Initial Problem
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f___1, n_f___2, n_f___3, n_start
Transitions:
0:n_f___1(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
1:n_f___1(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
2:n_f___2(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
3:n_f___2(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
4:n_f___3(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
5:n_f___3(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
6:n_start(Arg_0,Arg_1,Arg_2) -> n_f___3(Arg_0,Arg_1,Arg_2)
Preprocessing
Found invariant Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_f___1
Found invariant 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 for location n_f___2
Problem after Preprocessing
Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f___1, n_f___2, n_f___3, n_start
Transitions:
0:n_f___1(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
1:n_f___1(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
2:n_f___2(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
3:n_f___2(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
4:n_f___3(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
5:n_f___3(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
6:n_start(Arg_0,Arg_1,Arg_2) -> n_f___3(Arg_0,Arg_1,Arg_2)
MPRF for transition 0:n_f___1(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
2*Arg_0+2*Arg_2+2 {O(n)}
MPRF:
n_f___1 [Arg_0+1-Arg_2 ]
n_f___2 [Arg_0-Arg_2 ]
MPRF for transition 1:n_f___1(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
2*Arg_0+2*Arg_2+2 {O(n)}
MPRF:
n_f___1 [Arg_0+1-Arg_2 ]
n_f___2 [Arg_0-Arg_2 ]
MPRF for transition 2:n_f___2(Arg_0,Arg_1,Arg_2) -> n_f___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
2*Arg_0+2*Arg_1+2 {O(n)}
MPRF:
n_f___1 [Arg_0-Arg_1 ]
n_f___2 [Arg_0+1-Arg_1 ]
MPRF for transition 3:n_f___2(Arg_0,Arg_1,Arg_2) -> n_f___2(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:
new bound:
2*Arg_0+2*Arg_1+2 {O(n)}
MPRF:
n_f___1 [Arg_0-Arg_1 ]
n_f___2 [Arg_0+1-Arg_1 ]
All Bounds
Timebounds
Overall timebound:4*Arg_1+4*Arg_2+8*Arg_0+11 {O(n)}
0: n_f___1->n_f___1: 2*Arg_0+2*Arg_2+2 {O(n)}
1: n_f___1->n_f___2: 2*Arg_0+2*Arg_2+2 {O(n)}
2: n_f___2->n_f___1: 2*Arg_0+2*Arg_1+2 {O(n)}
3: n_f___2->n_f___2: 2*Arg_0+2*Arg_1+2 {O(n)}
4: n_f___3->n_f___1: 1 {O(1)}
5: n_f___3->n_f___2: 1 {O(1)}
6: n_start->n_f___3: 1 {O(1)}
Costbounds
Overall costbound: 4*Arg_1+4*Arg_2+8*Arg_0+11 {O(n)}
0: n_f___1->n_f___1: 2*Arg_0+2*Arg_2+2 {O(n)}
1: n_f___1->n_f___2: 2*Arg_0+2*Arg_2+2 {O(n)}
2: n_f___2->n_f___1: 2*Arg_0+2*Arg_1+2 {O(n)}
3: n_f___2->n_f___2: 2*Arg_0+2*Arg_1+2 {O(n)}
4: n_f___3->n_f___1: 1 {O(1)}
5: n_f___3->n_f___2: 1 {O(1)}
6: n_start->n_f___3: 1 {O(1)}
Sizebounds
0: n_f___1->n_f___1, Arg_0: 4*Arg_0 {O(n)}
0: n_f___1->n_f___1, Arg_1: 2*Arg_2+4*Arg_0+6*Arg_1+6 {O(n)}
0: n_f___1->n_f___1, Arg_2: 2*Arg_1+4*Arg_0+6*Arg_2+6 {O(n)}
1: n_f___1->n_f___2, Arg_0: 4*Arg_0 {O(n)}
1: n_f___1->n_f___2, Arg_1: 2*Arg_2+4*Arg_0+6*Arg_1+6 {O(n)}
1: n_f___1->n_f___2, Arg_2: 2*Arg_1+4*Arg_0+6*Arg_2+6 {O(n)}
2: n_f___2->n_f___1, Arg_0: 4*Arg_0 {O(n)}
2: n_f___2->n_f___1, Arg_1: 2*Arg_2+4*Arg_0+6*Arg_1+6 {O(n)}
2: n_f___2->n_f___1, Arg_2: 2*Arg_1+4*Arg_0+6*Arg_2+6 {O(n)}
3: n_f___2->n_f___2, Arg_0: 4*Arg_0 {O(n)}
3: n_f___2->n_f___2, Arg_1: 2*Arg_2+4*Arg_0+6*Arg_1+6 {O(n)}
3: n_f___2->n_f___2, Arg_2: 2*Arg_1+4*Arg_0+6*Arg_2+6 {O(n)}
4: n_f___3->n_f___1, Arg_0: Arg_0 {O(n)}
4: n_f___3->n_f___1, Arg_1: Arg_1 {O(n)}
4: n_f___3->n_f___1, Arg_2: Arg_2+1 {O(n)}
5: n_f___3->n_f___2, Arg_0: Arg_0 {O(n)}
5: n_f___3->n_f___2, Arg_1: Arg_1+1 {O(n)}
5: n_f___3->n_f___2, Arg_2: Arg_2 {O(n)}
6: n_start->n_f___3, Arg_0: Arg_0 {O(n)}
6: n_start->n_f___3, Arg_1: Arg_1 {O(n)}
6: n_start->n_f___3, Arg_2: Arg_2 {O(n)}