Left Termination proof of /tmp/tmp9rQGU5/rev2.pl

Left Termination of the query pattern rev_in_2(g, a) w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇐)

↳2 Prolog

↳3 PrologToPiTRSProof (⇐)

↳4 PiTRS

↳5 DependencyPairsProof (⇔)

↳6 PiDP

↳7 DependencyGraphProof (⇔)

↳8 PiDP

↳9 UsableRulesProof (⇔)

↳10 PiDP

↳11 PiDPToQDPProof (⇐)

↳12 QDP

↳13 QDPSizeChangeProof (⇔)

↳14 TRUE

(0) Obligation:

Clauses:

rev(L, R) :- rev(L, [], R).
rev([], Y, Y).
rev(L, S, R) :- ','(no(empty(L)), ','(head(L, X), ','(tail(L, T), rev(T, .(X, S), R)))).
head([], X1).
head(.(X, X2), X).
tail([], []).
tail(.(X3, Xs), Xs).
empty([]).
no(X) :- ','(X, ','(!, failure(a))).
no(X4).
failure(b).

Queries:

rev(g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: rev(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: rev(T1, T2), SCOPE: 1, CLAUSE: 0\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: rev(T3, [], T5)\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: rev(T3, [], T5), SCOPE: 2, CLAUSE: 1 | rev(T3, [], T5), SCOPE: 2, CLAUSE: 2\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: rev(T3, [], T5), SCOPE: 2, CLAUSE: 1\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: rev(T3, [], T5), SCOPE: 2, CLAUSE: 2\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\nX11 is free", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: ','(no(empty(T6)), ','(head(T6, X18), ','(tail(T6, X19), rev(X19, .(X18, []), T8))))\n\nT6 is ground\nX18 is free; \nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(no(empty(T6)), ','(head(T6, X18), ','(tail(T6, X19), rev(X19, .(X18, []), T8)))), SCOPE: 3, CLAUSE: 8 | ','(no(empty(T6)), ','(head(T6, X18), ','(tail(T6, X19), rev(X19, .(X18, []), T8)))), SCOPE: 3, CLAUSE: 9 | ?_3\n\nT6 is ground\nX18 is free; \nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(empty(T9), ','(!_3, ','(failure(a), ','(head(T9, X18), ','(tail(T9, X19), rev(X19, .(X18, []), T8)))))) | ','(no(empty(T9)), ','(head(T9, X18), ','(tail(T9, X19), rev(X19, .(X18, []), T8)))), SCOPE: 3, CLAUSE: 9 | ?_3\n\nT9 is ground\nX18 is free; \nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(empty(T9), ','(!_3, ','(failure(a), ','(head(T9, X18), ','(tail(T9, X19), rev(X19, .(X18, []), T8)))))), SCOPE: 4, CLAUSE: 7 | ','(no(empty(T9)), ','(head(T9, X18), ','(tail(T9, X19), rev(X19, .(X18, []), T8)))), SCOPE: 3, CLAUSE: 9 | ?_3\n\nT9 is ground\nX18 is free; \nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ','(!_3, ','(failure(a), ','(head([], X18), ','(tail([], X19), rev(X19, .(X18, []), T8))))) | ','(no(empty([])), ','(head([], X18), ','(tail([], X19), rev(X19, .(X18, []), T8)))), SCOPE: 3, CLAUSE: 9 | ?_3\n\nX18 is free\nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(no(empty(T9)), ','(head(T9, X18), ','(tail(T9, X19), rev(X19, .(X18, []), T8)))), SCOPE: 3, CLAUSE: 9\n\nT9 is ground\nX18 is free; \nX19 is free; \nempty(T9) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(failure(a), ','(head([], X18), ','(tail([], X19), rev(X19, .(X18, []), T8))))\n\nX18 is free\nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(failure(a), ','(head([], X18), ','(tail([], X19), rev(X19, .(X18, []), T8)))), SCOPE: 5, CLAUSE: 10\n\nX18 is free\nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(head(T10, X18), ','(tail(T10, X19), rev(X19, .(X18, []), T8)))\n\nT10 is ground\nX18 is free; \nX19 is free; \nempty(T10) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(head(T10, X18), ','(tail(T10, X19), rev(X19, .(X18, []), T8))), SCOPE: 6, CLAUSE: 3 | ','(head(T10, X18), ','(tail(T10, X19), rev(X19, .(X18, []), T8))), SCOPE: 6, CLAUSE: 4\n\nT10 is ground\nX18 is free; \nX19 is free; \nempty(T10) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(head(T10, X18), ','(tail(T10, X19), rev(X19, .(X18, []), T8))), SCOPE: 6, CLAUSE: 4\n\nT10 is ground\nX18 is free; \nX19 is free; \nX25 is free; \nempty(T10) !=? empty([])\nhead(T10, X18) !=? head([], X25)", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(tail(.(T11, T12), X19), rev(X19, .(T11, []), T8))\n\nT11 is ground\nT12 is ground\nX18 is free; \nX19 is free; \nX25 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\nX18 is free\nX25 is free; \nX28 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(tail(.(T11, T12), X19), rev(X19, .(T11, []), T8)), SCOPE: 7, CLAUSE: 5 | ','(tail(.(T11, T12), X19), rev(X19, .(T11, []), T8)), SCOPE: 7, CLAUSE: 6\n\nT11 is ground\nT12 is ground\nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(tail(.(T11, T12), X19), rev(X19, .(T11, []), T8)), SCOPE: 7, CLAUSE: 6\n\nT11 is ground\nT12 is ground\nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: rev(T14, .