Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f2, f4, f5
Transitions:
1:f0(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,1):|:1<=Arg_0
3:f0(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,0):|:Arg_0<=0
2:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1-1,Arg_2):|:1<=Arg_1
0:f4(Arg_0,Arg_1,Arg_2) -> f5(Arg_0,Arg_1,1):|:Arg_0<=0 && Arg_1<=0

Preprocessing

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

Found invariant Arg_1<=0 && Arg_0+Arg_1<=0 && Arg_0<=0 for location f5

Found invariant 1<=Arg_0 for location f2

Found invariant Arg_0<=0 for location f4

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f0, f2, f4, f5
Transitions:
8:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:1<=Arg_0
9:f0(Arg_0,Arg_1) -> f4(Arg_0,Arg_1):|:Arg_0<=0
11:f4(Arg_0,Arg_1) -> f4(Arg_0,Arg_1-1):|:Arg_0<=0 && 1<=Arg_1
10:f4(Arg_0,Arg_1) -> f5(Arg_0,Arg_1):|:Arg_0<=0 && Arg_0<=0 && Arg_1<=0

MPRF for transition 11:f4(Arg_0,Arg_1) -> f4(Arg_0,Arg_1-1):|:Arg_0<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

f4 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_1+3 {O(n)}
8: f0->f2: 1 {O(1)}
9: f0->f4: 1 {O(1)}
10: f4->f5: 1 {O(1)}
11: f4->f4: Arg_1 {O(n)}

Costbounds

Overall costbound: Arg_1+3 {O(n)}
8: f0->f2: 1 {O(1)}
9: f0->f4: 1 {O(1)}
10: f4->f5: 1 {O(1)}
11: f4->f4: Arg_1 {O(n)}

Sizebounds

8: f0->f2, Arg_0: Arg_0 {O(n)}
8: f0->f2, Arg_1: Arg_1 {O(n)}
9: f0->f4, Arg_0: Arg_0 {O(n)}
9: f0->f4, Arg_1: Arg_1 {O(n)}
10: f4->f5, Arg_0: 2*Arg_0 {O(n)}
10: f4->f5, Arg_1: 2*Arg_1 {O(n)}
11: f4->f4, Arg_0: Arg_0 {O(n)}
11: f4->f4, Arg_1: Arg_1 {O(n)}