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, Arg_18, Arg_19
Temp_Vars: A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, U, V, W, X, Y, Z
Locations: f0, f101, f14, f57, f6
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,Arg_18,Arg_19) -> f6(0,0,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_18,Arg_19)
2:f14(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,Arg_18,Arg_19) -> f14(Arg_0,Arg_1,Arg_2-1,U+V,W,X+Y,Z,A1+B1,C1,D1+E1,F1,U+V+D1+E1,U+V-D1-E1,X+Y+A1+B1,X+Y-A1-B1,G1,H1,I1+J1,K1+J1,J1):|:0<=Arg_2
5:f14(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,Arg_18,Arg_19) -> f57(Arg_0,Arg_1,7,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_18,Arg_19):|:Arg_2+1<=0
4:f57(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,Arg_18,Arg_19) -> f101(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,Arg_18,Arg_19):|:Arg_2+1<=0
3:f57(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,Arg_18,Arg_19) -> f57(Arg_0,Arg_1,Arg_2-1,U+V,W,X+Y,Z,A1+B1,C1,D1+E1,F1,U+V+D1+E1,U+V-D1-E1,X+Y+A1+B1,X+Y-A1-B1,G1,H1,I1+J1,K1+J1,J1):|:0<=Arg_2
6:f6(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,Arg_18,Arg_19) -> f14(Arg_0,Arg_1,7,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_18,Arg_19):|:64<=Arg_1
1:f6(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,Arg_18,Arg_19) -> f6(U,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,Arg_18,Arg_19):|:Arg_1<=63

Preprocessing

Eliminate variables {A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,U,V,W,X,Y,Z,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,Arg_18,Arg_19} that do not contribute to the problem

Found invariant Arg_1<=64 && 0<=Arg_1 for location f6

Found invariant Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 for location f57

Found invariant Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 for location f14

Found invariant 1+Arg_2<=0 && 65+Arg_2<=Arg_1 && Arg_1+Arg_2<=63 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 for location f101

Problem after Preprocessing

Start: f0
Program_Vars: Arg_1, Arg_2
Temp_Vars:
Locations: f0, f101, f14, f57, f6
Transitions:
17:f0(Arg_1,Arg_2) -> f6(0,Arg_2)
18:f14(Arg_1,Arg_2) -> f14(Arg_1,Arg_2-1):|:Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 && 0<=Arg_2
19:f14(Arg_1,Arg_2) -> f57(Arg_1,7):|:Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 && Arg_2+1<=0
21:f57(Arg_1,Arg_2) -> f101(Arg_1,Arg_2):|:Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 && Arg_2+1<=0
20:f57(Arg_1,Arg_2) -> f57(Arg_1,Arg_2-1):|:Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 && 0<=Arg_2
23:f6(Arg_1,Arg_2) -> f14(Arg_1,7):|:Arg_1<=64 && 0<=Arg_1 && 64<=Arg_1
22:f6(Arg_1,Arg_2) -> f6(Arg_1+1,Arg_2):|:Arg_1<=64 && 0<=Arg_1 && Arg_1<=63

MPRF for transition 22:f6(Arg_1,Arg_2) -> f6(Arg_1+1,Arg_2):|:Arg_1<=64 && 0<=Arg_1 && Arg_1<=63 of depth 1:

new bound:

64 {O(1)}

MPRF:

f6 [64-Arg_1 ]

MPRF for transition 18:f14(Arg_1,Arg_2) -> f14(Arg_1,Arg_2-1):|:Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 && 0<=Arg_2 of depth 1:

new bound:

8 {O(1)}

MPRF:

f14 [Arg_2+1 ]

MPRF for transition 20:f57(Arg_1,Arg_2) -> f57(Arg_1,Arg_2-1):|:Arg_2<=7 && 57+Arg_2<=Arg_1 && Arg_1+Arg_2<=71 && 0<=1+Arg_2 && 63<=Arg_1+Arg_2 && Arg_1<=65+Arg_2 && Arg_1<=64 && 64<=Arg_1 && 0<=Arg_2 of depth 1:

new bound:

8 {O(1)}

MPRF:

f57 [Arg_2+1 ]

All Bounds

Timebounds

Overall timebound:84 {O(1)}
17: f0->f6: 1 {O(1)}
18: f14->f14: 8 {O(1)}
19: f14->f57: 1 {O(1)}
20: f57->f57: 8 {O(1)}
21: f57->f101: 1 {O(1)}
22: f6->f6: 64 {O(1)}
23: f6->f14: 1 {O(1)}

Costbounds

Overall costbound: 84 {O(1)}
17: f0->f6: 1 {O(1)}
18: f14->f14: 8 {O(1)}
19: f14->f57: 1 {O(1)}
20: f57->f57: 8 {O(1)}
21: f57->f101: 1 {O(1)}
22: f6->f6: 64 {O(1)}
23: f6->f14: 1 {O(1)}

Sizebounds

17: f0->f6, Arg_1: 0 {O(1)}
17: f0->f6, Arg_2: Arg_2 {O(n)}
18: f14->f14, Arg_1: 64 {O(1)}
18: f14->f14, Arg_2: 6 {O(1)}
19: f14->f57, Arg_1: 64 {O(1)}
19: f14->f57, Arg_2: 7 {O(1)}
20: f57->f57, Arg_1: 64 {O(1)}
20: f57->f57, Arg_2: 6 {O(1)}
21: f57->f101, Arg_1: 64 {O(1)}
21: f57->f101, Arg_2: 1 {O(1)}
22: f6->f6, Arg_1: 64 {O(1)}
22: f6->f6, Arg_2: Arg_2 {O(n)}
23: f6->f14, Arg_1: 64 {O(1)}
23: f6->f14, Arg_2: 7 {O(1)}