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
Locations: f0, f12, f22, f29, f35, f37, f43, f48, f58, start
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f12(Arg_0,Arg_1,0,Arg_1,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_1+1<=Arg_0
21:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f58(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=Arg_1
1:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,J,I,Arg_7):|:Arg_4<=Arg_0 && J<=I
2:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f12(Arg_0,Arg_1,J,Arg_4,Arg_4+1,I,K,Arg_7):|:Arg_4<=Arg_0 && 1+K<=I
19:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f22(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:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f22(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:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f35(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
3:f22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,J):|:Arg_4<=Arg_0
17:f22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
4:f29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,J):|:Arg_4<=Arg_0
16:f29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
12:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f0(Arg_0,Arg_1+1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_2<=0 && 0<=Arg_2
5:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_2+1<=0
6:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1<=Arg_2
15:f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f0(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_3
11:f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f37(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5,Arg_6,0):|:Arg_3<=Arg_0
7:f37(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):|:Arg_3<=Arg_0 && I+1<=0
8:f37(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):|:Arg_3<=Arg_0 && 1<=I
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) -> f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
13:f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f37(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_0<=Arg_4
10:f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5,Arg_6,Arg_7):|:Arg_4<=Arg_0
22:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7)

Preprocessing

Cut unsatisfiable transition 3: f22->f22

Cut unsatisfiable transition 4: f29->f29

Cut unsatisfiable transition 10: f48->f48

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 f29

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 f48

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 f35

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 f37

Found invariant Arg_0<=Arg_1 for location f58

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_3<=Arg_0 && 1+Arg_1<=Arg_0 for location f12

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 f22

Cut unsatisfiable transition 68: f43->f43

Problem after Preprocessing

Start: start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: I, J, K
Locations: f0, f12, f22, f29, f35, f37, f43, f48, f58, start
Transitions:
52:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f12(Arg_0,Arg_1,0,Arg_1,Arg_4):|:Arg_1+1<=Arg_0
53:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f58(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=Arg_1
54:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f12(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
55:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f12(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
57:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f22(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
58:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f22(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
56:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f35(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
59:f22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f29(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
60:f29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f35(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
63:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f0(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
61:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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
62:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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
67:f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f0(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
66:f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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
64:f37(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 && Arg_3<=Arg_0 && I+1<=0
65:f37(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 && Arg_3<=Arg_0 && 1<=I
69:f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f48(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
70:f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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
71:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 52:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f12(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1 ]
f0 [Arg_0+1-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f48 [Arg_0-Arg_1 ]
f37 [Arg_0-Arg_1 ]

MPRF for transition 54:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f12(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:

f12 [Arg_0+1-Arg_4 ]
f22 [Arg_0+1-Arg_4 ]
f29 [Arg_0+1-Arg_4 ]
f35 [Arg_0+1-Arg_4 ]
f0 [Arg_0+1-Arg_4 ]
f43 [Arg_0+1-Arg_4 ]
f48 [Arg_0+1-Arg_4 ]
f37 [Arg_0+1-Arg_4 ]

MPRF for transition 55:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f12(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:

f12 [Arg_0+1-Arg_4 ]
f22 [Arg_0+1-Arg_4 ]
f29 [Arg_0+1-Arg_4 ]
f35 [Arg_0+1-Arg_4 ]
f0 [Arg_0+1-Arg_4 ]
f43 [Arg_0+1-Arg_4 ]
f48 [Arg_0+1-Arg_4 ]
f37 [Arg_0+1-Arg_4 ]

MPRF for transition 56:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f35(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+1 {O(n)}

MPRF:

f12 [Arg_0+1-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1 ]
f0 [Arg_0+1-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f48 [Arg_0-Arg_1 ]
f37 [Arg_0-Arg_1 ]

MPRF for transition 57:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f22(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 {O(n)}

MPRF:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1-1 ]
f29 [Arg_0-Arg_1-1 ]
f35 [Arg_0-Arg_1-1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f48 [Arg_0-Arg_1-1 ]
f37 [Arg_0-Arg_1-1 ]

MPRF for transition 58:f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f22(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 {O(n)}

MPRF:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1-1 ]
f29 [Arg_0-Arg_1-1 ]
f35 [Arg_0-Arg_1-1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f48 [Arg_0-Arg_1-1 ]
f37 [Arg_0-Arg_1-1 ]

MPRF for transition 59:f22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f29(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1-1 ]
f35 [Arg_0-Arg_1-1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f48 [Arg_0-Arg_1-1 ]
f37 [Arg_0-Arg_1-1 ]

MPRF for transition 60:f29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f35(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1-1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f48 [Arg_0-Arg_1-1 ]
f37 [Arg_0-Arg_1-1 ]

MPRF for transition 61:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f48 [Arg_0-Arg_1-1 ]
f37 [Arg_0-Arg_1-1 ]

