Initial Problem

Start: f3
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars: G, H
Locations: f2, f3, f4
Transitions:
0:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> f2(Arg_0-1,Arg_1-1,Arg_0,Arg_1,Arg_0-2,Arg_5):|:1<=Arg_0 && 1<=Arg_1
2:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> f4(Arg_0,G,Arg_2,Arg_3,Arg_4,H):|:Arg_1<=0 && G<=0
3:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> f4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,H):|:1<=Arg_1 && Arg_0<=0
1:f3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

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

Problem after Preprocessing

Start: f3
Program_Vars: Arg_0, Arg_1
Temp_Vars: G
Locations: f2, f3, f4
Transitions:
8:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1
9:f2(Arg_0,Arg_1) -> f4(Arg_0,G):|:Arg_1<=0 && G<=0
10:f2(Arg_0,Arg_1) -> f4(Arg_0,Arg_1):|:1<=Arg_1 && Arg_0<=0
11:f3(Arg_0,Arg_1) -> f2(Arg_0,Arg_1)

MPRF for transition 8:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1-1):|:1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

f2 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_1+3 {O(n)}
8: f2->f2: Arg_1 {O(n)}
9: f2->f4: 1 {O(1)}
10: f2->f4: 1 {O(1)}
11: f3->f2: 1 {O(1)}

Costbounds

Overall costbound: Arg_1+3 {O(n)}
8: f2->f2: Arg_1 {O(n)}
9: f2->f4: 1 {O(1)}
10: f2->f4: 1 {O(1)}
11: f3->f2: 1 {O(1)}

Sizebounds

8: f2->f2, Arg_0: Arg_0 {O(n)}
8: f2->f2, Arg_1: Arg_1 {O(n)}
9: f2->f4, Arg_0: 2*Arg_0 {O(n)}
10: f2->f4, Arg_0: 2*Arg_0 {O(n)}
10: f2->f4, Arg_1: 2*Arg_1 {O(n)}
11: f3->f2, Arg_0: Arg_0 {O(n)}
11: f3->f2, Arg_1: Arg_1 {O(n)}