Initial Problem

Start: f5
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars:
Locations: f4, f5, f6
Transitions:
0:f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f4(Arg_0+Arg_1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:0<=Arg_0
1:f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f6(Arg_0,Arg_1,0,0,0,0,0):|:Arg_0+1<=0
2:f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_1+1<=0
3:f5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f6(Arg_0,Arg_1,0,0,0,0,0):|:0<=Arg_1

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_4,Arg_5,Arg_6} that do not contribute to the problem

Found invariant 1+Arg_1<=0 for location f4

Problem after Preprocessing

Start: f5
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f4, f5, f6
Transitions:
7:f4(Arg_0,Arg_1) -> f4(Arg_0+Arg_1,Arg_1):|:1+Arg_1<=0 && 0<=Arg_0
8:f4(Arg_0,Arg_1) -> f6(Arg_0,Arg_1):|:1+Arg_1<=0 && Arg_0+1<=0
9:f5(Arg_0,Arg_1) -> f4(Arg_0,Arg_1):|:Arg_1+1<=0
10:f5(Arg_0,Arg_1) -> f6(Arg_0,Arg_1):|:0<=Arg_1

MPRF for transition 7:f4(Arg_0,Arg_1) -> f4(Arg_0+Arg_1,Arg_1):|:1+Arg_1<=0 && 0<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

f4 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+4 {O(n)}
7: f4->f4: Arg_0+1 {O(n)}
8: f4->f6: 1 {O(1)}
9: f5->f4: 1 {O(1)}
10: f5->f6: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+4 {O(n)}
7: f4->f4: Arg_0+1 {O(n)}
8: f4->f6: 1 {O(1)}
9: f5->f4: 1 {O(1)}
10: f5->f6: 1 {O(1)}

Sizebounds

7: f4->f4, Arg_0: 2*Arg_1+Arg_0 {O(n)}
7: f4->f4, Arg_1: Arg_1 {O(n)}
8: f4->f6, Arg_0: 2*Arg_0+2*Arg_1 {O(n)}
8: f4->f6, Arg_1: 2*Arg_1 {O(n)}
9: f5->f4, Arg_0: Arg_0 {O(n)}
9: f5->f4, Arg_1: Arg_1 {O(n)}
10: f5->f6, Arg_0: Arg_0 {O(n)}
10: f5->f6, Arg_1: Arg_1 {O(n)}