Initial Problem

Start: f
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f, g, h
Transitions:
0:f(Arg_0,Arg_1) -> g(Arg_0,1)
1:g(Arg_0,Arg_1) -> g(Arg_0-1,2*Arg_1):|:0<Arg_0
2:g(Arg_0,Arg_1) -> h(Arg_0,Arg_1):|:Arg_0<=0
3:h(Arg_0,Arg_1) -> h(Arg_0,Arg_1-1):|:0<Arg_1

Preprocessing

Found invariant 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location h

Found invariant 1<=Arg_1 for location g

Problem after Preprocessing

Start: f
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f, g, h
Transitions:
0:f(Arg_0,Arg_1) -> g(Arg_0,1)
1:g(Arg_0,Arg_1) -> g(Arg_0-1,2*Arg_1):|:1<=Arg_1 && 0<Arg_0
2:g(Arg_0,Arg_1) -> h(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=0
3:h(Arg_0,Arg_1) -> h(Arg_0,Arg_1-1):|:0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<Arg_1

MPRF for transition 1:g(Arg_0,Arg_1) -> g(Arg_0-1,2*Arg_1):|:1<=Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

g [Arg_0 ]

MPRF for transition 3:h(Arg_0,Arg_1) -> h(Arg_0,Arg_1-1):|: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)+Arg_0+4 {O(EXP)}
0: f->g: 1 {O(1)}
1: g->g: Arg_0 {O(n)}
2: g->h: 1 {O(1)}
3: h->h: 2^(Arg_0)+2 {O(EXP)}

Costbounds

Overall costbound: 2^(Arg_0)+Arg_0+4 {O(EXP)}
0: f->g: 1 {O(1)}
1: g->g: Arg_0 {O(n)}
2: g->h: 1 {O(1)}
3: 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)}
1: g->g, Arg_0: Arg_0 {O(n)}
1: g->g, Arg_1: 2^(Arg_0) {O(EXP)}
2: g->h, Arg_0: 2*Arg_0 {O(n)}
2: g->h, Arg_1: 2^(Arg_0)+1 {O(EXP)}
3: h->h, Arg_0: 2*Arg_0 {O(n)}
3: h->h, Arg_1: 2^(Arg_0)+1 {O(EXP)}