Initial Problem
Start: n_f6
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: NoDet0
Locations: n_f3___4, n_f4___3, n_f4___5, n_f6, n_f7___1, n_f7___2
Transitions:
0:n_f3___4(Arg_0,Arg_1,Arg_2) -> n_f4___3(-Arg_0-1,Arg_1,1):|:Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_2<=0 && 1+Arg_0<=0
1:n_f3___4(Arg_0,Arg_1,Arg_2) -> n_f7___2(0,NoDet0,Arg_2):|:Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 0<=Arg_0
2:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f3___4(1-Arg_0,Arg_1,0):|:Arg_2<=1 && 1<=Arg_2 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2
3:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f7___1(0,NoDet0,Arg_2):|:Arg_2<=1 && 1<=Arg_2 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
4:n_f4___5(Arg_0,Arg_1,Arg_2) -> n_f3___4(1-Arg_0,Arg_1,0):|:Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2
5:n_f6(Arg_0,Arg_1,Arg_2) -> n_f4___5(Arg_0,Arg_1,1):|:1<=Arg_0
Preprocessing
Eliminate variables {NoDet0,Arg_1} that do not contribute to the problem
Found invariant Arg_2<=1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_0 for location n_f4___3
Found invariant Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 for location n_f7___2
Found invariant Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 for location n_f3___4
Found invariant Arg_2<=1 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 for location n_f7___1
Found invariant Arg_2<=1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_0 for location n_f4___5
Problem after Preprocessing
Start: n_f6
Program_Vars: Arg_0, Arg_2
Temp_Vars:
Locations: n_f3___4, n_f4___3, n_f4___5, n_f6, n_f7___1, n_f7___2
Transitions:
12:n_f3___4(Arg_0,Arg_2) -> n_f4___3(-Arg_0-1,1):|:Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_2<=0 && 1+Arg_0<=0
13:n_f3___4(Arg_0,Arg_2) -> n_f7___2(0,Arg_2):|:Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0 && 0<=Arg_0
14:n_f4___3(Arg_0,Arg_2) -> n_f3___4(1-Arg_0,0):|:Arg_2<=1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2
15:n_f4___3(Arg_0,Arg_2) -> n_f7___1(0,Arg_2):|:Arg_2<=1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
16:n_f4___5(Arg_0,Arg_2) -> n_f3___4(1-Arg_0,0):|:Arg_2<=1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2
17:n_f6(Arg_0,Arg_2) -> n_f4___5(Arg_0,1):|:1<=Arg_0
MPRF for transition 12:n_f3___4(Arg_0,Arg_2) -> n_f4___3(-Arg_0-1,1):|:Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_2 && Arg_0<=0 && Arg_0<=0 && Arg_2<=0 && 0<=Arg_2 && Arg_2<=0 && 1+Arg_0<=0 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_f4___3 [Arg_0 ]
n_f3___4 [1-Arg_0 ]
MPRF for transition 14:n_f4___3(Arg_0,Arg_2) -> n_f3___4(1-Arg_0,0):|:Arg_2<=1 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_0+Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && 0<=Arg_0 && 1<=Arg_0 && Arg_2<=1 && 1<=Arg_2 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_f4___3 [Arg_0+1 ]
n_f3___4 [-Arg_0 ]
All Bounds
Timebounds
Overall timebound:2*Arg_0+5 {O(n)}
12: n_f3___4->n_f4___3: Arg_0+1 {O(n)}
13: n_f3___4->n_f7___2: 1 {O(1)}
14: n_f4___3->n_f3___4: Arg_0 {O(n)}
15: n_f4___3->n_f7___1: 1 {O(1)}
16: n_f4___5->n_f3___4: 1 {O(1)}
17: n_f6->n_f4___5: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_0+5 {O(n)}
12: n_f3___4->n_f4___3: Arg_0+1 {O(n)}
13: n_f3___4->n_f7___2: 1 {O(1)}
14: n_f4___3->n_f3___4: Arg_0 {O(n)}
15: n_f4___3->n_f7___1: 1 {O(1)}
16: n_f4___5->n_f3___4: 1 {O(1)}
17: n_f6->n_f4___5: 1 {O(1)}
Sizebounds
12: n_f3___4->n_f4___3, Arg_0: Arg_0 {O(n)}
12: n_f3___4->n_f4___3, Arg_2: 1 {O(1)}
13: n_f3___4->n_f7___2, Arg_0: 0 {O(1)}
13: n_f3___4->n_f7___2, Arg_2: 0 {O(1)}
14: n_f4___3->n_f3___4, Arg_0: Arg_0 {O(n)}
14: n_f4___3->n_f3___4, Arg_2: 0 {O(1)}
15: n_f4___3->n_f7___1, Arg_0: 0 {O(1)}
15: n_f4___3->n_f7___1, Arg_2: 1 {O(1)}
16: n_f4___5->n_f3___4, Arg_0: Arg_0 {O(n)}
16: n_f4___5->n_f3___4, Arg_2: 0 {O(1)}
17: n_f6->n_f4___5, Arg_0: Arg_0 {O(n)}
17: n_f6->n_f4___5, Arg_2: 1 {O(1)}