Initial Problem

Start: f23
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, Arg_20, Arg_21, Arg_22, Arg_23, Arg_24, Arg_25, Arg_26
Temp_Vars: B1, C1, D1, E1, F1, G1, H1, I1, J1
Locations: f2, f23, f8
Transitions:
2:f2(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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,B1,Arg_7-1,1+Arg_8,1+Arg_8,Arg_7-1,C1,D1,Arg_7-1,Arg_14,Arg_15,Arg_16,Arg_17,Arg_18,Arg_19,Arg_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26):|:Arg_6+1<=Arg_5 && 1<=Arg_7 && 0<=Arg_8
3:f2(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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,B1,Arg_7-1,1+Arg_8,1+Arg_8,Arg_7-1,C1,D1,Arg_7-1,Arg_14,Arg_15,Arg_16,Arg_17,Arg_18,Arg_19,Arg_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26):|:Arg_5+1<=Arg_6 && 1<=Arg_7 && 0<=Arg_8
6:f2(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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f8(Arg_0,F1,C1,C1,C1,Arg_6,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,B1,Arg_18,Arg_19,Arg_20,D1,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26):|:C1+1<=Arg_0 && 1<=Arg_7 && 0<=Arg_8 && Arg_6<=Arg_5 && Arg_5<=Arg_6
7:f2(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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f8(Arg_0,F1,C1,C1,C1,Arg_6,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,B1,Arg_18,Arg_19,Arg_20,D1,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26):|:Arg_0+1<=C1 && 1<=Arg_7 && 0<=Arg_8 && Arg_6<=Arg_5 && Arg_5<=Arg_6
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,Arg_18,Arg_19,Arg_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,B1,2,1,1,2,Arg_11,Arg_12,Arg_13,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0):|:E1+1<=Arg_5
5: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,Arg_18,Arg_19,Arg_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,B1,2,1,1,2,Arg_11,Arg_12,Arg_13,2,C1,D1,F1,G1,G1,G1,G1,H1,I1,2,J1,0):|:Arg_5+1<=E1
0:f8(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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f8(Arg_0,Arg_1,Arg_2,Arg_2,Arg_2,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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26):|:Arg_2+1<=Arg_0
1:f8(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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26) -> f8(Arg_0,Arg_1,Arg_2,Arg_2,Arg_2,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_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26):|:Arg_0+1<=Arg_2

Preprocessing

Eliminate variables {D1,F1,G1,H1,I1,J1,Arg_1,Arg_3,Arg_4,Arg_9,Arg_10,Arg_11,Arg_12,Arg_13,Arg_14,Arg_15,Arg_16,Arg_17,Arg_18,Arg_19,Arg_20,Arg_21,Arg_22,Arg_23,Arg_24,Arg_25,Arg_26} that do not contribute to the problem

Found invariant Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 for location f2

Found invariant Arg_8<=2 && Arg_8<=1+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 1<=Arg_7 && Arg_6<=Arg_5 && Arg_5<=Arg_6 for location f8

Problem after Preprocessing

Start: f23
Program_Vars: Arg_0, Arg_2, Arg_5, Arg_6, Arg_7, Arg_8
Temp_Vars: B1, C1, E1
Locations: f2, f23, f8
Transitions:
20:f2(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f2(Arg_0,Arg_2,Arg_5,B1,Arg_7-1,1+Arg_8):|:Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 && Arg_6+1<=Arg_5 && 1<=Arg_7 && 0<=Arg_8
21:f2(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f2(Arg_0,Arg_2,Arg_5,B1,Arg_7-1,1+Arg_8):|:Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 && Arg_5+1<=Arg_6 && 1<=Arg_7 && 0<=Arg_8
22:f2(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f8(Arg_0,C1,Arg_6,Arg_6,Arg_7,Arg_8):|:Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 && C1+1<=Arg_0 && 1<=Arg_7 && 0<=Arg_8 && Arg_6<=Arg_5 && Arg_5<=Arg_6
23:f2(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f8(Arg_0,C1,Arg_6,Arg_6,Arg_7,Arg_8):|:Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 && Arg_0+1<=C1 && 1<=Arg_7 && 0<=Arg_8 && Arg_6<=Arg_5 && Arg_5<=Arg_6
24:f23(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f2(Arg_0,Arg_2,Arg_5,B1,2,1):|:E1+1<=Arg_5
25:f23(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f2(Arg_0,Arg_2,Arg_5,B1,2,1):|:Arg_5+1<=E1
26:f8(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f8(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8):|:Arg_8<=2 && Arg_8<=1+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 1<=Arg_7 && Arg_6<=Arg_5 && Arg_5<=Arg_6 && Arg_2+1<=Arg_0
27:f8(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f8(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8):|:Arg_8<=2 && Arg_8<=1+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 1<=Arg_7 && Arg_6<=Arg_5 && Arg_5<=Arg_6 && Arg_0+1<=Arg_2