(T13, []), T8)\n\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: rev(T14, .(T13, []), T8), SCOPE: 8, CLAUSE: 1 | rev(T14, .(T13, []), T8), SCOPE: 8, CLAUSE: 2\n\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: rev(T14, .(T13, []), T8), SCOPE: 8, CLAUSE: 1\n\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: rev(T14, .(T13, []), T8), SCOPE: 8, CLAUSE: 2\n\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\nX36 is free", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(no(empty(T16)), ','(head(T16, X43), ','(tail(T16, X44), rev(X44, .(X43, .(T17, [])), T19))))\n\nT16 is ground\nT17 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(no(empty(T16)), ','(head(T16, X43), ','(tail(T16, X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 9, CLAUSE: 8 | ','(no(empty(T16)), ','(head(T16, X43), ','(tail(T16, X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT16 is ground\nT17 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: ','(empty(T20), ','(!_9, ','(failure(a), ','(head(T20, X43), ','(tail(T20, X44), rev(X44, .(X43, .(T17, [])), T19)))))) | ','(no(empty(T20)), ','(head(T20, X43), ','(tail(T20, X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT17 is ground\nT20 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(empty(T20), ','(!_9, ','(failure(a), ','(head(T20, X43), ','(tail(T20, X44), rev(X44, .(X43, .(T17, [])), T19)))))), SCOPE: 10, CLAUSE: 7 | ','(no(empty(T20)), ','(head(T20, X43), ','(tail(T20, X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT17 is ground\nT20 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(!_9, ','(failure(a), ','(head([], X43), ','(tail([], X44), rev(X44, .(X43, .(T17, [])), T19))))) | ','(no(empty([])), ','(head([], X43), ','(tail([], X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT17 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(no(empty(T20)), ','(head(T20, X43), ','(tail(T20, X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 9, CLAUSE: 9\n\nT17 is ground\nT20 is ground\nX43 is free; \nX44 is free; \nempty(T20) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(failure(a), ','(head([], X43), ','(tail([], X44), rev(X44, .(X43, .(T17, [])), T19))))\n\nT17 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(failure(a), ','(head([], X43), ','(tail([], X44), rev(X44, .(X43, .(T17, [])), T19)))), SCOPE: 11, CLAUSE: 10\n\nT17 is ground\nX43 is free; \nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(head(T21, X43), ','(tail(T21, X44), rev(X44, .(X43, .(T17, [])), T19)))\n\nT17 is ground\nT21 is ground\nX43 is free; \nX44 is free; \nempty(T21) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(head(T21, X43), ','(tail(T21, X44), rev(X44, .(X43, .(T17, [])), T19))), SCOPE: 12, CLAUSE: 3 | ','(head(T21, X43), ','(tail(T21, X44), rev(X44, .(X43, .(T17, [])), T19))), SCOPE: 12, CLAUSE: 4\n\nT17 is ground\nT21 is ground\nX43 is free; \nX44 is free; \nempty(T21) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(head(T21, X43), ','(tail(T21, X44), rev(X44, .(X43, .(T17, [])), T19))), SCOPE: 12, CLAUSE: 4\n\nT17 is ground\nT21 is ground\nX43 is free; \nX44 is free; \nX50 is free; \nempty(T21) !=? empty([])\nhead(T21, X43) !=? head([], X50)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(tail(.(T22, T23), X44), rev(X44, .(T22, .(T17, [])), T19))\n\nT17 is ground\nT22 is ground\nT23 is ground\nX43 is free; \nX44 is free; \nX50 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\nX43 is free\nX50 is free; \nX53 is free; \nX54 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(tail(.(T22, T23), X44), rev(X44, .(T22, .(T17, [])), T19)), SCOPE: 13, CLAUSE: 5 | ','(tail(.(T22, T23), X44), rev(X44, .(T22, .(T17, [])), T19)), SCOPE: 13, CLAUSE: 6\n\nT17 is ground\nT22 is ground\nT23 is ground\nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(tail(.(T22, T23), X44), rev(X44, .(T22, .(T17, [])), T19)), SCOPE: 13, CLAUSE: 6\n\nT17 is ground\nT22 is ground\nT23 is ground\nX44 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: rev(T25, .(T24, .(T17, [])), T19)\n\nT17 is ground\nT24 is ground\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: rev(T25, .(T24, .(T17, [])), T19), SCOPE: 14, CLAUSE: 1 | rev(T25, .(T24, .(T17, [])), T19), SCOPE: 14, CLAUSE: 2\n\nT17 is ground\nT24 is ground\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: rev(T25, .(T24, .(T17, [])), T19), SCOPE: 14, CLAUSE: 1\n\nT17 is ground\nT24 is ground\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: rev(T25, .(T24, .