MPRF for transition 62:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1-1 ]
f48 [Arg_0-Arg_1-1 ]
f37 [Arg_0-Arg_1-1 ]

MPRF for transition 63:f35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f0(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f48 [Arg_0-Arg_1 ]
f37 [Arg_0-Arg_1 ]

MPRF for transition 67:f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f0(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:

f12 [Arg_0-Arg_1 ]
f22 [Arg_0-Arg_1 ]
f29 [Arg_0-Arg_1 ]
f35 [Arg_0-Arg_1 ]
f0 [Arg_0-Arg_1 ]
f43 [Arg_0-Arg_1 ]
f48 [Arg_0-Arg_1 ]
f37 [Arg_0-Arg_1 ]

MPRF for transition 64:f37(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 && Arg_3<=Arg_0 && I+1<=0 of depth 1:

new bound:

116*Arg_0*Arg_1+46*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+70*Arg_0*Arg_0+42*Arg_0+42*Arg_1 {O(n^2)}

MPRF:

f12 [0 ]
f22 [0 ]
f29 [0 ]
f35 [0 ]
f0 [0 ]
f43 [Arg_0+Arg_4-Arg_1-Arg_3-2 ]
f48 [Arg_0+Arg_4-Arg_1-Arg_3-2 ]
f37 [Arg_0+Arg_4-Arg_1-Arg_3-1 ]

MPRF for transition 65:f37(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 && Arg_3<=Arg_0 && 1<=I of depth 1:

new bound:

102*Arg_0*Arg_1+40*Arg_1*Arg_1+54*Arg_0*Arg_4+54*Arg_1*Arg_4+62*Arg_0*Arg_0+38*Arg_0+38*Arg_1 {O(n^2)}

MPRF:

f12 [0 ]
f22 [0 ]
f29 [0 ]
f35 [0 ]
f0 [0 ]
f43 [Arg_0-Arg_3 ]
f48 [Arg_0-Arg_3 ]
f37 [Arg_0+1-Arg_3 ]

MPRF for transition 66:f37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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:

104*Arg_0*Arg_1+40*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+64*Arg_0*Arg_0+42*Arg_0+42*Arg_1 {O(n^2)}

MPRF:

f12 [0 ]
f22 [0 ]
f29 [0 ]
f35 [0 ]
f0 [0 ]
f43 [Arg_4-Arg_3 ]
f48 [Arg_4-Arg_3 ]
f37 [Arg_4+1-Arg_3 ]

MPRF for transition 69:f43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f48(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:

102*Arg_0*Arg_1+40*Arg_1*Arg_1+54*Arg_0*Arg_4+54*Arg_1*Arg_4+62*Arg_0*Arg_0+38*Arg_1+39*Arg_0+Arg_4 {O(n^2)}

MPRF:

f12 [Arg_0-Arg_4 ]
f22 [Arg_0-Arg_4 ]
f29 [Arg_0-Arg_4 ]
f35 [Arg_0-Arg_4 ]
f0 [Arg_0-Arg_4 ]
f43 [Arg_0+1-Arg_3 ]
f48 [Arg_0-Arg_3 ]
f37 [Arg_0+1-Arg_3 ]

MPRF for transition 70:f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f37(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:

104*Arg_0*Arg_1+40*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+64*Arg_0*Arg_0+40*Arg_0+40*Arg_1 {O(n^2)}

MPRF:

f12 [0 ]
f22 [0 ]
f29 [0 ]
f35 [0 ]
f0 [0 ]
f43 [Arg_4-Arg_3 ]
f48 [Arg_4-Arg_3 ]
f37 [Arg_4-Arg_3 ]

All Bounds

Timebounds

Overall timebound:206*Arg_1*Arg_1+288*Arg_0*Arg_4+288*Arg_1*Arg_4+322*Arg_0*Arg_0+528*Arg_0*Arg_1+210*Arg_1+213*Arg_0+3*Arg_4+6 {O(n^2)}
52: f0->f12: Arg_0+Arg_1+1 {O(n)}
53: f0->f58: 1 {O(1)}
54: f12->f12: Arg_0+Arg_4+1 {O(n)}
55: f12->f12: Arg_0+Arg_4+1 {O(n)}
56: f12->f35: Arg_0+Arg_1+1 {O(n)}
57: f12->f22: Arg_0+Arg_1 {O(n)}
58: f12->f22: Arg_0+Arg_1 {O(n)}
59: f22->f29: Arg_0+Arg_1 {O(n)}
60: f29->f35: Arg_0+Arg_1 {O(n)}
61: f35->f37: Arg_0+Arg_1 {O(n)}
62: f35->f37: Arg_0+Arg_1 {O(n)}
63: f35->f0: Arg_0+Arg_1 {O(n)}
64: f37->f43: 116*Arg_0*Arg_1+46*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+70*Arg_0*Arg_0+42*Arg_0+42*Arg_1 {O(n^2)}
65: f37->f43: 102*Arg_0*Arg_1+40*Arg_1*Arg_1+54*Arg_0*Arg_4+54*Arg_1*Arg_4+62*Arg_0*Arg_0+38*Arg_0+38*Arg_1 {O(n^2)}
66: f37->f37: 104*Arg_0*Arg_1+40*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+64*Arg_0*Arg_0+42*Arg_0+42*Arg_1 {O(n^2)}
67: f37->f0: Arg_0+Arg_1 {O(n)}
69: f43->f48: 102*Arg_0*Arg_1+40*Arg_1*Arg_1+54*Arg_0*Arg_4+54*Arg_1*Arg_4+62*Arg_0*Arg_0+38*Arg_1+39*Arg_0+Arg_4 {O(n^2)}
70: f48->f37: 104*Arg_0*Arg_1+40*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+64*Arg_0*Arg_0+40*Arg_0+40*Arg_1 {O(n^2)}
71: start->f0: 1 {O(1)}

