Initial Problem
Start: start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7
Temp_Vars: I, J, K, L
Locations: f1, f19, f2, f27, f34, f36, f43, f49, f8, start
Transitions:
3:f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,J):|:Arg_4<=Arg_0
17:f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
21:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=Arg_1
0:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f8(Arg_0,Arg_1,0,Arg_1,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_1+1<=Arg_0
4:f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,J):|:Arg_4<=Arg_0
16:f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
12:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f2(Arg_0,Arg_1+1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_2<=0 && 0<=Arg_2
5:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_2+1<=0
6:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1<=Arg_2
15:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f2(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_3
11:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f36(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5,Arg_6,0):|:Arg_3<=Arg_0
7:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,J):|:I+1<=0 && Arg_3<=Arg_0 && K*Arg_2<=I && I+1<=K*Arg_2+K && J<=K && L*Arg_2<=I && I+1<=L*Arg_2+L && L<=J
8:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,J):|:1<=I && Arg_3<=Arg_0 && K*Arg_2<=I && I+1<=K*Arg_2+K && J<=K && L*Arg_2<=I && I+1<=L*Arg_2+L && L<=J
9:f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,Arg_7):|:Arg_4<=Arg_0
14:f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
13:f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f36(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
10:f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,Arg_7):|:Arg_4<=Arg_0
19:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_3+1<=Arg_1 && 1+Arg_0<=Arg_4
20:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_1<=Arg_3 && 1+Arg_0<=Arg_4
18:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f34(Arg_0,Arg_1,Arg_2,Arg_1,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4 && Arg_1<=Arg_3 && Arg_3<=Arg_1
1:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,J,I,Arg_7):|:Arg_4<=Arg_0 && J<=I
2:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f8(Arg_0,Arg_1,J,Arg_4,Arg_4+1,I,K,Arg_7):|:Arg_4<=Arg_0 && 1+K<=I
22:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)
Preprocessing
Cut unsatisfiable transition 3: f19->f19
Cut unsatisfiable transition 4: f27->f27
Cut unsatisfiable transition 10: f49->f49
Eliminate variables {Arg_5,Arg_6,Arg_7} that do not contribute to the problem
Found invariant 1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f49
Found invariant 1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f19
Found invariant Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 for location f36
Found invariant 1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f27
Found invariant Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f8
Found invariant 1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f43
Found invariant Arg_0<=Arg_1 for location f1
Found invariant 1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f34
Cut unsatisfiable transition 63: f43->f43
Problem after Preprocessing
Start: start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: I, J, K, L
Locations: f1, f19, f2, f27, f34, f36, f43, f49, f8, start
Transitions:
52:f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4
54:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_1
53:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f8(Arg_0,Arg_1,0,Arg_1,Arg_4):|:Arg_1+1<=Arg_0
