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):|:Arg_1<=Arg_0
1:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(1+Arg_0,Arg_1,E,Arg_3):|:1<=E && 1+Arg_0<=Arg_1
2:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(1+Arg_0,Arg_1,E,Arg_3):|:E+1<=0 && 1+Arg_0<=Arg_1
3:f300(Arg_0,Arg_1,Arg_2,Arg_3) -> f300(Arg_0,Arg_1,0,Arg_3):|:1+Arg_0<=Arg_1

Preprocessing

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

Found invariant Arg_1<=Arg_0 for location f1

Problem after Preprocessing

Start: f2
Program_Vars: Arg_0, Arg_1
Temp_Vars: E
Locations: f1, f2, f300
Transitions:
12:f2(Arg_0,Arg_1) -> f300(Arg_0,Arg_1)
16:f300(Arg_0,Arg_1) -> f1(Arg_0,Arg_1):|:Arg_1<=Arg_0
13:f300(Arg_0,Arg_1) -> f300(1+Arg_0,Arg_1):|:1<=E && 1+Arg_0<=Arg_1
14:f300(Arg_0,Arg_1) -> f300(1+Arg_0,Arg_1):|:E+1<=0 && 1+Arg_0<=Arg_1
15:f300(Arg_0,Arg_1) -> f300(Arg_0,Arg_1):|:1+Arg_0<=Arg_1

MPRF for transition 13:f300(Arg_0,Arg_1) -> f300(1+Arg_0,Arg_1):|:1<=E && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

f300 [Arg_1-Arg_0 ]

MPRF for transition 14:f300(Arg_0,Arg_1) -> f300(1+Arg_0,Arg_1):|:E+1<=0 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

f300 [Arg_1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
12: f2->f300: 1 {O(1)}
13: f300->f300: Arg_0+Arg_1 {O(n)}
14: f300->f300: Arg_0+Arg_1 {O(n)}
15: f300->f300: inf {Infinity}
16: f300->f1: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
12: f2->f300: 1 {O(1)}
13: f300->f300: Arg_0+Arg_1 {O(n)}
14: f300->f300: Arg_0+Arg_1 {O(n)}
15: f300->f300: inf {Infinity}
16: f300->f1: 1 {O(1)}

Sizebounds

12: f2->f300, Arg_0: Arg_0 {O(n)}
12: f2->f300, Arg_1: Arg_1 {O(n)}
13: f300->f300, Arg_0: 2*Arg_1+5*Arg_0 {O(n)}
13: f300->f300, Arg_1: 3*Arg_1 {O(n)}
14: f300->f300, Arg_0: 2*Arg_1+5*Arg_0 {O(n)}
14: f300->f300, Arg_1: 3*Arg_1 {O(n)}
15: f300->f300, Arg_0: 2*Arg_1+5*Arg_0 {O(n)}
15: f300->f300, Arg_1: 3*Arg_1 {O(n)}
16: f300->f1, Arg_0: 11*Arg_0+4*Arg_1 {O(n)}
16: f300->f1, Arg_1: 7*Arg_1 {O(n)}