Costbounds

Overall costbound: 206*Arg_1*Arg_1+288*Arg_0*Arg_4+288*Arg_1*Arg_4+322*Arg_0*Arg_0+528*Arg_0*Arg_1+210*Arg_1+213*Arg_0+3*Arg_4+6 {O(n^2)}
52: f0->f12: Arg_0+Arg_1+1 {O(n)}
53: f0->f58: 1 {O(1)}
54: f12->f12: Arg_0+Arg_4+1 {O(n)}
55: f12->f12: Arg_0+Arg_4+1 {O(n)}
56: f12->f35: Arg_0+Arg_1+1 {O(n)}
57: f12->f22: Arg_0+Arg_1 {O(n)}
58: f12->f22: Arg_0+Arg_1 {O(n)}
59: f22->f29: Arg_0+Arg_1 {O(n)}
60: f29->f35: Arg_0+Arg_1 {O(n)}
61: f35->f37: Arg_0+Arg_1 {O(n)}
62: f35->f37: Arg_0+Arg_1 {O(n)}
63: f35->f0: Arg_0+Arg_1 {O(n)}
64: f37->f43: 116*Arg_0*Arg_1+46*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+70*Arg_0*Arg_0+42*Arg_0+42*Arg_1 {O(n^2)}
65: f37->f43: 102*Arg_0*Arg_1+40*Arg_1*Arg_1+54*Arg_0*Arg_4+54*Arg_1*Arg_4+62*Arg_0*Arg_0+38*Arg_0+38*Arg_1 {O(n^2)}
66: f37->f37: 104*Arg_0*Arg_1+40*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+64*Arg_0*Arg_0+42*Arg_0+42*Arg_1 {O(n^2)}
67: f37->f0: Arg_0+Arg_1 {O(n)}
69: f43->f48: 102*Arg_0*Arg_1+40*Arg_1*Arg_1+54*Arg_0*Arg_4+54*Arg_1*Arg_4+62*Arg_0*Arg_0+38*Arg_1+39*Arg_0+Arg_4 {O(n^2)}
70: f48->f37: 104*Arg_0*Arg_1+40*Arg_1*Arg_1+60*Arg_0*Arg_4+60*Arg_1*Arg_4+64*Arg_0*Arg_0+40*Arg_0+40*Arg_1 {O(n^2)}
71: start->f0: 1 {O(1)}