55:f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4
58:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f2(Arg_0,Arg_1+1,0,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=0 && 0<=Arg_2
56:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2+1<=0
57:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_2
62:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f2(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_3
61:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_0
59:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && I+1<=0 && Arg_3<=Arg_0 && K*Arg_2<=I && I+1<=K*Arg_2+K && J<=K && L*Arg_2<=I && I+1<=L*Arg_2+L && L<=J
60:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && 1<=I && Arg_3<=Arg_0 && K*Arg_2<=I && I+1<=K*Arg_2+K && J<=K && L*Arg_2<=I && I+1<=L*Arg_2+L && L<=J
64:f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4
65:f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4
69:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3+1<=Arg_1 && 1+Arg_0<=Arg_4
70:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_3 && 1+Arg_0<=Arg_4
68:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f34(Arg_0,Arg_1,Arg_2,Arg_1,Arg_4):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4 && Arg_1<=Arg_3 && Arg_3<=Arg_1
66:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_4<=Arg_0 && J<=I
67:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f8(Arg_0,Arg_1,J,Arg_4,Arg_4+1):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_4<=Arg_0 && 1+K<=I
71:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
MPRF for transition 52:f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4 of depth 1:
new bound:
Arg_0+Arg_1+1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0+1-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f49 [Arg_0-Arg_1 ]
f36 [Arg_0-Arg_1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0+1-Arg_1 ]
f19 [Arg_0+1-Arg_1 ]
MPRF for transition 53:f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f8(Arg_0,Arg_1,0,Arg_1,Arg_4):|:Arg_1+1<=Arg_0 of depth 1:
new bound:
Arg_0+Arg_1+1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0+1-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f49 [Arg_0-Arg_1 ]
f36 [Arg_0-Arg_1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 55:f27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f49 [Arg_0-Arg_1-1 ]
f36 [Arg_0-Arg_1-1 ]
f34 [Arg_0-Arg_1-1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 56:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2+1<=0 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f49 [Arg_0-Arg_1-1 ]
f36 [Arg_0-Arg_1-1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 57:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_2 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f49 [Arg_0-Arg_1-1 ]
f36 [Arg_0-Arg_1-1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 58:f34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f2(Arg_0,Arg_1+1,0,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=0 && 0<=Arg_2 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f49 [Arg_0-Arg_1 ]
f36 [Arg_0-Arg_1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 62:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f2(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_3 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f49 [Arg_0-Arg_1 ]
f36 [Arg_0-Arg_1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 66:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_4<=Arg_0 && J<=I of depth 1:
new bound:
Arg_0+Arg_4+1 {O(n)}
MPRF:
f27 [Arg_0+1-Arg_4 ]
f2 [Arg_0+1-Arg_4 ]
f43 [Arg_0+1-Arg_4 ]
f49 [Arg_0+1-Arg_4 ]
f36 [Arg_0+1-Arg_4 ]
f34 [Arg_0+1-Arg_4 ]
