Initial Problem
Start: n_f999
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f1___1, n_f1___4, n_f1___5, n_f2___2, n_f2___3, n_f999
Transitions:
0:n_f1___1(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1
1:n_f1___1(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
2:n_f1___4(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:1<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1
3:n_f1___4(Arg_0,Arg_1) -> n_f2___2(Arg_0-1,Arg_1):|:1<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
4:n_f1___5(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:1<=Arg_0 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1
5:n_f1___5(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:1<=Arg_0 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
6:n_f2___2(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_1
7:n_f2___2(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1+1):|:1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
8:n_f2___3(Arg_0,Arg_1) -> n_f1___1(Arg_0+1,Arg_1-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1
9:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1+1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
10:n_f999(Arg_0,Arg_1) -> n_f1___5(1,Arg_1-1):|:1<=Arg_1 && Arg_0<=0 && 0<=Arg_0
Preprocessing
Found invariant 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location n_f1___4
Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_f1___5
Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f1___1
Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f2___2
Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_f2___3
Problem after Preprocessing
Start: n_f999
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f1___1, n_f1___4, n_f1___5, n_f2___2, n_f2___3, n_f999
Transitions:
0:n_f1___1(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1
1:n_f1___1(Arg_0,Arg_1) -> n_f2___3(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 && 0<=Arg_1 && 1<=Arg_0
2:n_f1___4(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1
3:n_f1___4(Arg_0,Arg_1) -> n_f2___2(Arg_0-1,Arg_1):|:0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
4:n_f1___5(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1
5:n_f1___5(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0
6:n_f2___2(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_1
7:n_f2___2(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1+1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
8:n_f2___3(Arg_0,Arg_1) -> n_f1___1(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1
9:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1+1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
10:n_f999(Arg_0,Arg_1) -> n_f1___5(1,Arg_1-1):|:1<=Arg_1 && Arg_0<=0 && 0<=Arg_0
MPRF for transition 0:n_f1___1(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_1 of depth 1:
new bound:
2*Arg_1+3 {O(n)}
MPRF:
n_f1___4 [Arg_0+Arg_1-1 ]
n_f2___2 [Arg_0+Arg_1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
MPRF for transition 1:n_f1___1(Arg_0,Arg_1) -> n_f2___3(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 && 0<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_1+3 {O(n)}
MPRF:
n_f1___4 [Arg_0+Arg_1-1 ]
n_f2___2 [Arg_0+Arg_1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
MPRF for transition 3:n_f1___4(Arg_0,Arg_1) -> n_f2___2(Arg_0-1,Arg_1):|:0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_1+2 {O(n)}
MPRF:
n_f1___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
MPRF for transition 6:n_f2___2(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
2*Arg_1+2 {O(n)}
MPRF:
n_f1___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1+1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
MPRF for transition 7:n_f2___2(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1+1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_1+2 {O(n)}
MPRF:
n_f1___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1+1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
MPRF for transition 8:n_f2___3(Arg_0,Arg_1) -> n_f1___1(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
2*Arg_1+3 {O(n)}
MPRF:
n_f1___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1+1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1+1 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_f1___1->n_f1___4: 2*Arg_1+3 {O(n)}
1: n_f1___1->n_f2___3: 2*Arg_1+3 {O(n)}
2: n_f1___4->n_f1___4: inf {Infinity}
3: n_f1___4->n_f2___2: 2*Arg_1+2 {O(n)}
4: n_f1___5->n_f1___4: 1 {O(1)}
5: n_f1___5->n_f2___3: 1 {O(1)}
6: n_f2___2->n_f1___4: 2*Arg_1+2 {O(n)}
7: n_f2___2->n_f2___3: 2*Arg_1+2 {O(n)}
8: n_f2___3->n_f1___1: 2*Arg_1+3 {O(n)}
9: n_f2___3->n_f2___3: inf {Infinity}
10: n_f999->n_f1___5: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
0: n_f1___1->n_f1___4: 2*Arg_1+3 {O(n)}
1: n_f1___1->n_f2___3: 2*Arg_1+3 {O(n)}
2: n_f1___4->n_f1___4: inf {Infinity}
3: n_f1___4->n_f2___2: 2*Arg_1+2 {O(n)}
4: n_f1___5->n_f1___4: 1 {O(1)}
5: n_f1___5->n_f2___3: 1 {O(1)}
6: n_f2___2->n_f1___4: 2*Arg_1+2 {O(n)}
7: n_f2___2->n_f2___3: 2*Arg_1+2 {O(n)}
8: n_f2___3->n_f1___1: 2*Arg_1+3 {O(n)}
9: n_f2___3->n_f2___3: inf {Infinity}
10: n_f999->n_f1___5: 1 {O(1)}
Sizebounds
4: n_f1___5->n_f1___4, Arg_0: 2 {O(1)}
4: n_f1___5->n_f1___4, Arg_1: Arg_1 {O(n)}
5: n_f1___5->n_f2___3, Arg_0: 0 {O(1)}
5: n_f1___5->n_f2___3, Arg_1: Arg_1 {O(n)}
10: n_f999->n_f1___5, Arg_0: 1 {O(1)}
10: n_f999->n_f1___5, Arg_1: Arg_1 {O(n)}