Initial Problem

Start: f2
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: f1, f2, f300
Transitions:
0:f2(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(Arg_0,Arg_1,Arg_2,Arg_3)
4:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1,Arg_2,E):|:1<=Arg_0 && Arg_1+Arg_0<=0 && 1<=Arg_1
5:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1,Arg_2,E):|:1<=Arg_1 && Arg_0<=0
6:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1,Arg_2,E):|:Arg_1<=0
1:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(Arg_1-1,Arg_1-1,E,Arg_3):|:1<=Arg_0 && 1<=Arg_1 && 1<=E && 1<=Arg_1+Arg_0
2:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(Arg_1-1,Arg_1-1,E,Arg_3):|:1<=Arg_0 && 1<=Arg_1 && E+1<=0 && 1<=Arg_1+Arg_0
3:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(Arg_0-1,Arg_0-2,0,Arg_3):|:1<=Arg_0 && 1<=Arg_1+Arg_0 && 1<=Arg_1

Preprocessing

Cut unsatisfiable transition 4: f300->f1

Eliminate variables {Arg_2,Arg_3} that do not contribute to the problem

Problem after Preprocessing

Start: f2
Program_Vars: Arg_0, Arg_1
Temp_Vars: E
Locations: f1, f2, f300
Transitions:
21:f2(Arg_0,Arg_1) -> f300(Arg_0,Arg_1)
25:f300(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=0
26:f300(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:Arg_1<=0
22:f300(Arg_0,Arg_1) -> f300(Arg_1-1,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1 && 1<=E && 1<=Arg_1+Arg_0
23:f300(Arg_0,Arg_1) -> f300(Arg_1-1,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1 && E+1<=0 && 1<=Arg_1+Arg_0
24:f300(Arg_0,Arg_1) -> f300(Arg_0-1,Arg_0-2):|:1<=Arg_0 && 1<=Arg_1+Arg_0 && 1<=Arg_1

Analysing control-flow refined program

Found invariant 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 for location n_f300___1

Found invariant 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 for location n_f300___2

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 for location n_f300___3

MPRF for transition 73:n_f300___1(Arg_0,Arg_1) -> n_f300___1(Arg_0-1,Arg_0-2):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+Arg_0 {O(n)}

MPRF:

n_f300___1 [Arg_1+1 ]
n_f300___2 [Arg_0 ]
n_f300___3 [Arg_0 ]

MPRF for transition 74:n_f300___1(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_1+Arg_0+5 {O(n)}

MPRF:

n_f300___1 [Arg_0 ]
n_f300___2 [Arg_0-1 ]
n_f300___3 [Arg_1-2 ]

MPRF for transition 75:n_f300___1(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_1+Arg_0+5 {O(n)}

MPRF:

n_f300___1 [Arg_0 ]
n_f300___2 [Arg_0-1 ]
n_f300___3 [Arg_1-2 ]

MPRF for transition 76:n_f300___2(Arg_0,Arg_1) -> n_f300___1(Arg_0-1,Arg_0-2):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+Arg_0+1 {O(n)}

MPRF:

n_f300___1 [Arg_0-2 ]
n_f300___2 [Arg_0+1 ]
n_f300___3 [Arg_0 ]

MPRF for transition 77:n_f300___2(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_1+Arg_0+2 {O(n)}

MPRF:

n_f300___1 [Arg_0 ]
n_f300___2 [Arg_1+2 ]
n_f300___3 [Arg_0 ]

MPRF for transition 78:n_f300___2(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_1+Arg_0+2 {O(n)}

MPRF:

n_f300___1 [Arg_0 ]
n_f300___2 [Arg_1+2 ]
n_f300___3 [Arg_0 ]

MPRF for transition 79:n_f300___3(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,Arg_0-2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_1+Arg_0+2 {O(n)}

MPRF:

n_f300___1 [Arg_0-1 ]
n_f300___2 [Arg_1 ]
n_f300___3 [Arg_0+1 ]

MPRF for transition 80:n_f300___3(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_1+Arg_0+2 {O(n)}

MPRF:

n_f300___1 [Arg_0 ]
n_f300___2 [Arg_1 ]
n_f300___3 [Arg_1+1 ]

MPRF for transition 81:n_f300___3(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_1+Arg_0+2 {O(n)}

MPRF:

n_f300___1 [Arg_0 ]
n_f300___2 [Arg_1 ]
n_f300___3 [Arg_1+1 ]

CFR: Improvement to new bound with the following program:

new bound:

18*Arg_1+9*Arg_0+21 {O(n)}

cfr-program:

Start: f2
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f1, f2, f300, n_f300___1, n_f300___2, n_f300___3
Transitions:
21:f2(Arg_0,Arg_1) -> f300(Arg_0,Arg_1)
25:f300(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=0
26:f300(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:Arg_1<=0
82:f300(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,Arg_0-2):|:1<=Arg_0 && 1<=Arg_1
83:f300(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1<=Arg_1 && 1<=Arg_0
84:f300(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1<=Arg_1 && 1<=Arg_0
100:n_f300___1(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && Arg_1<=0
73:n_f300___1(Arg_0,Arg_1) -> n_f300___1(Arg_0-1,Arg_0-2):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_1
74:n_f300___1(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0
75:n_f300___1(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0
101:n_f300___2(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_1<=0
76:n_f300___2(Arg_0,Arg_1) -> n_f300___1(Arg_0-1,Arg_0-2):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_0 && 1<=Arg_1
77:n_f300___2(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0
78:n_f300___2(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && 0<=Arg_0 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 0<=1+Arg_1 && 1<=Arg_1 && 1<=Arg_0
102:n_f300___3(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_1<=0
79:n_f300___3(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,Arg_0-2):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
80:n_f300___3(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0
81:n_f300___3(Arg_0,Arg_1) -> n_f300___3(Arg_1-1,Arg_1-1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && 1<=Arg_0

