Initial Problem
Start: f
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f, g, g1, h
Transitions:
0:f(Arg_0,Arg_1,Arg_2) -> g(Arg_0,1,0)
1:g(Arg_0,Arg_1,Arg_2) -> g1(Arg_0-1,Arg_1,Arg_1):|:0<Arg_0
3:g(Arg_0,Arg_1,Arg_2) -> h(Arg_0,Arg_1,Arg_2):|:Arg_0<=0
2:g1(Arg_0,Arg_1,Arg_2) -> g(Arg_0,Arg_2+Arg_1,Arg_2)
4:h(Arg_0,Arg_1,Arg_2) -> h(Arg_0,Arg_1-1,Arg_2):|:0<Arg_1
Preprocessing
Found invariant 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location h
Found invariant Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location g1
Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 for location g
Problem after Preprocessing
Start: f
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f, g, g1, h
Transitions:
0:f(Arg_0,Arg_1,Arg_2) -> g(Arg_0,1,0)
1:g(Arg_0,Arg_1,Arg_2) -> g1(Arg_0-1,Arg_1,Arg_1):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && 0<Arg_0
3:g(Arg_0,Arg_1,Arg_2) -> h(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && Arg_0<=0
2:g1(Arg_0,Arg_1,Arg_2) -> g(Arg_0,Arg_2+Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0
4:h(Arg_0,Arg_1,Arg_2) -> h(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<Arg_1
MPRF for transition 1:g(Arg_0,Arg_1,Arg_2) -> g1(Arg_0-1,Arg_1,Arg_1):|:1+Arg_2<=Arg_1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_1 && 0<Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
g1 [Arg_0 ]
g [Arg_0 ]
MPRF for transition 2:g1(Arg_0,Arg_1,Arg_2) -> g(Arg_0,Arg_2+Arg_1,Arg_2):|:Arg_2<=Arg_1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 of depth 1:
new bound:
Arg_0 {O(n)}
MPRF:
g1 [Arg_0+1 ]
g [Arg_0 ]
MPRF for transition 4:h(Arg_0,Arg_1,Arg_2) -> h(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_0<=Arg_2 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<Arg_1 of depth 1:
new bound:
2^(Arg_0)+2 {O(EXP)}
MPRF:
h [Arg_1+1 ]
All Bounds
Timebounds
Overall timebound:2^(Arg_0)+2*Arg_0+4 {O(EXP)}
0: f->g: 1 {O(1)}
1: g->g1: Arg_0 {O(n)}
3: g->h: 1 {O(1)}
2: g1->g: Arg_0 {O(n)}
4: h->h: 2^(Arg_0)+2 {O(EXP)}
Costbounds
Overall costbound: 2^(Arg_0)+2*Arg_0+4 {O(EXP)}
0: f->g: 1 {O(1)}
1: g->g1: Arg_0 {O(n)}
3: g->h: 1 {O(1)}
2: g1->g: Arg_0 {O(n)}
4: h->h: 2^(Arg_0)+2 {O(EXP)}
Sizebounds
0: f->g, Arg_0: Arg_0 {O(n)}
0: f->g, Arg_1: 1 {O(1)}
0: f->g, Arg_2: 0 {O(1)}
1: g->g1, Arg_0: Arg_0 {O(n)}
1: g->g1, Arg_1: 2^(Arg_0) {O(EXP)}
1: g->g1, Arg_2: 2^(Arg_0)+1 {O(EXP)}
3: g->h, Arg_0: 2*Arg_0 {O(n)}
3: g->h, Arg_1: 2^(Arg_0)+1 {O(EXP)}
3: g->h, Arg_2: 2^(Arg_0)+1 {O(EXP)}
2: g1->g, Arg_0: Arg_0 {O(n)}
2: g1->g, Arg_1: 2^(Arg_0) {O(EXP)}
2: g1->g, Arg_2: 2^(Arg_0)+1 {O(EXP)}
4: h->h, Arg_0: 2*Arg_0 {O(n)}
4: h->h, Arg_1: 2^(Arg_0)+1 {O(EXP)}
4: h->h, Arg_2: 2^(Arg_0)+1 {O(EXP)}