Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f2
Transitions:
0:f0(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_2<=Arg_1
1:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0-1,Arg_1,Arg_2-1):|:1<=Arg_0 && Arg_2<=Arg_1+1
2:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1+Arg_2-1,Arg_2-1):|:0<=Arg_0 && 0<=Arg_1

Preprocessing

Found invariant Arg_2<=Arg_1 && 0<=Arg_0 for location f2

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f2
Transitions:
0:f0(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_2<=Arg_1
1:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && 1<=Arg_0 && Arg_2<=Arg_1+1
2:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1+Arg_2-1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1

MPRF for transition 1:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && 1<=Arg_0 && Arg_2<=Arg_1+1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

f2 [Arg_0+1 ]

Analysing control-flow refined program

Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_0 for location n_f2___1

Found invariant Arg_2<=Arg_1 && 0<=Arg_0 for location f2

Found invariant Arg_2<=Arg_1 && 0<=Arg_0 for location n_f2___2

Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_0 for location n_f2___3

MPRF for transition 39:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0-1,Arg_1,Arg_2-1):|:1+Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 1+Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_f2___3 [Arg_0+1 ]

MPRF for transition 34:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0-1,Arg_1,Arg_2-1):|:1+Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 1+Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1+2*Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f2___1 [Arg_0+1 ]
n_f2___2 [Arg_0 ]

MPRF for transition 35:n_f2___1(Arg_0,Arg_1,Arg_2) -> n_f2___2(Arg_0,Arg_1+Arg_2-1,Arg_2-1):|:1+Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 1+Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1+2*Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && Arg_2<=Arg_1 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f2___1 [Arg_0+1 ]
n_f2___2 [Arg_0 ]

MPRF for transition 36:n_f2___2(Arg_0,Arg_1,Arg_2) -> n_f2___1(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && Arg_2<=Arg_1 && 0<=Arg_0 && Arg_2<=Arg_1 && 1+2*Arg_2<=Arg_1 && 1<=Arg_0 && Arg_2<=Arg_1 of depth 1:

new bound:

3*Arg_0+2 {O(n)}

MPRF:

n_f2___1 [Arg_0+1 ]
n_f2___2 [Arg_0+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: f0->f2: 1 {O(1)}
1: f2->f2: Arg_0+1 {O(n)}
2: f2->f2: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
0: f0->f2: 1 {O(1)}
1: f2->f2: Arg_0+1 {O(n)}
2: f2->f2: inf {Infinity}

Sizebounds

0: f0->f2, Arg_0: Arg_0 {O(n)}
0: f0->f2, Arg_1: Arg_1 {O(n)}
0: f0->f2, Arg_2: Arg_2 {O(n)}
1: f2->f2, Arg_0: 2*Arg_0 {O(n)}
2: f2->f2, Arg_0: 2*Arg_0 {O(n)}