(T17, [])), T19), SCOPE: 14, CLAUSE: 2\n\nT17 is ground\nT24 is ground\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\nX61 is free", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(no(empty(T28)), ','(head(T28, X68), ','(tail(T28, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32))))\n\nT28 is ground\nT29 is ground\nT30 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(no(empty(T28)), ','(head(T28, X68), ','(tail(T28, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 15, CLAUSE: 8 | ','(no(empty(T28)), ','(head(T28, X68), ','(tail(T28, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT28 is ground\nT29 is ground\nT30 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(empty(T33), ','(!_15, ','(failure(a), ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))))) | ','(no(empty(T33)), ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT29 is ground\nT30 is ground\nT33 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(empty(T33), ','(!_15, ','(failure(a), ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))))), SCOPE: 16, CLAUSE: 7 | ','(no(empty(T33)), ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT29 is ground\nT30 is ground\nT33 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(!_15, ','(failure(a), ','(head([], X68), ','(tail([], X69), rev(X69, .(X68, .(T29, .(T30, []))), T32))))) | ','(no(empty([])), ','(head([], X68), ','(tail([], X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT29 is ground\nT30 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(no(empty(T33)), ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 15, CLAUSE: 9\n\nT29 is ground\nT30 is ground\nT33 is ground\nX68 is free; \nX69 is free; \nempty(T33) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(failure(a), ','(head([], X68), ','(tail([], X69), rev(X69, .(X68, .(T29, .(T30, []))), T32))))\n\nT29 is ground\nT30 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(failure(a), ','(head([], X68), ','(tail([], X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))), SCOPE: 17, CLAUSE: 10\n\nT29 is ground\nT30 is ground\nX68 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(head(T34, X68), ','(tail(T34, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32)))\n\nT29 is ground\nT30 is ground\nT34 is ground\nX68 is free; \nX69 is free; \nempty(T34) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(head(T34, X68), ','(tail(T34, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32))), SCOPE: 18, CLAUSE: 3 | ','(head(T34, X68), ','(tail(T34, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32))), SCOPE: 18, CLAUSE: 4\n\nT29 is ground\nT30 is ground\nT34 is ground\nX68 is free; \nX69 is free; \nempty(T34) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(head(T34, X68), ','(tail(T34, X69), rev(X69, .(X68, .(T29, .(T30, []))), T32))), SCOPE: 18, CLAUSE: 4\n\nT29 is ground\nT30 is ground\nT34 is ground\nX68 is free; \nX69 is free; \nX75 is free; \nempty(T34) !=? empty([])\nhead(T34, X68) !=? head([], X75)", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(tail(.(T35, T36), X69), rev(X69, .(T35, .(T29, .(T30, []))), T32))\n\nT29 is ground\nT30 is ground\nT35 is ground\nT36 is ground\nX68 is free; \nX69 is free; \nX75 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\nX68 is free\nX75 is free; \nX78 is free; \nX79 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(tail(.(T35, T36), X69), rev(X69, .(T35, .(T29, .(T30, []))), T32)), SCOPE: 19, CLAUSE: 5 | ','(tail(.(T35, T36), X69), rev(X69, .(T35, .(T29, .(T30, []))), T32)), SCOPE: 19, CLAUSE: 6\n\nT29 is ground\nT30 is ground\nT35 is ground\nT36 is ground\nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(tail(.(T35, T36), X69), rev(X69, .(T35, .(T29, .(T30, []))), T32)), SCOPE: 19, CLAUSE: 6\n\nT29 is ground\nT30 is ground\nT35 is ground\nT36 is ground\nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: rev(T38, .(T37, .(T29, .(T30, []))), T32)\n\nT29 is ground\nT30 is ground\nT37 is ground\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: rev(T38, .(T37, .(T29, .(T30, []))), T32), SCOPE: 20, CLAUSE: 1 | rev(T38, .(T37, .(T29, .(T30, []))), T32), SCOPE: 20, CLAUSE: 2\n\nT29 is ground\nT30 is ground\nT37 is ground\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: rev(T38, .(T37, .(T29, .(T30, []))), T32), SCOPE: 20, CLAUSE: 1\n\nT29 is ground\nT30 is ground\nT37 is ground\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: rev(T38, .(T37, .(T29, .(T30, []))), T32), SCOPE: 20, CLAUSE: 2\n\nT29 is ground\nT30 is ground\nT37 is ground\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(no(empty(T42)), ','(head(T42, X93), ','(tail(T42, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47))))\n\nT42 is ground\nT43 is ground\nT44 is ground\nT45 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(no(empty(T42)), ','(head(T42, X93), ','(tail(T42, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 21, CLAUSE: 8 | ','(no(empty(T42)), ','(head(T42, X93), ','(tail(T42, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 21, CLAUSE: 9 | ?