Initial Problem
Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8, Arg_9, Arg_10, Arg_11, Arg_12, Arg_13, Arg_14, Arg_15, Arg_16, Arg_17
Temp_Vars: S, T, U, V
Locations: f0, f13, f17, f23, f33, f46, f60
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f13(1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_0<=1 && 1<=Arg_0
1:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f17(Arg_0,1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_0<=0
2:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f17(Arg_0,1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:2<=Arg_0
16:f17(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f13(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:1+Arg_0<=Arg_1
3:f17(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f23(Arg_0,Arg_1,Arg_1+1,S,T,1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_1<=Arg_0
4:f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f23(Arg_0,Arg_1,Arg_2,S,T,Arg_5+1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_5<=Arg_1
13:f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_4+1<=0 && 1+Arg_1<=Arg_5
14:f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:1<=Arg_4 && 1+Arg_1<=Arg_5
15:f23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f33(Arg_0,Arg_1,Arg_2,Arg_3,0,1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:1+Arg_1<=Arg_5 && Arg_4<=0 && 0<=Arg_4
10:f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f13(Arg_0,Arg_1,Arg_0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:1+Arg_1<=Arg_5 && Arg_0<=Arg_2 && Arg_2<=Arg_0
5:f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_5<=Arg_1
11:f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f46(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,1,S,T,U,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_2+1<=Arg_0 && 1+Arg_1<=Arg_5
12:f33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f46(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,1,S,T,U,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_5
6:f46(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f46(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1,S,T,U,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:Arg_5<=Arg_1
9:f46(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f60(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,1,Arg_6,Arg_7,Arg_8,S,Arg_1,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,T,U):|:1+Arg_1<=Arg_5
8:f60(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f17(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17):|:1+Arg_9<=Arg_5
7:f60(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17) -> f60(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10-1,S,T,U,V,Arg_10,Arg_16,Arg_17):|:Arg_5<=Arg_9
Preprocessing
Eliminate variables {U,V,Arg_3,Arg_6,Arg_7,Arg_8,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17} that do not contribute to the problem
Found invariant Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 for location f33
Found invariant Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 for location f23
Found invariant 1<=Arg_1 for location f17
Found invariant Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 for location f46
