Initial Problem

Start: f1
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
16:f1(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,Arg_2)
1:f2(Arg_0,Arg_1,Arg_2) -> f2(1,2,Arg_2):|:D<=1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0
2:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,2,Arg_2):|:2<=Arg_0 && D<=1 && Arg_1<=1 && 1<=Arg_1
3:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,2,Arg_2):|:Arg_0<=0 && D<=1 && Arg_1<=1 && 1<=Arg_1
4:f2(Arg_0,Arg_1,Arg_2) -> f2(1,1+Arg_1,Arg_2):|:2<=Arg_1 && Arg_1<=1 && Arg_0<=1 && 1<=Arg_0
5:f2(Arg_0,Arg_1,Arg_2) -> f2(1,1+Arg_1,Arg_2):|:Arg_1<=0 && Arg_1<=1 && Arg_0<=1 && 1<=Arg_0
6:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:Arg_1<=1 && 2<=Arg_0 && 2<=Arg_1
7:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:Arg_1<=1 && 2<=Arg_0 && Arg_1<=0
8:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:Arg_1<=1 && Arg_0<=0 && 2<=Arg_1
9:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:Arg_1<=1 && Arg_0<=0 && Arg_1<=0
10:f2(Arg_0,Arg_1,Arg_2) -> f2(1,1+Arg_1,Arg_2):|:2<=Arg_1 && D<=2 && Arg_0<=1 && 1<=Arg_0
11:f2(Arg_0,Arg_1,Arg_2) -> f2(1,1+Arg_1,Arg_2):|:2<=Arg_1 && Arg_1<=0 && D<=2 && Arg_0<=1 && 1<=Arg_0
12:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:2<=Arg_1 && Arg_0<=2 && 2<=Arg_0
13:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:2<=Arg_1 && Arg_1<=0 && Arg_0<=2 && 2<=Arg_0
14:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:2<=Arg_1 && Arg_0<=2 && Arg_0<=0
15:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:2<=Arg_1 && Arg_0<=2 && Arg_0<=0 && Arg_1<=0
0:f2(Arg_0,Arg_1,Arg_2) -> f300(Arg_0,Arg_1,D):|:3<=Arg_0 && 2<=Arg_1

Preprocessing

Cut unsatisfiable transition 4: f2->f2

Cut unsatisfiable transition 6: f2->f2

Cut unsatisfiable transition 8: f2->f2

Cut unsatisfiable transition 11: f2->f2

Cut unsatisfiable transition 13: f2->f2

Cut unsatisfiable transition 15: f2->f2

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

Found invariant 2<=Arg_1 && 5<=Arg_0+Arg_1 && 3<=Arg_0 for location f300

Problem after Preprocessing

Start: f1
Program_Vars: Arg_0, Arg_1
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
211:f1(Arg_0,Arg_1) -> f2(Arg_0,Arg_1)
213:f2(Arg_0,Arg_1) -> f2(1,2):|:D<=1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0
214:f2(Arg_0,Arg_1) -> f2(1+Arg_0,2):|:2<=Arg_0 && D<=1 && Arg_1<=1 && 1<=Arg_1
215:f2(Arg_0,Arg_1) -> f2(1+Arg_0,2):|:Arg_0<=0 && D<=1 && Arg_1<=1 && 1<=Arg_1
216:f2(Arg_0,Arg_1) -> f2(1,1+Arg_1):|:Arg_1<=0 && Arg_1<=1 && Arg_0<=1 && 1<=Arg_0
217:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_1<=1 && 2<=Arg_0 && Arg_1<=0
218:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_1<=1 && Arg_0<=0 && Arg_1<=0
219:f2(Arg_0,Arg_1) -> f2(1,1+Arg_1):|:2<=Arg_1 && D<=2 && Arg_0<=1 && 1<=Arg_0
220:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:2<=Arg_1 && Arg_0<=2 && 2<=Arg_0
221:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:2<=Arg_1 && Arg_0<=2 && Arg_0<=0
212:f2(Arg_0,Arg_1) -> f300(Arg_0,Arg_1):|:3<=Arg_0 && 2<=Arg_1

knowledge_propagation leads to new time bound 1 {O(1)} for transition 220:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:2<=Arg_1 && Arg_0<=2 && 2<=Arg_0

