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_2-1):|:0<=Arg_0 && Arg_2<=Arg_1^3
1:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1+Arg_2,Arg_2-1):|:0<=Arg_0 && Arg_2<=Arg_1^3
2:start(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1,Arg_2)

Preprocessing

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_2-1):|:0<=Arg_0 && Arg_2<=Arg_1^3
1:eval(Arg_0,Arg_1,Arg_2) -> eval(Arg_0,Arg_1+Arg_2,Arg_2-1):|:0<=Arg_0 && Arg_2<=Arg_1^3
2: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_2-1):|:0<=Arg_0 && Arg_2<=Arg_1^3 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

eval [Arg_0+1 ]

Analysing control-flow refined program

Eliminate variables {Arg_1,Arg_2} that do not contribute to the problem

Found invariant 0<=Arg_0 for location n_eval___1

Found invariant 0<=1+Arg_0 for location n_eval___2

MPRF for transition 50:n_eval___1(Arg_0) -> n_eval___2(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_0+3 {O(n)}

MPRF:

n_eval___1 [Arg_0+1 ]
n_eval___2 [Arg_0+1 ]

MPRF for transition 51:n_eval___2(Arg_0) -> n_eval___1(Arg_0):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_0+2 {O(n)}

MPRF:

n_eval___1 [Arg_0 ]
n_eval___2 [Arg_0+1 ]

MPRF for transition 52:n_eval___2(Arg_0) -> n_eval___2(Arg_0-1):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

2*Arg_0+2 {O(n)}

MPRF:

n_eval___1 [Arg_0 ]
n_eval___2 [Arg_0+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: eval->eval: Arg_0+1 {O(n)}
1: eval->eval: inf {Infinity}
2: start->eval: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: eval->eval: Arg_0+1 {O(n)}
1: eval->eval: inf {Infinity}
2: start->eval: 1 {O(1)}

Sizebounds

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