Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: f0, f23, f8
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3) -> f8(0,Arg_1,Arg_2,Arg_3)
3:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f23(Arg_0,Arg_1,Arg_2,Arg_3):|:4<=Arg_0 && E+1<=0
4:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f23(Arg_0,Arg_1,Arg_2,Arg_3):|:4<=Arg_0
1:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f8(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_0<=3
2:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f8(Arg_0+1,Arg_0,Arg_0+1,E):|:Arg_0<=3

Preprocessing

Eliminate variables {Arg_1,Arg_2,Arg_3} that do not contribute to the problem

Found invariant Arg_0<=4 && 4<=Arg_0 for location f23

Found invariant Arg_0<=4 && 0<=Arg_0 for location f8

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0
Temp_Vars: E
Locations: f0, f23, f8
Transitions:
11:f0(Arg_0) -> f8(0)
14:f8(Arg_0) -> f23(Arg_0):|:Arg_0<=4 && 0<=Arg_0 && 4<=Arg_0 && E+1<=0
15:f8(Arg_0) -> f23(Arg_0):|:Arg_0<=4 && 0<=Arg_0 && 4<=Arg_0
12:f8(Arg_0) -> f8(Arg_0+1):|:Arg_0<=4 && 0<=Arg_0 && Arg_0<=3
13:f8(Arg_0) -> f8(Arg_0+1):|:Arg_0<=4 && 0<=Arg_0 && Arg_0<=3

MPRF for transition 12:f8(Arg_0) -> f8(Arg_0+1):|:Arg_0<=4 && 0<=Arg_0 && Arg_0<=3 of depth 1:

new bound:

4 {O(1)}

MPRF:

f8 [4-Arg_0 ]

MPRF for transition 13:f8(Arg_0) -> f8(Arg_0+1):|:Arg_0<=4 && 0<=Arg_0 && Arg_0<=3 of depth 1:

new bound:

4 {O(1)}

MPRF:

f8 [4-Arg_0 ]

All Bounds

Timebounds

Overall timebound:11 {O(1)}
11: f0->f8: 1 {O(1)}
12: f8->f8: 4 {O(1)}
13: f8->f8: 4 {O(1)}
14: f8->f23: 1 {O(1)}
15: f8->f23: 1 {O(1)}

Costbounds

Overall costbound: 11 {O(1)}
11: f0->f8: 1 {O(1)}
12: f8->f8: 4 {O(1)}
13: f8->f8: 4 {O(1)}
14: f8->f23: 1 {O(1)}
15: f8->f23: 1 {O(1)}

Sizebounds

11: f0->f8, Arg_0: 0 {O(1)}
12: f8->f8, Arg_0: 4 {O(1)}
13: f8->f8, Arg_0: 4 {O(1)}
14: f8->f23, Arg_0: 4 {O(1)}
15: f8->f23, Arg_0: 4 {O(1)}