Found invariant 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 for location f60
Problem after Preprocessing
Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_4, Arg_5, Arg_9
Temp_Vars: S, T
Locations: f0, f13, f17, f23, f33, f46, f60
Transitions:
36:f0(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f13(1,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9):|:Arg_0<=1 && 1<=Arg_0
37:f0(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f17(Arg_0,1,Arg_2,Arg_4,Arg_5,Arg_9):|:Arg_0<=0
38:f0(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f17(Arg_0,1,Arg_2,Arg_4,Arg_5,Arg_9):|:2<=Arg_0
40:f17(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f13(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9):|:1<=Arg_1 && 1+Arg_0<=Arg_1
39:f17(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f23(Arg_0,Arg_1,Arg_1+1,T,1,Arg_9):|:1<=Arg_1 && Arg_1<=Arg_0
41:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f23(Arg_0,Arg_1,Arg_2,T,Arg_5+1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_1
42:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_4+1<=0 && 1+Arg_1<=Arg_5
43:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1<=Arg_4 && 1+Arg_1<=Arg_5
44:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,0,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_1<=Arg_5 && Arg_4<=0 && 0<=Arg_4
46:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f13(Arg_0,Arg_1,Arg_0,Arg_4,Arg_5,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_1<=Arg_5 && Arg_0<=Arg_2 && Arg_2<=Arg_0
45:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5+1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_1
47:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f46(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_2+1<=Arg_0 && 1+Arg_1<=Arg_5
48:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f46(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_5
49:f46(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f46(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5+1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_1
50:f46(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f60(Arg_0,Arg_1,Arg_2,Arg_4,1,S):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_1<=Arg_5
52:f60(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f17(Arg_0,Arg_1+1,Arg_2,Arg_4,Arg_5,Arg_9):|:1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_9<=Arg_5
51:f60(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f60(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5+1,Arg_9):|:1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_9
MPRF for transition 39:f17(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f23(Arg_0,Arg_1,Arg_1+1,T,1,Arg_9):|:1<=Arg_1 && Arg_1<=Arg_0 of depth 1:
new bound:
Arg_0+2 {O(n)}
MPRF:
f23 [Arg_0-Arg_1 ]
f33 [Arg_0-Arg_1 ]
f46 [Arg_0+1-Arg_2 ]
f60 [Arg_0-Arg_1 ]
f17 [Arg_0+1-Arg_1 ]
MPRF for transition 47:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f46(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_2+1<=Arg_0 && 1+Arg_1<=Arg_5 of depth 1:
new bound:
Arg_0+2 {O(n)}
MPRF:
f23 [Arg_0-Arg_1-1 ]
f33 [Arg_0-Arg_1-1 ]
f46 [Arg_0-Arg_1-2 ]
f60 [Arg_0-Arg_1-2 ]
f17 [Arg_0-Arg_1-1 ]
MPRF for transition 42:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_4+1<=0 && 1+Arg_1<=Arg_5 of depth 1:
