Initial Problem

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: eval, start
Transitions:
0:eval(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:Arg_1+1<=Arg_0 && Arg_3+1<=Arg_2
1:eval(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:Arg_1+1<=Arg_0 && Arg_3+1<=Arg_2
2:eval(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4+1):|:Arg_0<=Arg_1 && Arg_3+1<=Arg_2
3:eval(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4+1):|:Arg_1+1<=Arg_0 && Arg_2<=Arg_3
4:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> eval(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Eliminate variables {Arg_4} that do not contribute to the problem

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: eval, start
Transitions:
10:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_1+1<=Arg_0 && Arg_3+1<=Arg_2
11:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_1+1<=Arg_0 && Arg_3+1<=Arg_2
12:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_0<=Arg_1 && Arg_3+1<=Arg_2
13:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_1+1<=Arg_0 && Arg_2<=Arg_3
14:start(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1,Arg_2,Arg_3)

MPRF for transition 10:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_1+1<=Arg_0 && Arg_3+1<=Arg_2 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

eval [Arg_0-Arg_1 ]

MPRF for transition 11:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_1+1<=Arg_0 && Arg_3+1<=Arg_2 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval [Arg_2-Arg_3 ]

MPRF for transition 12:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1,Arg_2,Arg_3+1):|:Arg_0<=Arg_1 && Arg_3+1<=Arg_2 of depth 1:

new bound:

Arg_2+Arg_3 {O(n)}

MPRF:

eval [Arg_2-Arg_3 ]

MPRF for transition 13:eval(Arg_0,Arg_1,Arg_2,Arg_3) -> eval(Arg_0,Arg_1+1,Arg_2,Arg_3):|:Arg_1+1<=Arg_0 && Arg_2<=Arg_3 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

eval [Arg_0-Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+2*Arg_1+2*Arg_2+2*Arg_3+1 {O(n)}
10: eval->eval: Arg_0+Arg_1 {O(n)}
11: eval->eval: Arg_2+Arg_3 {O(n)}
12: eval->eval: Arg_2+Arg_3 {O(n)}
13: eval->eval: Arg_0+Arg_1 {O(n)}
14: start->eval: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+2*Arg_1+2*Arg_2+2*Arg_3+1 {O(n)}
10: eval->eval: Arg_0+Arg_1 {O(n)}
11: eval->eval: Arg_2+Arg_3 {O(n)}
12: eval->eval: Arg_2+Arg_3 {O(n)}
13: eval->eval: Arg_0+Arg_1 {O(n)}
14: start->eval: 1 {O(1)}

Sizebounds

10: eval->eval, Arg_0: 2*Arg_0 {O(n)}
10: eval->eval, Arg_1: 3*Arg_1+Arg_0 {O(n)}
10: eval->eval, Arg_2: 2*Arg_2 {O(n)}
10: eval->eval, Arg_3: 3*Arg_3+Arg_2 {O(n)}
11: eval->eval, Arg_0: 2*Arg_0 {O(n)}
11: eval->eval, Arg_1: 3*Arg_1+Arg_0 {O(n)}
11: eval->eval, Arg_2: 2*Arg_2 {O(n)}
11: eval->eval, Arg_3: 3*Arg_3+Arg_2 {O(n)}
12: eval->eval, Arg_0: 3*Arg_0 {O(n)}
12: eval->eval, Arg_1: 4*Arg_1+Arg_0 {O(n)}
12: eval->eval, Arg_2: 3*Arg_2 {O(n)}
12: eval->eval, Arg_3: 2*Arg_2+5*Arg_3 {O(n)}
13: eval->eval, Arg_0: 3*Arg_0 {O(n)}
13: eval->eval, Arg_1: 2*Arg_0+5*Arg_1 {O(n)}
13: eval->eval, Arg_2: 3*Arg_2 {O(n)}
13: eval->eval, Arg_3: 4*Arg_3+Arg_2 {O(n)}
14: start->eval, Arg_0: Arg_0 {O(n)}
14: start->eval, Arg_1: Arg_1 {O(n)}
14: start->eval, Arg_2: Arg_2 {O(n)}
14: start->eval, Arg_3: Arg_3 {O(n)}