_21\n\nT42 is ground\nT43 is ground\nT44 is ground\nT45 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(empty(T48), ','(!_21, ','(failure(a), ','(head(T48, X93), ','(tail(T48, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))))) | ','(no(empty(T48)), ','(head(T48, X93), ','(tail(T48, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 21, CLAUSE: 9 | ?_21\n\nT43 is ground\nT44 is ground\nT45 is ground\nT48 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(empty(T48), ','(!_21, ','(failure(a), ','(head(T48, X93), ','(tail(T48, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))))), SCOPE: 22, CLAUSE: 7 | ','(no(empty(T48)), ','(head(T48, X93), ','(tail(T48, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 21, CLAUSE: 9 | ?_21\n\nT43 is ground\nT44 is ground\nT45 is ground\nT48 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(!_21, ','(failure(a), ','(head([], X93), ','(tail([], X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47))))) | ','(no(empty([])), ','(head([], X93), ','(tail([], X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 21, CLAUSE: 9 | ?_21\n\nT43 is ground\nT44 is ground\nT45 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(no(empty(T48)), ','(head(T48, X93), ','(tail(T48, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 21, CLAUSE: 9\n\nT43 is ground\nT44 is ground\nT45 is ground\nT48 is ground\nX93 is free; \nX94 is free; \nempty(T48) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(failure(a), ','(head([], X93), ','(tail([], X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47))))\n\nT43 is ground\nT44 is ground\nT45 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(failure(a), ','(head([], X93), ','(tail([], X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))), SCOPE: 23, CLAUSE: 10\n\nT43 is ground\nT44 is ground\nT45 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ','(head(T49, X93), ','(tail(T49, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47)))\n\nT43 is ground\nT44 is ground\nT45 is ground\nT49 is ground\nX93 is free; \nX94 is free; \nempty(T49) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(head(T49, X93), ','(tail(T49, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47))), SCOPE: 24, CLAUSE: 3 | ','(head(T49, X93), ','(tail(T49, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47))), SCOPE: 24, CLAUSE: 4\n\nT43 is ground\nT44 is ground\nT45 is ground\nT49 is ground\nX93 is free; \nX94 is free; \nempty(T49) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(head(T49, X93), ','(tail(T49, X94), rev(X94, .(X93, .(T43, .(T44, .(T45, [])))), T47))), SCOPE: 24, CLAUSE: 4\n\nT43 is ground\nT44 is ground\nT45 is ground\nT49 is ground\nX93 is free; \nX94 is free; \nX100 is free; \nempty(T49) !=? empty([])\nhead(T49, X93) !=? head([], X100)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(tail(.(T50, T51), X94), rev(X94, .(T50, .(T43, .(T44, .(T45, [])))), T47))\n\nT43 is ground\nT44 is ground\nT45 is ground\nT50 is ground\nT51 is ground\nX93 is free; \nX94 is free; \nX100 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\nX93 is free\nX100 is free; \nX103 is free; \nX104 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(tail(.(T50, T51), X94), rev(X94, .(T50, .(T43, .(T44, .(T45, [])))), T47)), SCOPE: 25, CLAUSE: 5 | ','(tail(.(T50, T51), X94), rev(X94, .(T50, .(T43, .(T44, .(T45, [])))), T47)), SCOPE: 25, CLAUSE: 6\n\nT43 is ground\nT44 is ground\nT45 is ground\nT50 is ground\nT51 is ground\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(tail(.(T50, T51), X94), rev(X94, .(T50, .(T43, .(T44, .(T45, [])))), T47)), SCOPE: 25, CLAUSE: 6\n\nT43 is ground\nT44 is ground\nT45 is ground\nT50 is ground\nT51 is ground\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: rev(T53, .(T52, .(T43, .(T44, .(T45, [])))), T47)\n\nT43 is ground\nT44 is ground\nT45 is ground\nT52 is ground\nT53 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: rev(T53, .(T52, .(T43, .(T44, .(T45, [])))), T47), SCOPE: 26, CLAUSE: 1 | rev(T53, .(T52, .(T43, .(T44, .(T45, [])))), T47), SCOPE: 26, CLAUSE: 2\n\nT43 is ground\nT44 is ground\nT45 is ground\nT52 is ground\nT53 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: rev(T53, .(T52, .(T43, .(T44, .(T45, [])))), T47), SCOPE: 26, CLAUSE: 1\n\nT43 is ground\nT44 is ground\nT45 is ground\nT52 is ground\nT53 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: rev(T53, .