MPRF for transition 213:f2(Arg_0,Arg_1) -> f2(1,2):|:D<=1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

f2 [2-Arg_1 ]

MPRF for transition 214:f2(Arg_0,Arg_1) -> f2(1+Arg_0,2):|:2<=Arg_0 && D<=1 && Arg_1<=1 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+2 {O(n)}

MPRF:

f2 [2-Arg_1 ]

MPRF for transition 215:f2(Arg_0,Arg_1) -> f2(1+Arg_0,2):|:Arg_0<=0 && D<=1 && Arg_1<=1 && 1<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

f2 [1-Arg_0 ]

MPRF for transition 216:f2(Arg_0,Arg_1) -> f2(1,1+Arg_1):|:Arg_1<=0 && Arg_1<=1 && Arg_0<=1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

f2 [1-Arg_1 ]

MPRF for transition 217:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_1<=1 && 2<=Arg_0 && Arg_1<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

f2 [1-Arg_1 ]

MPRF for transition 218:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_1<=1 && Arg_0<=0 && Arg_1<=0 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

f2 [1-Arg_1 ]

MPRF for transition 221:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:2<=Arg_1 && Arg_0<=2 && Arg_0<=0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

f2 [1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
211: f1->f2: 1 {O(1)}
212: f2->f300: 1 {O(1)}
213: f2->f2: Arg_1+2 {O(n)}
214: f2->f2: Arg_1+2 {O(n)}
215: f2->f2: Arg_0+1 {O(n)}
216: f2->f2: Arg_1+1 {O(n)}
217: f2->f2: Arg_1+1 {O(n)}
218: f2->f2: Arg_1+1 {O(n)}
219: f2->f2: inf {Infinity}
220: f2->f2: 1 {O(1)}
221: f2->f2: Arg_0+1 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
211: f1->f2: 1 {O(1)}
212: f2->f300: 1 {O(1)}
213: f2->f2: Arg_1+2 {O(n)}
214: f2->f2: Arg_1+2 {O(n)}
215: f2->f2: Arg_0+1 {O(n)}
216: f2->f2: Arg_1+1 {O(n)}
217: f2->f2: Arg_1+1 {O(n)}
218: f2->f2: Arg_1+1 {O(n)}
219: f2->f2: inf {Infinity}
220: f2->f2: 1 {O(1)}
221: f2->f2: Arg_0+1 {O(n)}

Sizebounds

211: f1->f2, Arg_0: Arg_0 {O(n)}
211: f1->f2, Arg_1: Arg_1 {O(n)}
212: f2->f300, Arg_0: 3*Arg_0+Arg_1+6 {O(n)}
212: f2->f300, Arg_1: 2*Arg_1+3 {O(n)}
213: f2->f2, Arg_0: 1 {O(1)}
213: f2->f2, Arg_1: 2 {O(1)}
214: f2->f2, Arg_0: 2*Arg_0+Arg_1+3 {O(n)}
214: f2->f2, Arg_1: 2 {O(1)}
215: f2->f2, Arg_0: 2*Arg_0+3 {O(n)}
215: f2->f2, Arg_1: 2 {O(1)}
216: f2->f2, Arg_0: 1 {O(1)}
216: f2->f2, Arg_1: 2*Arg_1+2 {O(n)}
217: f2->f2, Arg_0: Arg_0+Arg_1+1 {O(n)}
217: f2->f2, Arg_1: Arg_1+1 {O(n)}
218: f2->f2, Arg_0: Arg_0+1 {O(n)}
218: f2->f2, Arg_1: Arg_1+1 {O(n)}
219: f2->f2, Arg_0: 1 {O(1)}
220: f2->f2, Arg_0: 3 {O(1)}
220: f2->f2, Arg_1: Arg_1+1 {O(n)}
221: f2->f2, Arg_0: 3*Arg_0+4 {O(n)}
221: f2->f2, Arg_1: Arg_0+Arg_1+3 {O(n)}