Initial Problem
Start: n_f0
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f0, n_f3___1, n_f3___2
Transitions:
0:n_f0(Arg_0) -> n_f3___2(Arg_0)
1:n_f3___1(Arg_0) -> n_f3___1(Arg_0-1):|:1<=Arg_0 && 2<=Arg_0
2:n_f3___1(Arg_0) -> n_f3___2(Arg_0-1):|:1<=Arg_0
3:n_f3___2(Arg_0) -> n_f3___1(Arg_0-1):|:2<=Arg_0
4:n_f3___2(Arg_0) -> n_f3___2(Arg_0-1)
Preprocessing
Found invariant 1<=Arg_0 for location n_f3___1
Problem after Preprocessing
Start: n_f0
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f0, n_f3___1, n_f3___2
Transitions:
0:n_f0(Arg_0) -> n_f3___2(Arg_0)
1:n_f3___1(Arg_0) -> n_f3___1(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && 2<=Arg_0
2:n_f3___1(Arg_0) -> n_f3___2(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0
3:n_f3___2(Arg_0) -> n_f3___1(Arg_0-1):|:2<=Arg_0
4:n_f3___2(Arg_0) -> n_f3___2(Arg_0-1)
MPRF for transition 1:n_f3___1(Arg_0) -> n_f3___1(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
n_f3___1 [Arg_0 ]
n_f3___2 [Arg_0 ]
MPRF for transition 2:n_f3___1(Arg_0) -> n_f3___2(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_f3___1 [Arg_0 ]
n_f3___2 [Arg_0-1 ]
MPRF for transition 3:n_f3___2(Arg_0) -> n_f3___1(Arg_0-1):|:2<=Arg_0 of depth 1:
new bound:
Arg_0+1 {O(n)}
MPRF:
n_f3___1 [Arg_0-2 ]
n_f3___2 [Arg_0-1 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_f0->n_f3___2: 1 {O(1)}
1: n_f3___1->n_f3___1: Arg_0 {O(n)}
2: n_f3___1->n_f3___2: Arg_0+1 {O(n)}
3: n_f3___2->n_f3___1: Arg_0+1 {O(n)}
4: n_f3___2->n_f3___2: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
0: n_f0->n_f3___2: 1 {O(1)}
1: n_f3___1->n_f3___1: Arg_0 {O(n)}
2: n_f3___1->n_f3___2: Arg_0+1 {O(n)}
3: n_f3___2->n_f3___1: Arg_0+1 {O(n)}
4: n_f3___2->n_f3___2: inf {Infinity}
Sizebounds
0: n_f0->n_f3___2, Arg_0: Arg_0 {O(n)}