Initial Problem
Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: f0, f16, f20, f4, f8
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3) -> f4(0,Arg_1,Arg_2,Arg_3)
6:f16(Arg_0,Arg_1,Arg_2,Arg_3) -> f4(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=0
7:f16(Arg_0,Arg_1,Arg_2,Arg_3) -> f4(Arg_0-1,Arg_1,Arg_2,Arg_3):|:1<=Arg_2
8:f4(Arg_0,Arg_1,Arg_2,Arg_3) -> f20(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_0
1:f4(Arg_0,Arg_1,Arg_2,Arg_3) -> f8(Arg_0+1,Arg_1,0,Arg_3):|:Arg_0+1<=Arg_1
2:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f16(Arg_0,Arg_1,Arg_2,0):|:Arg_0+1<=Arg_1
3:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f16(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<=Arg_0
4:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f8(Arg_0+1,Arg_1,Arg_2+1,E):|:Arg_0+1<=Arg_1 && E+1<=0
5:f8(Arg_0,Arg_1,Arg_2,Arg_3) -> f8(Arg_0+1,Arg_1,Arg_2+1,E):|:Arg_0+1<=Arg_1 && 1<=E
Preprocessing
Eliminate variables {Arg_3} that do not contribute to the problem
Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location f16
Found invariant Arg_1<=Arg_0 && 0<=Arg_0 for location f20
Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location f8
Found invariant 0<=Arg_0 for location f4
Problem after Preprocessing
Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: E
Locations: f0, f16, f20, f4, f8
Transitions:
19:f0(Arg_0,Arg_1,Arg_2) -> f4(0,Arg_1,Arg_2)
20:f16(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=0
21:f16(Arg_0,Arg_1,Arg_2) -> f4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_2
23:f4(Arg_0,Arg_1,Arg_2) -> f20(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_1<=Arg_0
22:f4(Arg_0,Arg_1,Arg_2) -> f8(Arg_0+1,Arg_1,0):|:0<=Arg_0 && Arg_0+1<=Arg_1
24:f8(Arg_0,Arg_1,Arg_2) -> f16(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_1
25:f8(Arg_0,Arg_1,Arg_2) -> f16(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0
26:f8(Arg_0,Arg_1,Arg_2) -> f8(Arg_0+1,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_1 && E+1<=0
27:f8(Arg_0,Arg_1,Arg_2) -> f8(Arg_0+1,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_1 && 1<=E
MPRF for transition 20:f16(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_2<=0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0 ]
f16 [Arg_1+1-Arg_0 ]
f8 [Arg_1+1-Arg_0 ]
MPRF for transition 21:f16(Arg_0,Arg_1,Arg_2) -> f4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_2 of depth 1:
new bound:
Arg_1+1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0-1 ]
f16 [Arg_1+Arg_2-Arg_0 ]
f8 [Arg_1+Arg_2-Arg_0 ]
MPRF for transition 22:f4(Arg_0,Arg_1,Arg_2) -> f8(Arg_0+1,Arg_1,0):|:0<=Arg_0 && Arg_0+1<=Arg_1 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0 ]
f16 [Arg_1+Arg_2-Arg_0 ]
f8 [Arg_1+Arg_2-Arg_0 ]
MPRF for transition 24:f8(Arg_0,Arg_1,Arg_2) -> f16(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_1 of depth 1:
new bound:
Arg_1+1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0-1 ]
f16 [Arg_1+Arg_2-Arg_0-1 ]
f8 [Arg_1+Arg_2-Arg_0 ]
MPRF for transition 25:f8(Arg_0,Arg_1,Arg_2) -> f16(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0 ]
f16 [Arg_1+Arg_2-Arg_0 ]
f8 [Arg_1+Arg_2+1-Arg_0 ]
MPRF for transition 26:f8(Arg_0,Arg_1,Arg_2) -> f8(Arg_0+1,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_1 && E+1<=0 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0 ]
f16 [Arg_1+1-Arg_0 ]
f8 [Arg_1+1-Arg_0 ]
MPRF for transition 27:f8(Arg_0,Arg_1,Arg_2) -> f8(Arg_0+1,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0+1<=Arg_1 && 1<=E of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
f4 [Arg_1-Arg_0 ]
f16 [Arg_1+1-Arg_0 ]
f8 [Arg_1+1-Arg_0 ]
All Bounds
Timebounds
Overall timebound:7*Arg_1+4 {O(n)}
19: f0->f4: 1 {O(1)}
20: f16->f4: Arg_1 {O(n)}
21: f16->f4: Arg_1+1 {O(n)}
22: f4->f8: Arg_1 {O(n)}
23: f4->f20: 1 {O(1)}
24: f8->f16: Arg_1+1 {O(n)}
25: f8->f16: Arg_1 {O(n)}
26: f8->f8: Arg_1 {O(n)}
27: f8->f8: Arg_1 {O(n)}
Costbounds
Overall costbound: 7*Arg_1+4 {O(n)}
19: f0->f4: 1 {O(1)}
20: f16->f4: Arg_1 {O(n)}
21: f16->f4: Arg_1+1 {O(n)}
22: f4->f8: Arg_1 {O(n)}
23: f4->f20: 1 {O(1)}
24: f8->f16: Arg_1+1 {O(n)}
25: f8->f16: Arg_1 {O(n)}
26: f8->f8: Arg_1 {O(n)}
27: f8->f8: Arg_1 {O(n)}
Sizebounds
19: f0->f4, Arg_0: 0 {O(1)}
19: f0->f4, Arg_1: Arg_1 {O(n)}
19: f0->f4, Arg_2: Arg_2 {O(n)}
20: f16->f4, Arg_0: 3*Arg_1 {O(n)}
20: f16->f4, Arg_1: Arg_1 {O(n)}
20: f16->f4, Arg_2: 0 {O(1)}
21: f16->f4, Arg_0: 3*Arg_1 {O(n)}
21: f16->f4, Arg_1: Arg_1 {O(n)}
21: f16->f4, Arg_2: 8*Arg_1 {O(n)}
22: f4->f8, Arg_0: 3*Arg_1 {O(n)}
22: f4->f8, Arg_1: Arg_1 {O(n)}
22: f4->f8, Arg_2: 0 {O(1)}
23: f4->f20, Arg_0: 3*Arg_1 {O(n)}
23: f4->f20, Arg_1: 2*Arg_1 {O(n)}
23: f4->f20, Arg_2: Arg_2 {O(n)}
24: f8->f16, Arg_0: 3*Arg_1 {O(n)}
24: f8->f16, Arg_1: Arg_1 {O(n)}
24: f8->f16, Arg_2: 4*Arg_1 {O(n)}
25: f8->f16, Arg_0: 3*Arg_1 {O(n)}
25: f8->f16, Arg_1: Arg_1 {O(n)}
25: f8->f16, Arg_2: 4*Arg_1 {O(n)}
26: f8->f8, Arg_0: 3*Arg_1 {O(n)}
26: f8->f8, Arg_1: Arg_1 {O(n)}
26: f8->f8, Arg_2: 2*Arg_1 {O(n)}
27: f8->f8, Arg_0: 3*Arg_1 {O(n)}
27: f8->f8, Arg_1: Arg_1 {O(n)}
27: f8->f8, Arg_2: 2*Arg_1 {O(n)}