Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0):|:Arg_0<=0 && Arg_1<=1 && 1<=Arg_1
1:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0):|:1<=Arg_1 && 0<=1+Arg_1 && Arg_0+1<=Arg_1
2:eval(Arg_0,Arg_1) -> eval(Arg_0,0):|:1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
3:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_1-1):|:1<=Arg_1 && 0<=1+Arg_1 && Arg_1<=Arg_0
4:start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0):|:Arg_0<=0 && Arg_1<=1 && 1<=Arg_1
1:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0):|:1<=Arg_1 && 0<=1+Arg_1 && Arg_0+1<=Arg_1
2:eval(Arg_0,Arg_1) -> eval(Arg_0,0):|:1<=Arg_0 && Arg_1<=1 && 1<=Arg_1
3:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_1-1):|:1<=Arg_1 && 0<=1+Arg_1 && Arg_1<=Arg_0
4:start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1)

knowledge_propagation leads to new time bound 1 {O(1)} for transition 0:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0):|:Arg_0<=0 && Arg_1<=1 && 1<=Arg_1

knowledge_propagation leads to new time bound 1 {O(1)} for transition 1:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_0):|:1<=Arg_1 && 0<=1+Arg_1 && Arg_0+1<=Arg_1

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

new bound:

Arg_1 {O(n)}

MPRF:

eval [Arg_1 ]

MPRF for transition 3:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_1-1):|:1<=Arg_1 && 0<=1+Arg_1 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

eval [Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+3 {O(n)}
0: eval->eval: 1 {O(1)}
1: eval->eval: 1 {O(1)}
2: eval->eval: Arg_1 {O(n)}
3: eval->eval: Arg_1 {O(n)}
4: start->eval: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+3 {O(n)}
0: eval->eval: 1 {O(1)}
1: eval->eval: 1 {O(1)}
2: eval->eval: Arg_1 {O(n)}
3: eval->eval: Arg_1 {O(n)}
4: start->eval: 1 {O(1)}

Sizebounds

0: eval->eval, Arg_0: Arg_0 {O(n)}
0: eval->eval, Arg_1: Arg_0 {O(n)}
1: eval->eval, Arg_0: Arg_0 {O(n)}
1: eval->eval, Arg_1: Arg_0 {O(n)}
2: eval->eval, Arg_0: 4*Arg_0 {O(n)}
2: eval->eval, Arg_1: 0 {O(1)}
3: eval->eval, Arg_0: 2*Arg_0 {O(n)}
3: eval->eval, Arg_1: Arg_0+Arg_1 {O(n)}
4: start->eval, Arg_0: Arg_0 {O(n)}
4: start->eval, Arg_1: Arg_1 {O(n)}