(T52, .(T43, .(T44, .(T45, [])))), T47), SCOPE: 26, CLAUSE: 2\n\nT43 is ground\nT44 is ground\nT45 is ground\nT52 is ground\nT53 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\nX111 is free", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(no(empty(T58)), ','(head(T58, X118), ','(tail(T58, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64))))\n\nT58 is ground\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(no(empty(T58)), ','(head(T58, X118), ','(tail(T58, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 27, CLAUSE: 8 | ','(no(empty(T58)), ','(head(T58, X118), ','(tail(T58, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 27, CLAUSE: 9 | ?_27\n\nT58 is ground\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(empty(T65), ','(!_27, ','(failure(a), ','(head(T65, X118), ','(tail(T65, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))))) | ','(no(empty(T65)), ','(head(T65, X118), ','(tail(T65, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 27, CLAUSE: 9 | ?_27\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT65 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(empty(T65), ','(!_27, ','(failure(a), ','(head(T65, X118), ','(tail(T65, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))))), SCOPE: 28, CLAUSE: 7 | ','(no(empty(T65)), ','(head(T65, X118), ','(tail(T65, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 27, CLAUSE: 9 | ?_27\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT65 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(!_27, ','(failure(a), ','(head([], X118), ','(tail([], X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64))))) | ','(no(empty([])), ','(head([], X118), ','(tail([], X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 27, CLAUSE: 9 | ?_27\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ','(no(empty(T65)), ','(head(T65, X118), ','(tail(T65, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 27, CLAUSE: 9\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT65 is ground\nX118 is free; \nX119 is free; \nempty(T65) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(failure(a), ','(head([], X118), ','(tail([], X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64))))\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(failure(a), ','(head([], X118), ','(tail([], X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))), SCOPE: 29, CLAUSE: 10\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nX118 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(head(T66, X118), ','(tail(T66, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64)))\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT66 is ground\nX118 is free; \nX119 is free; \nempty(T66) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(head(T66, X118), ','(tail(T66, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64))), SCOPE: 30, CLAUSE: 3 | ','(head(T66, X118), ','(tail(T66, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64))), SCOPE: 30, CLAUSE: 4\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT66 is ground\nX118 is free; \nX119 is free; \nempty(T66) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(head(T66, X118), ','(tail(T66, X119), rev(X119, .(X118, .(T59, .(T60, .(T61, .(T62, []))))), T64))), SCOPE: 30, CLAUSE: 4\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT66 is ground\nX118 is free; \nX119 is free; \nX125 is free; \nempty(T66) !=? empty([])\nhead(T66, X118) !=? head([], X125)", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(tail(.(T67, T68), X119), rev(X119, .(T67, .(T59, .(T60, .(T61, .(T62, []))))), T64))\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT67 is ground\nT68 is ground\nX118 is free; \nX119 is free; \nX125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: \n\nX118 is free\nX125 is free; \nX128 is free; \nX129 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(tail(.(T67, T68), X119), rev(X119, .(T67, .(T59, .(T60, .(T61, .(T62, []))))), T64)), SCOPE: 31, CLAUSE: 5 | ','(tail(.(T67, T68), X119), rev(X119, .(T67, .(T59, .(T60, .(T61, .(T62, []))))), T64)), SCOPE: 31, CLAUSE: 6\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT67 is ground\nT68 is ground\nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(tail(.(T67, T68), X119), rev(X119, .(T67, .(T59, .(T60, .(T61, .(T62, []))))), T64)), SCOPE: 31, CLAUSE: 6\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT67 is ground\nT68 is ground\nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: rev(T70, .(T69, .(T59, .(T60, .(T61, .