Initial Problem

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

Preprocessing

Problem after Preprocessing

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

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

new bound:

Arg_0+1 {O(n)}

MPRF:

eval [Arg_0+1 ]

Analysing control-flow refined program

Found invariant 0<=1+Arg_1 && 0<=2+Arg_0+Arg_1 && 0<=1+Arg_0 for location n_eval___1

Found invariant 0<=1+Arg_1 for location n_eval___2

Found invariant 0<=1+Arg_0 for location n_eval___3

MPRF for transition 31:n_eval___2(Arg_0,Arg_1) -> n_eval___2(Arg_0,Arg_1-1):|:0<=1+Arg_1 && 0<=1+Arg_1 && 0<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

n_eval___2 [Arg_1+1 ]

MPRF for transition 30:n_eval___1(Arg_0,Arg_1) -> n_eval___3(Arg0_P,NoDet0):|:0<=1+Arg_1 && 0<=2+Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_1 && 0<=1+Arg0_P && Arg_0<=Arg0_P+1 && 1+Arg0_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+7 {O(n)}

MPRF:

n_eval___1 [Arg_0+2 ]
n_eval___3 [Arg_0+2 ]

MPRF for transition 33:n_eval___3(Arg_0,Arg_1) -> n_eval___1(Arg_0,Arg_1-1):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_1 of depth 1:

new bound:

3*Arg_0+7 {O(n)}

MPRF:

n_eval___1 [Arg_0+1 ]
n_eval___3 [Arg_0+2 ]

MPRF for transition 34:n_eval___3(Arg_0,Arg_1) -> n_eval___3(Arg0_P,NoDet0):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=1+Arg0_P && Arg_0<=Arg0_P+1 && 1+Arg0_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+7 {O(n)}

MPRF:

n_eval___1 [Arg_0+1 ]
n_eval___3 [Arg_0+2 ]

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)}