Initial Problem

Start: f999
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f1, f2, f999
Transitions:
3:f1(Arg_0,Arg_1) -> f1(Arg_0+1,Arg_1-1):|:1<=Arg_1
0:f1(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:1<=Arg_0
4:f2(Arg_0,Arg_1) -> f1(Arg_0+1,Arg_1-1):|:1<=Arg_1
1:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1+1):|:1<=Arg_0
2:f999(Arg_0,Arg_1) -> f1(1,Arg_1-1):|:1<=Arg_1 && Arg_0<=0 && 0<=Arg_0

Preprocessing

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

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location f1

Problem after Preprocessing

Start: f999
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f1, f2, f999
Transitions:
3:f1(Arg_0,Arg_1) -> f1(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1
0:f1(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0
4:f2(Arg_0,Arg_1) -> f1(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1
1:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1+1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_0
2:f999(Arg_0,Arg_1) -> f1(1,Arg_1-1):|:1<=Arg_1 && Arg_0<=0 && 0<=Arg_0

MPRF for transition 0:f1(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

f2 [Arg_0+Arg_1 ]
f1 [Arg_0+Arg_1 ]

MPRF for transition 4:f2(Arg_0,Arg_1) -> f1(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

f2 [Arg_0+Arg_1+1 ]
f1 [Arg_0+Arg_1 ]

Analysing control-flow refined program

Found invariant 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location n_f1___5

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f1___1

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_f2___2

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_f2___4

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=1 && 1<=Arg_0 for location f1

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

MPRF for transition 54:n_f1___1(Arg_0,Arg_1) -> n_f1___5(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1-1 ]
n_f2___3 [Arg_0+Arg_1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1 ]

MPRF for transition 55:n_f1___1(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,Arg_1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

2*Arg_1+2 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1+1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1 ]

MPRF for transition 57:n_f1___5(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0 && 2<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1-1 ]
n_f2___3 [Arg_0+Arg_1-1 ]
n_f1___1 [Arg_0+Arg_1-1 ]
n_f2___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1-1 ]

MPRF for transition 60:n_f2___2(Arg_0,Arg_1) -> n_f1___1(Arg_0+1,Arg_1-1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1+1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___4 [Arg_0+Arg_1+1 ]
n_f2___2 [Arg_0+Arg_1+1 ]

MPRF for transition 62:n_f2___3(Arg_0,Arg_1) -> n_f1___5(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+2 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1+1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___4 [Arg_0+Arg_1 ]
n_f2___2 [Arg_0+Arg_1 ]

MPRF for transition 63:n_f2___3(Arg_0,Arg_1) -> n_f2___2(Arg_0-1,Arg_1+1):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

2*Arg_1+4 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1+1 ]
n_f2___3 [Arg_0+Arg_1+2 ]
n_f1___1 [Arg_0+Arg_1+1 ]
n_f2___4 [Arg_0+Arg_1+1 ]
n_f2___2 [Arg_0+Arg_1+1 ]

MPRF for transition 64:n_f2___4(Arg_0,Arg_1) -> n_f1___1(Arg_0+1,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___4 [Arg_0+Arg_1+1 ]
n_f2___2 [Arg_0+Arg_1 ]

MPRF for transition 65:n_f2___4(Arg_0,Arg_1) -> n_f2___2(Arg_0-1,Arg_1+1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 0<=Arg_1 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

n_f1___5 [Arg_0+Arg_1 ]
n_f2___3 [Arg_0+Arg_1 ]
n_f1___1 [Arg_0+Arg_1 ]
n_f2___4 [Arg_0+Arg_1+1 ]
n_f2___2 [Arg_0+Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: f1->f2: Arg_1+1 {O(n)}
3: f1->f1: inf {Infinity}
1: f2->f2: inf {Infinity}
4: f2->f1: Arg_1+1 {O(n)}
2: f999->f1: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: f1->f2: Arg_1+1 {O(n)}
3: f1->f1: inf {Infinity}
1: f2->f2: inf {Infinity}
4: f2->f1: Arg_1+1 {O(n)}
2: f999->f1: 1 {O(1)}

Sizebounds

2: f999->f1, Arg_0: 1 {O(1)}
2: f999->f1, Arg_1: Arg_1 {O(n)}