Initial Problem

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

Preprocessing

Found invariant Arg_2<=Arg_1 && 0<=Arg_0 for location f2

Problem after Preprocessing

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

MPRF for transition 1:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0-1,Arg_1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && 1<=Arg_0 && Arg_2<=Arg_1+1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

f2 [Arg_0+1 ]

MPRF for transition 2:f2(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1+Arg_2-1,Arg_2-1):|:Arg_2<=Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 of depth 2:

new bound:

8*Arg_1+8*Arg_2+1 {O(n)}

MPRF:

f2 [Arg_2 ; Arg_1 ]

All Bounds

Timebounds

Overall timebound:8*Arg_1+8*Arg_2+Arg_0+3 {O(n)}
0: f0->f2: 1 {O(1)}
1: f2->f2: Arg_0+1 {O(n)}
2: f2->f2: 8*Arg_1+8*Arg_2+1 {O(n)}

Costbounds

Overall costbound: 8*Arg_1+8*Arg_2+Arg_0+3 {O(n)}
0: f0->f2: 1 {O(1)}
1: f2->f2: Arg_0+1 {O(n)}
2: f2->f2: 8*Arg_1+8*Arg_2+1 {O(n)}

Sizebounds

0: f0->f2, Arg_0: Arg_0 {O(n)}
0: f0->f2, Arg_1: Arg_1 {O(n)}
0: f0->f2, Arg_2: Arg_2 {O(n)}
1: f2->f2, Arg_0: 2*Arg_0 {O(n)}
1: f2->f2, Arg_1: 128*Arg_1*Arg_1+16*Arg_0*Arg_1+16*Arg_0*Arg_2+168*Arg_2*Arg_2+296*Arg_1*Arg_2+4*Arg_0+74*Arg_1+82*Arg_2+9 {O(n^2)}
1: f2->f2, Arg_2: 10*Arg_2+8*Arg_1+Arg_0+2 {O(n)}
2: f2->f2, Arg_0: 2*Arg_0 {O(n)}
2: f2->f2, Arg_1: 128*Arg_1*Arg_1+16*Arg_0*Arg_1+16*Arg_0*Arg_2+168*Arg_2*Arg_2+296*Arg_1*Arg_2+4*Arg_0+74*Arg_1+82*Arg_2+9 {O(n^2)}
2: f2->f2, Arg_2: 10*Arg_2+8*Arg_1+Arg_0+2 {O(n)}