(T62, []))))), T64)\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT69 is ground\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: rev(T70, .(T69, .(T59, .(T60, .(T61, .(T62, []))))), T64), SCOPE: 32, CLAUSE: 1 | rev(T70, .(T69, .(T59, .(T60, .(T61, .(T62, []))))), T64), SCOPE: 32, CLAUSE: 2\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT69 is ground\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: rev(T70, .(T69, .(T59, .(T60, .(T61, .(T62, []))))), T64), SCOPE: 32, CLAUSE: 1\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT69 is ground\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: rev(T70, .(T69, .(T59, .(T60, .(T61, .(T62, []))))), T64), SCOPE: 32, CLAUSE: 2\n\nT59 is ground\nT60 is ground\nT61 is ground\nT62 is ground\nT69 is ground\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\nX136 is free", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(no(empty(T76)), ','(head(T76, X143), ','(tail(T76, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))))\n\nT76 is ground\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ','(no(empty(T76)), ','(head(T76, X143), ','(tail(T76, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 33, CLAUSE: 8 | ','(no(empty(T76)), ','(head(T76, X143), ','(tail(T76, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 33, CLAUSE: 9 | ?_33\n\nT76 is ground\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(empty(T84), ','(!_33, ','(failure(a), ','(head(T84, X143), ','(tail(T84, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))))) | ','(no(empty(T84)), ','(head(T84, X143), ','(tail(T84, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 33, CLAUSE: 9 | ?_33\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT84 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(empty(T84), ','(!_33, ','(failure(a), ','(head(T84, X143), ','(tail(T84, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))))), SCOPE: 34, CLAUSE: 7 | ','(no(empty(T84)), ','(head(T84, X143), ','(tail(T84, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 33, CLAUSE: 9 | ?_33\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT84 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(!_33, ','(failure(a), ','(head([], X143), ','(tail([], X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))))) | ','(no(empty([])), ','(head([], X143), ','(tail([], X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 33, CLAUSE: 9 | ?_33\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: ','(no(empty(T84)), ','(head(T84, X143), ','(tail(T84, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 33, CLAUSE: 9\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT84 is ground\nX143 is free; \nX144 is free; \nempty(T84) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(failure(a), ','(head([], X143), ','(tail([], X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))))\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ','(failure(a), ','(head([], X143), ','(tail([], X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))), SCOPE: 35, CLAUSE: 10\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX143 is free; \nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(head(T85, X143), ','(tail(T85, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)))\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT85 is ground\nX143 is free; \nX144 is free; \nempty(T85) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(head(T85, X143), ','(tail(T85, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))), SCOPE: 36, CLAUSE: 3 | ','(head(T85, X143), ','(tail(T85, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))), SCOPE: 36, CLAUSE: 4\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT85 is ground\nX143 is free; \nX144 is free; \nempty(T85) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ','(head(T85, X143), ','(tail(T85, X144), rev(X144, .(X143, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))), SCOPE: 36, CLAUSE: 4\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT85 is ground\nX143 is free; \nX144 is free; \nX150 is free; \nempty(T85) !=? empty([])\nhead(T85, X143) !=? head([], X150)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(tail(.(T86, T87), X144), rev(X144, .(T86, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83))\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT86 is ground\nT87 is ground\nX143 is free; \nX144 is free; \nX150 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\nX143 is free\nX150 is free; \nX153 is free; \nX154 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(tail(.(T86, T87), X144), rev(X144, .(T86, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)), SCOPE: 37, CLAUSE: 5 | ','(tail(.