Initial Problem
Start: n_f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f1, n_f3___1, n_f3___2
Transitions:
0:n_f1(Arg_0,Arg_1) -> n_f3___2(Arg_0,Arg_0):|:1<=Arg_0
1:n_f3___1(Arg_0,Arg_1) -> n_f3___1(Arg_0,Arg_1-1):|:0<=Arg_1 && 1<=Arg_1
2:n_f3___1(Arg_0,Arg_1) -> n_f3___2(Arg_0-1,Arg_0-1):|:0<=Arg_1 && 2<=Arg_0 && Arg_1<=0
3:n_f3___2(Arg_0,Arg_1) -> n_f3___1(Arg_0,Arg_1-1):|:1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
Preprocessing
Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_f3___2
Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f3___1
Problem after Preprocessing
Start: n_f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f1, n_f3___1, n_f3___2
Transitions:
0:n_f1(Arg_0,Arg_1) -> n_f3___2(Arg_0,Arg_0):|:1<=Arg_0
1:n_f3___1(Arg_0,Arg_1) -> n_f3___1(Arg_0,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1
2:n_f3___1(Arg_0,Arg_1) -> n_f3___2(Arg_0-1,Arg_0-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0 && Arg_1<=0
3:n_f3___2(Arg_0,Arg_1) -> n_f3___1(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1
MPRF for transition 2:n_f3___1(Arg_0,Arg_1) -> n_f3___2(Arg_0-1,Arg_0-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0 && Arg_1<=0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_f3___2 [Arg_0 ]
n_f3___1 [Arg_0 ]
MPRF for transition 3:n_f3___2(Arg_0,Arg_1) -> n_f3___1(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_f3___2 [Arg_0 ]
n_f3___1 [Arg_0-1 ]
MPRF for transition 1:n_f3___1(Arg_0,Arg_1) -> n_f3___1(Arg_0,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 of depth 1:
new bound:
2*Arg_0*Arg_0+Arg_0 {O(n^2)}
MPRF:
n_f3___1 [Arg_1+1 ]
n_f3___2 [0 ]
All Bounds
Timebounds
Overall timebound:2*Arg_0*Arg_0+3*Arg_0+1 {O(n^2)}
0: n_f1->n_f3___2: 1 {O(1)}
1: n_f3___1->n_f3___1: 2*Arg_0*Arg_0+Arg_0 {O(n^2)}
2: n_f3___1->n_f3___2: Arg_0 {O(n)}
3: n_f3___2->n_f3___1: Arg_0 {O(n)}
Costbounds
Overall costbound: 2*Arg_0*Arg_0+3*Arg_0+1 {O(n^2)}
0: n_f1->n_f3___2: 1 {O(1)}
1: n_f3___1->n_f3___1: 2*Arg_0*Arg_0+Arg_0 {O(n^2)}
2: n_f3___1->n_f3___2: Arg_0 {O(n)}
3: n_f3___2->n_f3___1: Arg_0 {O(n)}
Sizebounds
0: n_f1->n_f3___2, Arg_0: Arg_0 {O(n)}
0: n_f1->n_f3___2, Arg_1: Arg_0 {O(n)}
1: n_f3___1->n_f3___1, Arg_0: Arg_0 {O(n)}
1: n_f3___1->n_f3___1, Arg_1: 2*Arg_0 {O(n)}
2: n_f3___1->n_f3___2, Arg_0: Arg_0 {O(n)}
2: n_f3___1->n_f3___2, Arg_1: Arg_0 {O(n)}
3: n_f3___2->n_f3___1, Arg_0: Arg_0 {O(n)}
3: n_f3___2->n_f3___1, Arg_1: 2*Arg_0 {O(n)}