f8 [Arg_0+1-Arg_4 ]
f19 [Arg_0+1-Arg_4 ]
MPRF for transition 67:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f8(Arg_0,Arg_1,J,Arg_4,Arg_4+1):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_4<=Arg_0 && 1+K<=I of depth 1:
new bound:
Arg_0+Arg_4+1 {O(n)}
MPRF:
f27 [Arg_0+1-Arg_4 ]
f2 [Arg_0+1-Arg_4 ]
f43 [Arg_0+1-Arg_4 ]
f49 [Arg_0+1-Arg_4 ]
f36 [Arg_0+1-Arg_4 ]
f34 [Arg_0+1-Arg_4 ]
f8 [Arg_0+1-Arg_4 ]
f19 [Arg_0+1-Arg_4 ]
MPRF for transition 68:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f34(Arg_0,Arg_1,Arg_2,Arg_1,Arg_4):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4 && Arg_1<=Arg_3 && Arg_3<=Arg_1 of depth 1:
new bound:
Arg_0+Arg_1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1-1 ]
f2 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f49 [Arg_0-Arg_1-1 ]
f36 [Arg_0-Arg_1-1 ]
f34 [Arg_0-Arg_1-1 ]
f8 [Arg_0-Arg_1 ]
f19 [Arg_0-Arg_1-1 ]
MPRF for transition 69:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_3+1<=Arg_1 && 1+Arg_0<=Arg_4 of depth 1:
new bound:
Arg_0+Arg_1+1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0+1-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f49 [Arg_0-Arg_1 ]
f36 [Arg_0-Arg_1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0+1-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 70:f8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f19(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_3 && 1+Arg_0<=Arg_4 of depth 1:
new bound:
Arg_0+Arg_1+1 {O(n)}
MPRF:
f27 [Arg_0-Arg_1 ]
f2 [Arg_0+1-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f49 [Arg_0-Arg_1 ]
f36 [Arg_0-Arg_1 ]
f34 [Arg_0-Arg_1 ]
f8 [Arg_0+1-Arg_1 ]
f19 [Arg_0-Arg_1 ]
MPRF for transition 59:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && I+1<=0 && Arg_3<=Arg_0 && K*Arg_2<=I && I+1<=K*Arg_2+K && J<=K && L*Arg_2<=I && I+1<=L*Arg_2+L && L<=J of depth 1:
new bound:
20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+41*Arg_1+57*Arg_0+24 {O(n^2)}
MPRF:
f19 [Arg_4+1-Arg_3 ]
f27 [Arg_4+1-Arg_3 ]
f34 [Arg_4+1-Arg_3 ]
f2 [0 ]
f43 [Arg_4-Arg_3 ]
f49 [Arg_4-Arg_3 ]
f36 [Arg_4+1-Arg_3 ]
f8 [0 ]
MPRF for transition 60:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && 1<=I && Arg_3<=Arg_0 && K*Arg_2<=I && I+1<=K*Arg_2+K && J<=K && L*Arg_2<=I && I+1<=L*Arg_2+L && L<=J of depth 1:
new bound:
20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+41*Arg_1+57*Arg_0+24 {O(n^2)}
MPRF:
f19 [Arg_4+1-Arg_3 ]
f27 [Arg_4+1-Arg_3 ]
f34 [Arg_4+1-Arg_3 ]
f2 [0 ]
f43 [Arg_4-Arg_3 ]
f49 [Arg_4-Arg_3 ]
f36 [Arg_4+1-Arg_3 ]
f8 [0 ]
MPRF for transition 61:f36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=1+Arg_0 && 1+Arg_1<=Arg_0 && Arg_3<=Arg_0 of depth 1:
new bound:
20*Arg_1*Arg_1+27*Arg_0*Arg_4+27*Arg_1*Arg_4+33*Arg_0*Arg_0+53*Arg_0*Arg_1+27*Arg_4+35*Arg_1+49*Arg_0+20 {O(n^2)}
MPRF:
f19 [Arg_0+1-Arg_3 ]
f27 [Arg_0+1-Arg_3 ]
f34 [Arg_0+1-Arg_3 ]
f2 [0 ]
f43 [Arg_0-Arg_3 ]
f49 [Arg_0-Arg_3 ]
f36 [Arg_0+1-Arg_3 ]
f8 [0 ]
MPRF for transition 64:f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4 of depth 1:
new bound:
27*Arg_0*Arg_4+27*Arg_1*Arg_4+38*Arg_1*Arg_1+51*Arg_0*Arg_0+89*Arg_0*Arg_1+28*Arg_4+47*Arg_1+62*Arg_0+18 {O(n^2)}
MPRF:
f19 [3*Arg_0-2*Arg_1-Arg_3 ]
f27 [3*Arg_0-2*Arg_1-Arg_3 ]
f34 [3*Arg_0-2*Arg_1-Arg_3-1 ]
f2 [3*Arg_0-2*Arg_1-Arg_4 ]
f43 [3*Arg_0-2*Arg_1-Arg_3-1 ]
f49 [3*Arg_0-2*Arg_1-Arg_3-2 ]
f36 [3*Arg_0-2*Arg_1-Arg_3-1 ]
f8 [3*Arg_0-2*Arg_1-Arg_4 ]
MPRF for transition 65:f49(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f36(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:1+Arg_3<=Arg_4 && 2+Arg_1<=Arg_4 && 1+Arg_0<=Arg_4 && Arg_3<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_4 of depth 1:
new bound:
