Initial Problem

Start: f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: f2, f3, f4
Transitions:
0:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0-Arg_1,1+Arg_1,Arg_2):|:1<=Arg_0
2:f2(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,D):|:Arg_0<=0
1:f3(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,Arg_2):|:1<=Arg_1
3:f3(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,D):|:Arg_1<=0

Preprocessing

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

Found invariant 1<=Arg_1 for location f2

Problem after Preprocessing

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

MPRF for transition 7:f2(Arg_0,Arg_1) -> f2(Arg_0-Arg_1,1+Arg_1):|:1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

f2 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:Arg_0+3 {O(n)}
7: f2->f2: Arg_0 {O(n)}
8: f2->f4: 1 {O(1)}
9: f3->f2: 1 {O(1)}
10: f3->f4: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+3 {O(n)}
7: f2->f2: Arg_0 {O(n)}
8: f2->f4: 1 {O(1)}
9: f3->f2: 1 {O(1)}
10: f3->f4: 1 {O(1)}

Sizebounds

7: f2->f2, Arg_0: 2*Arg_0+2*Arg_1 {O(n)}
7: f2->f2, Arg_1: Arg_0+Arg_1 {O(n)}
8: f2->f4, Arg_0: 2*Arg_1+3*Arg_0 {O(n)}
8: f2->f4, Arg_1: 2*Arg_1+Arg_0 {O(n)}
9: f3->f2, Arg_0: Arg_0 {O(n)}
9: f3->f2, Arg_1: Arg_1 {O(n)}
10: f3->f4, Arg_0: Arg_0 {O(n)}
10: f3->f4, Arg_1: Arg_1 {O(n)}