Initial Problem

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

Preprocessing

Cut unsatisfiable transition 3: eval->eval

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_0-1,Arg_1):|:1<=Arg_0+Arg_1 && Arg_1+1<=Arg_0
1:eval(Arg_0,Arg_1) -> eval(Arg_0-1,Arg_1):|:1<=2*Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1
2:eval(Arg_0,Arg_1) -> eval(Arg_0,Arg_1-1):|:1<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0+1<=Arg_1
4:start(Arg_0,Arg_1) -> eval(Arg_0,Arg_1)

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

new bound:

2*Arg_0 {O(n)}

MPRF:

eval [2*Arg_0 ]

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

new bound:

2*Arg_0 {O(n)}

MPRF:

eval [2*Arg_0 ]

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

new bound:

2*Arg_1 {O(n)}

MPRF:

eval [2*Arg_1 ]

All Bounds

Timebounds

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

Costbounds

Overall costbound: 2*Arg_1+4*Arg_0+1 {O(n)}
0: eval->eval: 2*Arg_0 {O(n)}
1: eval->eval: 2*Arg_0 {O(n)}
2: eval->eval: 2*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_1 {O(n)}
1: eval->eval, Arg_0: 3*Arg_0 {O(n)}
1: eval->eval, Arg_1: 3*Arg_1 {O(n)}
2: eval->eval, Arg_0: 3*Arg_0 {O(n)}
2: eval->eval, Arg_1: 3*Arg_1 {O(n)}
4: start->eval, Arg_0: Arg_0 {O(n)}
4: start->eval, Arg_1: Arg_1 {O(n)}