Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: f0, f2
Transitions:
1:f0(Arg_0,Arg_1) -> f2(C,Arg_1-1):|:1<=Arg_1
0:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:1<=Arg_0
2:f2(Arg_0,Arg_1) -> f2(C,Arg_1-1):|:1<=Arg_1 && Arg_0<=0

Preprocessing

Found invariant 0<=Arg_1 for location f2

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: f0, f2
Transitions:
1:f0(Arg_0,Arg_1) -> f2(C,Arg_1-1):|:1<=Arg_1
0:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0
2:f2(Arg_0,Arg_1) -> f2(C,Arg_1-1):|:0<=Arg_1 && 1<=Arg_1 && Arg_0<=0

MPRF for transition 2:f2(Arg_0,Arg_1) -> f2(C,Arg_1-1):|:0<=Arg_1 && 1<=Arg_1 && Arg_0<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

f2 [Arg_1+1 ]

Analysing control-flow refined program

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_f2___1

Found invariant 0<=Arg_1 for location f2

MPRF for transition 36:f2(Arg_0,Arg_1) -> n_f2___1(Arg_0-1,Arg_1):|:0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f2___1 [Arg_1 ]
f2 [Arg_1+1 ]

MPRF for transition 37:f2(Arg_0,Arg_1) -> f2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f2___1 [Arg_1 ]
f2 [Arg_1+1 ]

MPRF for transition 35:n_f2___1(Arg_0,Arg_1) -> f2(NoDet0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f2___1 [Arg_1+1 ]
f2 [Arg_1+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
1: f0->f2: 1 {O(1)}
0: f2->f2: inf {Infinity}
2: f2->f2: Arg_1+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
1: f0->f2: 1 {O(1)}
0: f2->f2: inf {Infinity}
2: f2->f2: Arg_1+1 {O(n)}

Sizebounds

1: f0->f2, Arg_1: Arg_1 {O(n)}
0: f2->f2, Arg_1: 2*Arg_1 {O(n)}
2: f2->f2, Arg_1: 2*Arg_1 {O(n)}