(T86, T87), X144), rev(X144, .(T86, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)), SCOPE: 37, CLAUSE: 6\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT86 is ground\nT87 is ground\nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ','(tail(.(T86, T87), X144), rev(X144, .(T86, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)), SCOPE: 37, CLAUSE: 6\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT86 is ground\nT87 is ground\nX144 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: rev(T89, .(T88, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83)\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT88 is ground\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: rev(T89, .(T88, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83), SCOPE: 38, CLAUSE: 1 | rev(T89, .(T88, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83), SCOPE: 38, CLAUSE: 2\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT88 is ground\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: rev(T89, .(T88, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83), SCOPE: 38, CLAUSE: 1\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT88 is ground\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: rev(T89, .(T88, .(T77, .(T78, .(T79, .(T80, .(T81, [])))))), T83), SCOPE: 38, CLAUSE: 2\n\nT77 is ground\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nT88 is ground\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\nX161 is free", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(no(empty(T96)), ','(head(T96, X168), ','(tail(T96, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))))\n\nT96 is ground\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(no(empty(T96)), ','(head(T96, X168), ','(tail(T96, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 39, CLAUSE: 8 | ','(no(empty(T96)), ','(head(T96, X168), ','(tail(T96, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 39, CLAUSE: 9 | ?_39\n\nT96 is ground\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(empty(T105), ','(!_39, ','(failure(a), ','(head(T105, X168), ','(tail(T105, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))))) | ','(no(empty(T105)), ','(head(T105, X168), ','(tail(T105, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 39, CLAUSE: 9 | ?_39\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT105 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: ','(empty(T105), ','(!_39, ','(failure(a), ','(head(T105, X168), ','(tail(T105, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))))), SCOPE: 40, CLAUSE: 7 | ','(no(empty(T105)), ','(head(T105, X168), ','(tail(T105, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 39, CLAUSE: 9 | ?_39\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT105 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(!_39, ','(failure(a), ','(head([], X168), ','(tail([], X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))))) | ','(no(empty([])), ','(head([], X168), ','(tail([], X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 39, CLAUSE: 9 | ?_39\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(no(empty(T105)), ','(head(T105, X168), ','(tail(T105, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 39, CLAUSE: 9\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT105 is ground\nX168 is free; \nX169 is free; \nempty(T105) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(failure(a), ','(head([], X168), ','(tail([], X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))))\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(failure(a), ','(head([], X168), ','(tail([], X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))), SCOPE: 41, CLAUSE: 10\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(head(T106, X168), ','(tail(T106, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)))\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT106 is ground\nX168 is free; \nX169 is free; \nempty(T106) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(head(T106, X168), ','(tail(T106, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))), SCOPE: 42, CLAUSE: 3 | ','(head(T106, X168), ','(tail(T106, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))), SCOPE: 42, CLAUSE: 4\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT106 is ground\nX168 is free; \nX169 is free; \nempty(T106) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(head(T106, X168), ','(tail(T106, X169), rev(X169, .(X168, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))), SCOPE: 42, CLAUSE: 4\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT106 is ground\nX168 is free; \nX169 is free; \nX175 is free; \nempty(T106) !