new bound:
Arg_0+2 {O(n)}
MPRF:
f23 [1 ]
f33 [1-Arg_1 ]
f46 [-Arg_1 ]
f60 [-Arg_1 ]
f17 [-Arg_1 ]
MPRF for transition 43:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1<=Arg_4 && 1+Arg_1<=Arg_5 of depth 1:
new bound:
2*Arg_0+4 {O(n)}
MPRF:
f23 [2 ]
f33 [2-Arg_5 ]
f46 [-Arg_2 ]
f60 [-Arg_2 ]
f17 [-Arg_2 ]
MPRF for transition 44:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,0,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_1<=Arg_5 && Arg_4<=0 && 0<=Arg_4 of depth 1:
new bound:
2*Arg_0+4 {O(n)}
MPRF:
f23 [2 ]
f33 [2-Arg_2 ]
f46 [-Arg_2 ]
f60 [-Arg_2 ]
f17 [-Arg_2 ]
MPRF for transition 48:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f46(Arg_0,Arg_1,Arg_2,Arg_4,1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_5 of depth 1:
new bound:
2*Arg_0+4 {O(n)}
MPRF:
f23 [2 ]
f33 [2 ]
f46 [1 ]
f60 [0 ]
f17 [0 ]
MPRF for transition 50:f46(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f60(Arg_0,Arg_1,Arg_2,Arg_4,1,S):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_1<=Arg_5 of depth 1:
new bound:
2*Arg_0+4 {O(n)}
MPRF:
f23 [2 ]
f33 [2 ]
f46 [2 ]
f60 [Arg_2-Arg_1 ]
f17 [Arg_2-Arg_1 ]
MPRF for transition 52:f60(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f17(Arg_0,Arg_1+1,Arg_2,Arg_4,Arg_5,Arg_9):|:1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && 1+Arg_9<=Arg_5 of depth 1:
new bound:
3*Arg_0+6 {O(n)}
MPRF:
f23 [3 ]
f33 [Arg_1+4-Arg_2 ]
f46 [Arg_1+4-Arg_2 ]
f60 [3 ]
f17 [2 ]
MPRF for transition 41:f23(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f23(Arg_0,Arg_1,Arg_2,T,Arg_5+1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_1 of depth 1:
new bound:
12*Arg_0*Arg_0+46*Arg_0+43 {O(n^2)}
MPRF:
f17 [Arg_0+Arg_1 ]
f23 [2*Arg_1-Arg_5 ]
f33 [2*Arg_1-Arg_2 ]
f46 [3*Arg_1+1-2*Arg_2 ]
f60 [3*Arg_1-2*Arg_2 ]
MPRF for transition 45:f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f33(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5+1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_1 of depth 1:
new bound:
12*Arg_0*Arg_0+46*Arg_0+43 {O(n^2)}
MPRF:
f17 [Arg_0+Arg_1 ]
f23 [2*Arg_1 ]
f33 [2*Arg_1-Arg_5 ]
f46 [2*Arg_1-Arg_2 ]
f60 [2*Arg_1-Arg_2 ]
MPRF for transition 49:f46(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5,Arg_9) -> f46(Arg_0,Arg_1,Arg_2,Arg_4,Arg_5+1,Arg_9):|:Arg_5<=Arg_2 && Arg_5<=1+Arg_1 && 1<=Arg_5 && 3<=Arg_2+Arg_5 && 2<=Arg_1+Arg_5 && Arg_2<=1+Arg_1 && 2<=Arg_2 && 3<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_1 && Arg_5<=Arg_1 of depth 1:
new bound:
9*Arg_0*Arg_0+42*Arg_0+50 {O(n^2)}
MPRF:
f17 [Arg_1+1 ]
f23 [Arg_1+1 ]
f33 [Arg_2 ]
f46 [Arg_1+1-Arg_5 ]
f60 [Arg_1-Arg_2 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
36: f0->f13: 1 {O(1)}
37: f0->f17: 1 {O(1)}
38: f0->f17: 1 {O(1)}
39: f17->f23: Arg_0+2 {O(n)}
40: f17->f13: 1 {O(1)}
41: f23->f23: 12*Arg_0*Arg_0+46*Arg_0+43 {O(n^2)}
42: f23->f33: Arg_0+2 {O(n)}
43: f23->f33: 2*Arg_0+4 {O(n)}
44: f23->f33: 2*Arg_0+4 {O(n)}
45: f33->f33: 12*Arg_0*Arg_0+46*Arg_0+43 {O(n^2)}
46: f33->f13: 1 {O(1)}
47: f33->f46: Arg_0+2 {O(n)}
48: f33->f46: 2*Arg_0+4 {O(n)}
49: f46->f46: 9*Arg_0*Arg_0+42*Arg_0+50 {O(n^2)}
50: f46->f60: 2*Arg_0+4 {O(n)}
51: f60->f60: inf {Infinity}