20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+38*Arg_1+54*Arg_0+23 {O(n^2)}
MPRF:
f19 [Arg_4-Arg_3 ]
f27 [Arg_4-Arg_3 ]
f34 [Arg_4-Arg_3 ]
f2 [-1 ]
f43 [Arg_4-Arg_3 ]
f49 [Arg_4-Arg_3 ]
f36 [Arg_4-Arg_3 ]
f8 [-1 ]
All Bounds
Timebounds
Overall timebound:118*Arg_1*Arg_1+162*Arg_0*Arg_4+162*Arg_1*Arg_4+192*Arg_0*Arg_0+310*Arg_0*Arg_1+156*Arg_4+212*Arg_1+291*Arg_0+117 {O(n^2)}
52: f19->f27: Arg_0+Arg_1+1 {O(n)}
53: f2->f8: Arg_0+Arg_1+1 {O(n)}
54: f2->f1: 1 {O(1)}
55: f27->f34: Arg_0+Arg_1 {O(n)}
56: f34->f36: Arg_0+Arg_1 {O(n)}
57: f34->f36: Arg_0+Arg_1 {O(n)}
58: f34->f2: Arg_0+Arg_1 {O(n)}
59: f36->f43: 20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+41*Arg_1+57*Arg_0+24 {O(n^2)}
60: f36->f43: 20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+41*Arg_1+57*Arg_0+24 {O(n^2)}
61: f36->f36: 20*Arg_1*Arg_1+27*Arg_0*Arg_4+27*Arg_1*Arg_4+33*Arg_0*Arg_0+53*Arg_0*Arg_1+27*Arg_4+35*Arg_1+49*Arg_0+20 {O(n^2)}
62: f36->f2: Arg_0+Arg_1 {O(n)}
64: f43->f49: 27*Arg_0*Arg_4+27*Arg_1*Arg_4+38*Arg_1*Arg_1+51*Arg_0*Arg_0+89*Arg_0*Arg_1+28*Arg_4+47*Arg_1+62*Arg_0+18 {O(n^2)}
65: f49->f36: 20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+38*Arg_1+54*Arg_0+23 {O(n^2)}
66: f8->f8: Arg_0+Arg_4+1 {O(n)}
67: f8->f8: Arg_0+Arg_4+1 {O(n)}
68: f8->f34: Arg_0+Arg_1 {O(n)}
69: f8->f19: Arg_0+Arg_1+1 {O(n)}
70: f8->f19: Arg_0+Arg_1+1 {O(n)}
71: start->f2: 1 {O(1)}
Costbounds
Overall costbound: 118*Arg_1*Arg_1+162*Arg_0*Arg_4+162*Arg_1*Arg_4+192*Arg_0*Arg_0+310*Arg_0*Arg_1+156*Arg_4+212*Arg_1+291*Arg_0+117 {O(n^2)}
52: f19->f27: Arg_0+Arg_1+1 {O(n)}
53: f2->f8: Arg_0+Arg_1+1 {O(n)}
54: f2->f1: 1 {O(1)}
55: f27->f34: Arg_0+Arg_1 {O(n)}
56: f34->f36: Arg_0+Arg_1 {O(n)}
57: f34->f36: Arg_0+Arg_1 {O(n)}
58: f34->f2: Arg_0+Arg_1 {O(n)}
59: f36->f43: 20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+41*Arg_1+57*Arg_0+24 {O(n^2)}
60: f36->f43: 20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+41*Arg_1+57*Arg_0+24 {O(n^2)}
61: f36->f36: 20*Arg_1*Arg_1+27*Arg_0*Arg_4+27*Arg_1*Arg_4+33*Arg_0*Arg_0+53*Arg_0*Arg_1+27*Arg_4+35*Arg_1+49*Arg_0+20 {O(n^2)}
62: f36->f2: Arg_0+Arg_1 {O(n)}
64: f43->f49: 27*Arg_0*Arg_4+27*Arg_1*Arg_4+38*Arg_1*Arg_1+51*Arg_0*Arg_0+89*Arg_0*Arg_1+28*Arg_4+47*Arg_1+62*Arg_0+18 {O(n^2)}
65: f49->f36: 20*Arg_1*Arg_1+36*Arg_0*Arg_0+36*Arg_0*Arg_4+36*Arg_1*Arg_4+56*Arg_0*Arg_1+33*Arg_4+38*Arg_1+54*Arg_0+23 {O(n^2)}
66: f8->f8: Arg_0+Arg_4+1 {O(n)}
67: f8->f8: Arg_0+Arg_4+1 {O(n)}
68: f8->f34: Arg_0+Arg_1 {O(n)}
69: f8->f19: Arg_0+Arg_1+1 {O(n)}
70: f8->f19: Arg_0+Arg_1+1 {O(n)}
71: start->f2: 1 {O(1)}
Sizebounds
52: f19->f27, Arg_0: Arg_0 {O(n)}
52: f19->f27, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
52: f19->f27, Arg_3: 14*Arg_1+26*Arg_0+27*Arg_4+18 {O(n)}
52: f19->f27, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
53: f2->f8, Arg_0: Arg_0 {O(n)}
53: f2->f8, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
53: f2->f8, Arg_2: 0 {O(1)}
53: f2->f8, Arg_3: 4*Arg_0+7*Arg_1 {O(n)}
53: f2->f8, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
54: f2->f1, Arg_0: 3*Arg_0 {O(n)}
54: f2->f1, Arg_1: 4*Arg_0+7*Arg_1 {O(n)}
54: f2->f1, Arg_3: 126*Arg_0*Arg_4+126*Arg_1*Arg_4+138*Arg_0*Arg_0+218*Arg_0*Arg_1+80*Arg_1*Arg_1+406*Arg_1+471*Arg_4+596*Arg_0+Arg_3+320 {O(n^2)}
54: f2->f1, Arg_4: 4*Arg_0+7*Arg_4+4 {O(n)}
55: f27->f34, Arg_0: Arg_0 {O(n)}
55: f27->f34, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
55: f27->f34, Arg_3: 14*Arg_1+26*Arg_0+27*Arg_4+18 {O(n)}
55: f27->f34, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
56: f34->f36, Arg_0: Arg_0 {O(n)}
56: f34->f36, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
56: f34->f36, Arg_3: 20*Arg_1+27*Arg_4+30*Arg_0+18 {O(n)}