All Bounds

Timebounds

Overall timebound:18*Arg_1+9*Arg_0+30 {O(n)}
21: f2->f300: 1 {O(1)}
25: f300->f1: 1 {O(1)}
26: f300->f1: 1 {O(1)}
82: f300->n_f300___2: 1 {O(1)}
83: f300->n_f300___3: 1 {O(1)}
84: f300->n_f300___3: 1 {O(1)}
73: n_f300___1->n_f300___1: 2*Arg_1+Arg_0 {O(n)}
74: n_f300___1->n_f300___3: 2*Arg_1+Arg_0+5 {O(n)}
75: n_f300___1->n_f300___3: 2*Arg_1+Arg_0+5 {O(n)}
100: n_f300___1->f1: 1 {O(1)}
76: n_f300___2->n_f300___1: 2*Arg_1+Arg_0+1 {O(n)}
77: n_f300___2->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
78: n_f300___2->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
101: n_f300___2->f1: 1 {O(1)}
79: n_f300___3->n_f300___2: 2*Arg_1+Arg_0+2 {O(n)}
80: n_f300___3->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
81: n_f300___3->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
102: n_f300___3->f1: 1 {O(1)}

Costbounds

Overall costbound: 18*Arg_1+9*Arg_0+30 {O(n)}
21: f2->f300: 1 {O(1)}
25: f300->f1: 1 {O(1)}
26: f300->f1: 1 {O(1)}
82: f300->n_f300___2: 1 {O(1)}
83: f300->n_f300___3: 1 {O(1)}
84: f300->n_f300___3: 1 {O(1)}
73: n_f300___1->n_f300___1: 2*Arg_1+Arg_0 {O(n)}
74: n_f300___1->n_f300___3: 2*Arg_1+Arg_0+5 {O(n)}
75: n_f300___1->n_f300___3: 2*Arg_1+Arg_0+5 {O(n)}
100: n_f300___1->f1: 1 {O(1)}
76: n_f300___2->n_f300___1: 2*Arg_1+Arg_0+1 {O(n)}
77: n_f300___2->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
78: n_f300___2->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
101: n_f300___2->f1: 1 {O(1)}
79: n_f300___3->n_f300___2: 2*Arg_1+Arg_0+2 {O(n)}
80: n_f300___3->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
81: n_f300___3->n_f300___3: 2*Arg_1+Arg_0+2 {O(n)}
102: n_f300___3->f1: 1 {O(1)}

Sizebounds

21: f2->f300, Arg_0: Arg_0 {O(n)}
21: f2->f300, Arg_1: Arg_1 {O(n)}
25: f300->f1, Arg_0: Arg_0 {O(n)}
25: f300->f1, Arg_1: Arg_1 {O(n)}
26: f300->f1, Arg_0: Arg_0 {O(n)}
26: f300->f1, Arg_1: Arg_1 {O(n)}
82: f300->n_f300___2, Arg_0: Arg_0 {O(n)}
82: f300->n_f300___2, Arg_1: Arg_0 {O(n)}
83: f300->n_f300___3, Arg_0: Arg_1 {O(n)}
83: f300->n_f300___3, Arg_1: Arg_1 {O(n)}
84: f300->n_f300___3, Arg_0: Arg_1 {O(n)}
84: f300->n_f300___3, Arg_1: Arg_1 {O(n)}
73: n_f300___1->n_f300___1, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
73: n_f300___1->n_f300___1, Arg_1: 12*Arg_1+6*Arg_0 {O(n)}
74: n_f300___1->n_f300___3, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
74: n_f300___1->n_f300___3, Arg_1: 10*Arg_0+18*Arg_1 {O(n)}
75: n_f300___1->n_f300___3, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
75: n_f300___1->n_f300___3, Arg_1: 10*Arg_0+18*Arg_1 {O(n)}
100: n_f300___1->f1, Arg_0: 1 {O(1)}
100: n_f300___1->f1, Arg_1: 0 {O(1)}
76: n_f300___2->n_f300___1, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
76: n_f300___2->n_f300___1, Arg_1: 4*Arg_0+6*Arg_1 {O(n)}
77: n_f300___2->n_f300___3, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
77: n_f300___2->n_f300___3, Arg_1: 19*Arg_0+38*Arg_1 {O(n)}
78: n_f300___2->n_f300___3, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
78: n_f300___2->n_f300___3, Arg_1: 19*Arg_0+38*Arg_1 {O(n)}
101: n_f300___2->f1, Arg_0: 1 {O(1)}
101: n_f300___2->f1, Arg_1: 1 {O(1)}
79: n_f300___3->n_f300___2, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
79: n_f300___3->n_f300___2, Arg_1: 18*Arg_0+38*Arg_1 {O(n)}
80: n_f300___3->n_f300___3, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
80: n_f300___3->n_f300___3, Arg_1: 116*Arg_0+228*Arg_1 {O(n)}
81: n_f300___3->n_f300___3, Arg_0: 3*Arg_0+6*Arg_1 {O(n)}
81: n_f300___3->n_f300___3, Arg_1: 116*Arg_0+228*Arg_1 {O(n)}
102: n_f300___3->f1, Arg_0: 0 {O(1)}
102: n_f300___3->f1, Arg_1: 0 {O(1)}