Sizebounds

52: f0->f12, Arg_0: Arg_0 {O(n)}
52: f0->f12, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
52: f0->f12, Arg_2: 0 {O(1)}
52: f0->f12, Arg_3: 4*Arg_0+7*Arg_1 {O(n)}
52: f0->f12, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
53: f0->f58, Arg_0: 3*Arg_0 {O(n)}
53: f0->f58, Arg_1: 4*Arg_0+7*Arg_1 {O(n)}
53: f0->f58, Arg_3: 160*Arg_1*Arg_1+240*Arg_0*Arg_4+240*Arg_1*Arg_4+256*Arg_0*Arg_0+416*Arg_0*Arg_1+351*Arg_4+424*Arg_1+554*Arg_0+Arg_3+234 {O(n^2)}
53: f0->f58, Arg_4: 4*Arg_0+7*Arg_4+4 {O(n)}
54: f12->f12, Arg_0: Arg_0 {O(n)}
54: f12->f12, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
54: f12->f12, Arg_3: 10*Arg_0+7*Arg_1+9*Arg_4+6 {O(n)}
54: f12->f12, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
55: f12->f12, Arg_0: Arg_0 {O(n)}
55: f12->f12, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
55: f12->f12, Arg_3: 6*Arg_0+9*Arg_4+6 {O(n)}
55: f12->f12, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
56: f12->f35, Arg_0: Arg_0 {O(n)}
56: f12->f35, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
56: f12->f35, Arg_3: 4*Arg_0+6*Arg_1 {O(n)}
56: f12->f35, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
57: f12->f22, Arg_0: Arg_0 {O(n)}
57: f12->f22, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
57: f12->f22, Arg_3: 10*Arg_0+7*Arg_1+9*Arg_4+6 {O(n)}
57: f12->f22, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
58: f12->f22, Arg_0: Arg_0 {O(n)}
58: f12->f22, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
58: f12->f22, Arg_3: 16*Arg_0+18*Arg_4+7*Arg_1+12 {O(n)}
58: f12->f22, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
59: f22->f29, Arg_0: Arg_0 {O(n)}
59: f22->f29, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
59: f22->f29, Arg_3: 14*Arg_1+26*Arg_0+27*Arg_4+18 {O(n)}
59: f22->f29, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
60: f29->f35, Arg_0: Arg_0 {O(n)}
60: f29->f35, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
60: f29->f35, Arg_3: 14*Arg_1+26*Arg_0+27*Arg_4+18 {O(n)}
60: f29->f35, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
61: f35->f37, Arg_0: Arg_0 {O(n)}
61: f35->f37, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
61: f35->f37, Arg_3: 20*Arg_1+27*Arg_4+30*Arg_0+18 {O(n)}
61: f35->f37, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
62: f35->f37, Arg_0: Arg_0 {O(n)}
62: f35->f37, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
62: f35->f37, Arg_3: 20*Arg_1+27*Arg_4+30*Arg_0+18 {O(n)}
62: f35->f37, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
63: f35->f0, Arg_0: Arg_0 {O(n)}
63: f35->f0, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
63: f35->f0, Arg_2: 0 {O(1)}
63: f35->f0, Arg_3: 20*Arg_1+27*Arg_4+30*Arg_0+18 {O(n)}
63: f35->f0, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
64: f37->f43, Arg_0: Arg_0 {O(n)}
64: f37->f43, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
64: f37->f43, Arg_3: 120*Arg_0*Arg_4+120*Arg_1*Arg_4+128*Arg_0*Arg_0+208*Arg_0*Arg_1+80*Arg_1*Arg_1+162*Arg_4+202*Arg_1+262*Arg_0+108 {O(n^2)}
64: f37->f43, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
65: f37->f43, Arg_0: Arg_0 {O(n)}
65: f37->f43, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
65: f37->f43, Arg_3: 120*Arg_0*Arg_4+120*Arg_1*Arg_4+128*Arg_0*Arg_0+208*Arg_0*Arg_1+80*Arg_1*Arg_1+162*Arg_4+202*Arg_1+262*Arg_0+108 {O(n^2)}
65: f37->f43, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
66: f37->f37, Arg_0: Arg_0 {O(n)}
66: f37->f37, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
66: f37->f37, Arg_3: 120*Arg_0*Arg_4+120*Arg_1*Arg_4+128*Arg_0*Arg_0+208*Arg_0*Arg_1+80*Arg_1*Arg_1+162*Arg_4+202*Arg_1+262*Arg_0+108 {O(n^2)}
66: f37->f37, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
67: f37->f0, Arg_0: Arg_0 {O(n)}
67: f37->f0, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
67: f37->f0, Arg_3: 160*Arg_1*Arg_1+240*Arg_0*Arg_4+240*Arg_1*Arg_4+256*Arg_0*Arg_0+416*Arg_0*Arg_1+324*Arg_4+404*Arg_1+524*Arg_0+216 {O(n^2)}
67: f37->f0, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
69: f43->f48, Arg_0: Arg_0 {O(n)}
69: f43->f48, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
69: f43->f48, Arg_3: 120*Arg_0*Arg_4+120*Arg_1*Arg_4+128*Arg_0*Arg_0+208*Arg_0*Arg_1+80*Arg_1*Arg_1+162*Arg_4+202*Arg_1+262*Arg_0+108 {O(n^2)}
69: f43->f48, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
70: f48->f37, Arg_0: Arg_0 {O(n)}
70: f48->f37, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
70: f48->f37, Arg_3: 120*Arg_0*Arg_4+120*Arg_1*Arg_4+128*Arg_0*Arg_0+208*Arg_0*Arg_1+80*Arg_1*Arg_1+162*Arg_4+202*Arg_1+262*Arg_0+108 {O(n^2)}
70: f48->f37, Arg_4: 2*Arg_0+3*Arg_4+2 {O(n)}
71: start->f0, Arg_0: Arg_0 {O(n)}
71: start->f0, Arg_1: Arg_1 {O(n)}
71: start->f0, Arg_2: Arg_2 {O(n)}
71: start->f0, Arg_3: Arg_3 {O(n)}
71: start->f0, Arg_4: Arg_4 {O(n)}