56: f34->f36, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
57: f34->f36, Arg_0: Arg_0 {O(n)}
57: f34->f36, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
57: f34->f36, Arg_3: 20*Arg_1+27*Arg_4+30*Arg_0+18 {O(n)}
57: f34->f36, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
58: f34->f2, Arg_0: Arg_0 {O(n)}
58: f34->f2, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
58: f34->f2, Arg_2: 0 {O(1)}
58: f34->f2, Arg_3: 20*Arg_1+27*Arg_4+30*Arg_0+18 {O(n)}
58: f34->f2, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
59: f36->f43, Arg_0: Arg_0 {O(n)}
59: f36->f43, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
59: f36->f43, Arg_3: 109*Arg_0*Arg_1+40*Arg_1*Arg_1+63*Arg_0*Arg_4+63*Arg_1*Arg_4+69*Arg_0*Arg_0+193*Arg_1+222*Arg_4+283*Arg_0+151 {O(n^2)}
59: f36->f43, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
60: f36->f43, Arg_0: Arg_0 {O(n)}
60: f36->f43, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
60: f36->f43, Arg_3: 109*Arg_0*Arg_1+40*Arg_1*Arg_1+63*Arg_0*Arg_4+63*Arg_1*Arg_4+69*Arg_0*Arg_0+193*Arg_1+222*Arg_4+283*Arg_0+151 {O(n^2)}
60: f36->f43, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
61: f36->f36, Arg_0: Arg_0 {O(n)}
61: f36->f36, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
61: f36->f36, Arg_3: 109*Arg_0*Arg_1+40*Arg_1*Arg_1+63*Arg_0*Arg_4+63*Arg_1*Arg_4+69*Arg_0*Arg_0+193*Arg_1+222*Arg_4+283*Arg_0+151 {O(n^2)}
61: f36->f36, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
62: f36->f2, Arg_0: Arg_0 {O(n)}
62: f36->f2, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
62: f36->f2, Arg_3: 126*Arg_0*Arg_4+126*Arg_1*Arg_4+138*Arg_0*Arg_0+218*Arg_0*Arg_1+80*Arg_1*Arg_1+386*Arg_1+444*Arg_4+566*Arg_0+302 {O(n^2)}
62: f36->f2, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
64: f43->f49, Arg_0: Arg_0 {O(n)}
64: f43->f49, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
64: f43->f49, Arg_3: 109*Arg_0*Arg_1+40*Arg_1*Arg_1+63*Arg_0*Arg_4+63*Arg_1*Arg_4+69*Arg_0*Arg_0+193*Arg_1+222*Arg_4+283*Arg_0+151 {O(n^2)}
64: f43->f49, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
65: f49->f36, Arg_0: Arg_0 {O(n)}
65: f49->f36, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
65: f49->f36, Arg_3: 109*Arg_0*Arg_1+40*Arg_1*Arg_1+63*Arg_0*Arg_4+63*Arg_1*Arg_4+69*Arg_0*Arg_0+193*Arg_1+222*Arg_4+283*Arg_0+151 {O(n^2)}
65: f49->f36, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
66: f8->f8, Arg_0: Arg_0 {O(n)}
66: f8->f8, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
66: f8->f8, Arg_3: 10*Arg_0+7*Arg_1+9*Arg_4+6 {O(n)}
66: f8->f8, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
67: f8->f8, Arg_0: Arg_0 {O(n)}
67: f8->f8, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
67: f8->f8, Arg_3: 6*Arg_0+9*Arg_4+6 {O(n)}
67: f8->f8, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
68: f8->f34, Arg_0: Arg_0 {O(n)}
68: f8->f34, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
68: f8->f34, Arg_3: 4*Arg_0+6*Arg_1 {O(n)}
68: f8->f34, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
69: f8->f19, Arg_0: Arg_0 {O(n)}
69: f8->f19, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
69: f8->f19, Arg_3: 10*Arg_0+7*Arg_1+9*Arg_4+6 {O(n)}
69: f8->f19, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
70: f8->f19, Arg_0: Arg_0 {O(n)}
70: f8->f19, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
70: f8->f19, Arg_3: 16*Arg_0+18*Arg_4+7*Arg_1+12 {O(n)}
70: f8->f19, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
71: start->f2, Arg_0: Arg_0 {O(n)}
71: start->f2, Arg_1: Arg_1 {O(n)}
71: start->f2, Arg_2: Arg_2 {O(n)}
71: start->f2, Arg_3: Arg_3 {O(n)}
71: start->f2, Arg_4: Arg_4 {O(n)}