n_merge___3, n_start
Transitions:
0:n_merge___1(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
1:n_merge___1(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
2:n_merge___2(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
3:n_merge___2(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
4:n_merge___3(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
5:n_merge___3(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_1
6:n_start(Arg_0,Arg_1) -> n_merge___3(Arg_0,Arg_1)

MPRF for transition 0:n_merge___1(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+1 {O(n)}

MPRF:

n_merge___1 [Arg_1+1 ]
n_merge___2 [Arg_1 ]

MPRF for transition 1:n_merge___1(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_0 {O(n)}

MPRF:

n_merge___1 [Arg_0 ]
n_merge___2 [Arg_0 ]

MPRF for transition 2:n_merge___2(Arg_0,Arg_1) -> n_merge___1(Arg_0,Arg_1-1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_0+1 {O(n)}

MPRF:

n_merge___1 [Arg_0 ]
n_merge___2 [Arg_0+1 ]

MPRF for transition 3:n_merge___2(Arg_0,Arg_1) -> n_merge___2(Arg_0-1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_0+1 {O(n)}

MPRF:

n_merge___1 [Arg_0 ]
n_merge___2 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+6*Arg_0+6 {O(n)}
0: n_merge___1->n_merge___1: 2*Arg_1+1 {O(n)}
1: n_merge___1->n_merge___2: 2*Arg_0 {O(n)}
2: n_merge___2->n_merge___1: 2*Arg_0+1 {O(n)}
3: n_merge___2->n_merge___2: 2*Arg_0+1 {O(n)}
4: n_merge___3->n_merge___1: 1 {O(1)}
5: n_merge___3->n_merge___2: 1 {O(1)}
6: n_start->n_merge___3: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+6*Arg_0+6 {O(n)}
0: n_merge___1->n_merge___1: 2*Arg_1+1 {O(n)}
1: n_merge___1->n_merge___2: 2*Arg_0 {O(n)}
2: n_merge___2->n_merge___1: 2*Arg_0+1 {O(n)}
3: n_merge___2->n_merge___2: 2*Arg_0+1 {O(n)}
4: n_merge___3->n_merge___1: 1 {O(1)}
5: n_merge___3->n_merge___2: 1 {O(1)}
6: n_start->n_merge___3: 1 {O(1)}

Sizebounds

0: n_merge___1->n_merge___1, Arg_0: 4*Arg_0 {O(n)}
0: n_merge___1->n_merge___1, Arg_1: 4*Arg_1 {O(n)}
1: n_merge___1->n_merge___2, Arg_0: 4*Arg_0 {O(n)}
1: n_merge___1->n_merge___2, Arg_1: 4*Arg_1 {O(n)}
2: n_merge___2->n_merge___1, Arg_0: 4*Arg_0 {O(n)}
2: n_merge___2->n_merge___1, Arg_1: 4*Arg_1 {O(n)}
3: n_merge___2->n_merge___2, Arg_0: 4*Arg_0 {O(n)}
3: n_merge___2->n_merge___2, Arg_1: 4*Arg_1 {O(n)}
4: n_merge___3->n_merge___1, Arg_0: Arg_0 {O(n)}
4: n_merge___3->n_merge___1, Arg_1: Arg_1 {O(n)}
5: n_merge___3->n_merge___2, Arg_0: Arg_0 {O(n)}
5: n_merge___3->n_merge___2, Arg_1: Arg_1 {O(n)}
6: n_start->n_merge___3, Arg_0: Arg_0 {O(n)}
6: n_start->n_merge___3, Arg_1: Arg_1 {O(n)}