MPRF for transition 20:f2(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f2(Arg_0,Arg_2,Arg_5,B1,Arg_7-1,1+Arg_8):|:Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 && Arg_6+1<=Arg_5 && 1<=Arg_7 && 0<=Arg_8 of depth 1:

new bound:

6 {O(1)}

MPRF:

f2 [Arg_7+1 ]

MPRF for transition 21:f2(Arg_0,Arg_2,Arg_5,Arg_6,Arg_7,Arg_8) -> f2(Arg_0,Arg_2,Arg_5,B1,Arg_7-1,1+Arg_8):|:Arg_8<=3 && Arg_8<=3+Arg_7 && Arg_7+Arg_8<=3 && 1<=Arg_8 && 3<=Arg_7+Arg_8 && Arg_7<=1+Arg_8 && Arg_7<=2 && 0<=Arg_7 && Arg_5+1<=Arg_6 && 1<=Arg_7 && 0<=Arg_8 of depth 1:

new bound:

6 {O(1)}

MPRF:

f2 [Arg_7+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
20: f2->f2: 6 {O(1)}
21: f2->f2: 6 {O(1)}
22: f2->f8: 1 {O(1)}
23: f2->f8: 1 {O(1)}
24: f23->f2: 1 {O(1)}
25: f23->f2: 1 {O(1)}
26: f8->f8: inf {Infinity}
27: f8->f8: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
20: f2->f2: 6 {O(1)}
21: f2->f2: 6 {O(1)}
22: f2->f8: 1 {O(1)}
23: f2->f8: 1 {O(1)}
24: f23->f2: 1 {O(1)}
25: f23->f2: 1 {O(1)}
26: f8->f8: inf {Infinity}
27: f8->f8: inf {Infinity}

Sizebounds

20: f2->f2, Arg_0: 4*Arg_0 {O(n)}
20: f2->f2, Arg_2: 4*Arg_2 {O(n)}
20: f2->f2, Arg_5: 4*Arg_5 {O(n)}
20: f2->f2, Arg_7: 1 {O(1)}
20: f2->f2, Arg_8: 3 {O(1)}
21: f2->f2, Arg_0: 4*Arg_0 {O(n)}
21: f2->f2, Arg_2: 4*Arg_2 {O(n)}
21: f2->f2, Arg_5: 4*Arg_5 {O(n)}
21: f2->f2, Arg_7: 1 {O(1)}
21: f2->f2, Arg_8: 3 {O(1)}
22: f2->f8, Arg_0: 10*Arg_0 {O(n)}
22: f2->f8, Arg_5: 10*Arg_5 {O(n)}
22: f2->f8, Arg_7: 2 {O(1)}
22: f2->f8, Arg_8: 2 {O(1)}
23: f2->f8, Arg_0: 10*Arg_0 {O(n)}
23: f2->f8, Arg_5: 10*Arg_5 {O(n)}
23: f2->f8, Arg_7: 2 {O(1)}
23: f2->f8, Arg_8: 2 {O(1)}
24: f23->f2, Arg_0: Arg_0 {O(n)}
24: f23->f2, Arg_2: Arg_2 {O(n)}
24: f23->f2, Arg_5: Arg_5 {O(n)}
24: f23->f2, Arg_7: 2 {O(1)}
24: f23->f2, Arg_8: 1 {O(1)}
25: f23->f2, Arg_0: Arg_0 {O(n)}
25: f23->f2, Arg_2: Arg_2 {O(n)}
25: f23->f2, Arg_5: Arg_5 {O(n)}
25: f23->f2, Arg_7: 2 {O(1)}
25: f23->f2, Arg_8: 1 {O(1)}
26: f8->f8, Arg_0: 10*Arg_0 {O(n)}
26: f8->f8, Arg_5: 10*Arg_5 {O(n)}
26: f8->f8, Arg_7: 2 {O(1)}
26: f8->f8, Arg_8: 2 {O(1)}
27: f8->f8, Arg_0: 10*Arg_0 {O(n)}
27: f8->f8, Arg_5: 10*Arg_5 {O(n)}
27: f8->f8, Arg_7: 2 {O(1)}
27: f8->f8, Arg_8: 2 {O(1)}