52: f60->f17: 3*Arg_0+6 {O(n)}
Costbounds
Overall costbound: inf {Infinity}
36: f0->f13: 1 {O(1)}
37: f0->f17: 1 {O(1)}
38: f0->f17: 1 {O(1)}
39: f17->f23: Arg_0+2 {O(n)}
40: f17->f13: 1 {O(1)}
41: f23->f23: 12*Arg_0*Arg_0+46*Arg_0+43 {O(n^2)}
42: f23->f33: Arg_0+2 {O(n)}
43: f23->f33: 2*Arg_0+4 {O(n)}
44: f23->f33: 2*Arg_0+4 {O(n)}
45: f33->f33: 12*Arg_0*Arg_0+46*Arg_0+43 {O(n^2)}
46: f33->f13: 1 {O(1)}
47: f33->f46: Arg_0+2 {O(n)}
48: f33->f46: 2*Arg_0+4 {O(n)}
49: f46->f46: 9*Arg_0*Arg_0+42*Arg_0+50 {O(n^2)}
50: f46->f60: 2*Arg_0+4 {O(n)}
51: f60->f60: inf {Infinity}
52: f60->f17: 3*Arg_0+6 {O(n)}
Sizebounds
36: f0->f13, Arg_0: 1 {O(1)}
36: f0->f13, Arg_1: Arg_1 {O(n)}
36: f0->f13, Arg_2: Arg_2 {O(n)}
36: f0->f13, Arg_4: Arg_4 {O(n)}
36: f0->f13, Arg_5: Arg_5 {O(n)}
36: f0->f13, Arg_9: Arg_9 {O(n)}
37: f0->f17, Arg_0: Arg_0 {O(n)}
37: f0->f17, Arg_1: 1 {O(1)}
37: f0->f17, Arg_2: Arg_2 {O(n)}
37: f0->f17, Arg_4: Arg_4 {O(n)}
37: f0->f17, Arg_5: Arg_5 {O(n)}
37: f0->f17, Arg_9: Arg_9 {O(n)}
38: f0->f17, Arg_0: Arg_0 {O(n)}
38: f0->f17, Arg_1: 1 {O(1)}
38: f0->f17, Arg_2: Arg_2 {O(n)}
38: f0->f17, Arg_4: Arg_4 {O(n)}
38: f0->f17, Arg_5: Arg_5 {O(n)}
38: f0->f17, Arg_9: Arg_9 {O(n)}
39: f17->f23, Arg_0: Arg_0 {O(n)}
39: f17->f23, Arg_1: 3*Arg_0+7 {O(n)}
39: f17->f23, Arg_2: 3*Arg_0+10 {O(n)}
39: f17->f23, Arg_5: 1 {O(1)}
40: f17->f13, Arg_0: 2*Arg_0 {O(n)}
40: f17->f13, Arg_1: 3*Arg_0+8 {O(n)}
40: f17->f13, Arg_2: 36*Arg_0+Arg_2+120 {O(n)}
41: f23->f23, Arg_0: Arg_0 {O(n)}
41: f23->f23, Arg_1: 3*Arg_0+7 {O(n)}
41: f23->f23, Arg_2: 3*Arg_0+10 {O(n)}
41: f23->f23, Arg_5: 12*Arg_0*Arg_0+46*Arg_0+44 {O(n^2)}
42: f23->f33, Arg_0: Arg_0 {O(n)}
42: f23->f33, Arg_1: 3*Arg_0+7 {O(n)}
42: f23->f33, Arg_2: 3*Arg_0+10 {O(n)}
42: f23->f33, Arg_5: 1 {O(1)}
43: f23->f33, Arg_0: Arg_0 {O(n)}
43: f23->f33, Arg_1: 3*Arg_0+7 {O(n)}
43: f23->f33, Arg_2: 3*Arg_0+10 {O(n)}
43: f23->f33, Arg_5: 1 {O(1)}
44: f23->f33, Arg_0: Arg_0 {O(n)}
44: f23->f33, Arg_1: 3*Arg_0+7 {O(n)}
44: f23->f33, Arg_2: 3*Arg_0+10 {O(n)}
44: f23->f33, Arg_4: 0 {O(1)}
44: f23->f33, Arg_5: 1 {O(1)}
45: f33->f33, Arg_0: Arg_0 {O(n)}
45: f33->f33, Arg_1: 3*Arg_0+7 {O(n)}
45: f33->f33, Arg_2: 9*Arg_0+30 {O(n)}
45: f33->f33, Arg_5: 12*Arg_0*Arg_0+46*Arg_0+46 {O(n^2)}
46: f33->f13, Arg_0: Arg_0 {O(n)}
46: f33->f13, Arg_1: 3*Arg_0+7 {O(n)}
46: f33->f13, Arg_2: Arg_0 {O(n)}
46: f33->f13, Arg_5: 12*Arg_0*Arg_0+46*Arg_0+46 {O(n^2)}
47: f33->f46, Arg_0: Arg_0 {O(n)}
47: f33->f46, Arg_1: 3*Arg_0+7 {O(n)}
47: f33->f46, Arg_2: 9*Arg_0+30 {O(n)}
47: f33->f46, Arg_5: 1 {O(1)}
48: f33->f46, Arg_0: Arg_0 {O(n)}
48: f33->f46, Arg_1: 3*Arg_0+7 {O(n)}
48: f33->f46, Arg_2: 9*Arg_0+30 {O(n)}
48: f33->f46, Arg_5: 1 {O(1)}
49: f46->f46, Arg_0: Arg_0 {O(n)}
49: f46->f46, Arg_1: 3*Arg_0+7 {O(n)}
49: f46->f46, Arg_2: 18*Arg_0+60 {O(n)}
49: f46->f46, Arg_5: 9*Arg_0*Arg_0+42*Arg_0+52 {O(n^2)}
50: f46->f60, Arg_0: Arg_0 {O(n)}
50: f46->f60, Arg_1: 3*Arg_0+7 {O(n)}
50: f46->f60, Arg_2: 18*Arg_0+60 {O(n)}
50: f46->f60, Arg_5: 1 {O(1)}
51: f60->f60, Arg_0: Arg_0 {O(n)}
51: f60->f60, Arg_1: 3*Arg_0+7 {O(n)}
51: f60->f60, Arg_2: 18*Arg_0+60 {O(n)}
52: f60->f17, Arg_0: Arg_0 {O(n)}
52: f60->f17, Arg_1: 3*Arg_0+7 {O(n)}
52: f60->f17, Arg_2: 36*Arg_0+120 {O(n)}