Initial Problem
Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f4
Transitions:
2:f0(Arg_0,Arg_1,Arg_2) -> f4(0,0,Arg_2):|:1<=Arg_2
0:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1+1,Arg_2):|:Arg_1+1<=Arg_0
1:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0+1,0,Arg_2):|:Arg_0+2<=Arg_2 && Arg_0<=Arg_1
Preprocessing
Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location f4
Problem after Preprocessing
Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f4
Transitions:
2:f0(Arg_0,Arg_1,Arg_2) -> f4(0,0,Arg_2):|:1<=Arg_2
0:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0
1:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0+1,0,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0+2<=Arg_2 && Arg_0<=Arg_1
MPRF for transition 1:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0+1,0,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0+2<=Arg_2 && Arg_0<=Arg_1 of depth 1:
new bound:
Arg_2 {O(n)}
MPRF:
f4 [Arg_2-Arg_0 ]
MPRF for transition 0:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:
new bound:
Arg_2*Arg_2+Arg_2 {O(n^2)}
MPRF:
f4 [Arg_0+1-Arg_1 ]
Analysing control-flow refined program
Found invariant 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f4___1
Found invariant 2<=Arg_2 && 2<=Arg_1+Arg_2 && 2+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f4___2
Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location f4
MPRF for transition 36:n_f4___1(Arg_0,Arg_1,Arg_2) -> n_f4___2(Arg_0+1,0,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 && 2+Arg_0<=Arg_2 && 0<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
n_f4___2 [Arg_2-Arg_0 ]
n_f4___1 [Arg_2-Arg_0 ]
MPRF for transition 37:n_f4___2(Arg_0,Arg_1,Arg_2) -> n_f4___1(Arg_0,Arg_1+1,Arg_2):|:2<=Arg_2 && 2<=Arg_1+Arg_2 && 2+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 2+Arg_1<=Arg_2 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
n_f4___2 [Arg_2-Arg_0 ]
n_f4___1 [Arg_2-Arg_0-1 ]
MPRF for transition 35:n_f4___1(Arg_0,Arg_1,Arg_2) -> n_f4___1(Arg_0,Arg_1+1,Arg_2):|:2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 1<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 of depth 1:
new bound:
Arg_2*Arg_2+5*Arg_2+4 {O(n^2)}
MPRF:
n_f4___1 [Arg_0+1-Arg_1 ]
n_f4___2 [0 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
2: f0->f4: 1 {O(1)}
0: f4->f4: Arg_2*Arg_2+Arg_2 {O(n^2)}
1: f4->f4: Arg_2 {O(n)}
Costbounds
Overall costbound: Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
2: f0->f4: 1 {O(1)}
0: f4->f4: Arg_2*Arg_2+Arg_2 {O(n^2)}
1: f4->f4: Arg_2 {O(n)}
Sizebounds
2: f0->f4, Arg_0: 0 {O(1)}
2: f0->f4, Arg_1: 0 {O(1)}
2: f0->f4, Arg_2: Arg_2 {O(n)}
0: f4->f4, Arg_0: Arg_2 {O(n)}
0: f4->f4, Arg_1: Arg_2*Arg_2+Arg_2 {O(n^2)}
0: f4->f4, Arg_2: Arg_2 {O(n)}
1: f4->f4, Arg_0: Arg_2 {O(n)}
1: f4->f4, Arg_1: 0 {O(1)}
1: f4->f4, Arg_2: Arg_2 {O(n)}