Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0-1,Arg_1,Arg_2):|:Arg_1+1<=Arg_0
1:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0-1,Arg_1,Arg_2):|:Arg_1+1<=Arg_2 && Arg_1+1<=Arg_0
2:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2-1):|:Arg_1+1<=Arg_0 && Arg_0<=Arg_1 && Arg_1+1<=Arg_2
3:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2-1):|:Arg_1+1<=Arg_2 && Arg_0<=Arg_1
4:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_0 && Arg_0<=Arg_1 && Arg_2<=Arg_1
5:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2):|:Arg_1+1<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=Arg_1
6:start(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2)

Preprocessing

Cut unsatisfiable transition 2: eval->eval

Cut unsatisfiable transition 4: eval->eval

Cut unsatisfiable transition 5: eval->eval

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0-1,Arg_1,Arg_2):|:Arg_1+1<=Arg_0
1:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0-1,Arg_1,Arg_2):|:Arg_1+1<=Arg_2 && Arg_1+1<=Arg_0
3:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2-1):|:Arg_1+1<=Arg_2 && Arg_0<=Arg_1
6:start(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2)

MPRF for transition 0:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0-1,Arg_1,Arg_2):|:Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

eval [Arg_0-Arg_1 ]

MPRF for transition 1:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0-1,Arg_1,Arg_2):|:Arg_1+1<=Arg_2 && Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

eval [Arg_0-Arg_1 ]

MPRF for transition 3:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2-1):|:Arg_1+1<=Arg_2 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+Arg_2 {O(n)}

MPRF:

eval [Arg_2-Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+3*Arg_1+Arg_2+1 {O(n)}
0: eval->eval: Arg_0+Arg_1 {O(n)}
1: eval->eval: Arg_0+Arg_1 {O(n)}
3: eval->eval: Arg_1+Arg_2 {O(n)}
6: start->eval: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+3*Arg_1+Arg_2+1 {O(n)}
0: eval->eval: Arg_0+Arg_1 {O(n)}
1: eval->eval: Arg_0+Arg_1 {O(n)}
3: eval->eval: Arg_1+Arg_2 {O(n)}
6: start->eval: 1 {O(1)}

Sizebounds

0: eval->eval, Arg_0: 2*Arg_1+4*Arg_0 {O(n)}
0: eval->eval, Arg_1: 2*Arg_1 {O(n)}
0: eval->eval, Arg_2: 2*Arg_2 {O(n)}
1: eval->eval, Arg_0: 2*Arg_1+4*Arg_0 {O(n)}
1: eval->eval, Arg_1: 2*Arg_1 {O(n)}
1: eval->eval, Arg_2: 2*Arg_2 {O(n)}
3: eval->eval, Arg_0: 4*Arg_1+9*Arg_0 {O(n)}
3: eval->eval, Arg_1: 5*Arg_1 {O(n)}
3: eval->eval, Arg_2: 6*Arg_2+Arg_1 {O(n)}
6: start->eval, Arg_0: Arg_0 {O(n)}
6: start->eval, Arg_1: Arg_1 {O(n)}
6: start->eval, Arg_2: Arg_2 {O(n)}