=? empty([])\nhead(T106, X168) !=? head([], X175)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(tail(.(T107, T108), X169), rev(X169, .(T107, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104))\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT107 is ground\nT108 is ground\nX168 is free; \nX169 is free; \nX175 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\nX168 is free\nX175 is free; \nX178 is free; \nX179 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(tail(.(T107, T108), X169), rev(X169, .(T107, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)), SCOPE: 43, CLAUSE: 5 | ','(tail(.(T107, T108), X169), rev(X169, .(T107, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)), SCOPE: 43, CLAUSE: 6\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT107 is ground\nT108 is ground\nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(tail(.(T107, T108), X169), rev(X169, .(T107, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)), SCOPE: 43, CLAUSE: 6\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT107 is ground\nT108 is ground\nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: rev(T110, .(T109, .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))), T104)\n\nT97 is ground\nT98 is ground\nT99 is ground\nT100 is ground\nT101 is ground\nT102 is ground\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: rev(T110, .(T111, T112), T104)\n\nT110 is ground\nT111 is ground\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: rev(T110, .(T111, T112), T104), SCOPE: 44, CLAUSE: 1 | rev(T110, .(T111, T112), T104), SCOPE: 44, CLAUSE: 2\n\nT110 is ground\nT111 is ground\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: rev(T110, .(T111, T112), T104), SCOPE: 44, CLAUSE: 1\n\nT110 is ground\nT111 is ground\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: rev(T110, .(T111, T112), T104), SCOPE: 44, CLAUSE: 2\n\nT110 is ground\nT111 is ground\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\nX186 is free", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(no(empty(T115)), ','(head(T115, X193), ','(tail(T115, X194), rev(X194, .(X193, .(T116, T117)), T119))))\n\nT115 is ground\nT116 is ground\nT117 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(no(empty(T115)), ','(head(T115, X193), ','(tail(T115, X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 45, CLAUSE: 8 | ','(no(empty(T115)), ','(head(T115, X193), ','(tail(T115, X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 45, CLAUSE: 9 | ?_45\n\nT115 is ground\nT116 is ground\nT117 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: ','(empty(T120), ','(!_45, ','(failure(a), ','(head(T120, X193), ','(tail(T120, X194), rev(X194, .(X193, .(T116, T117)), T119)))))) | ','(no(empty(T120)), ','(head(T120, X193), ','(tail(T120, X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 45, CLAUSE: 9 | ?_45\n\nT116 is ground\nT117 is ground\nT120 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: ','(empty(T120), ','(!_45, ','(failure(a), ','(head(T120, X193), ','(tail(T120, X194), rev(X194, .(X193, .(T116, T117)), T119)))))), SCOPE: 46, CLAUSE: 7 | ','(no(empty(T120)), ','(head(T120, X193), ','(tail(T120, X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 45, CLAUSE: 9 | ?_45\n\nT116 is ground\nT117 is ground\nT120 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: ','(!_45, ','(failure(a), ','(head([], X193), ','(tail([], X194), rev(X194, .(X193, .(T116, T117)), T119))))) | ','(no(empty([])), ','(head([], X193), ','(tail([], X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 45, CLAUSE: 9 | ?_45\n\nT116 is ground\nT117 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(no(empty(T120)), ','(head(T120, X193), ','(tail(T120, X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 45, CLAUSE: 9\n\nT116 is ground\nT117 is ground\nT120 is ground\nX193 is free; \nX194 is free; \nempty(T120) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ','(failure(a), ','(head([], X193), ','(tail([], X194), rev(X194, .(X193, .(T116, T117)), T119))))\n\nT116 is ground\nT117 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(failure(a), ','(head([], X193), ','(tail([], X194), rev(X194, .(X193, .(T116, T117)), T119)))), SCOPE: 47, CLAUSE: 10\n\nT116 is ground\nT117 is ground\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(head(T121, X193), ','(tail(T121, X194), rev(X194, .(X193, .(T116, T117)), T119)))\n\nT116 is ground\nT117 is ground\nT121 is ground\nX193 is free; \nX194 is free; \nempty(T121) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: ','(head(T121, X193), ','(tail(T121, X194), rev(X194, .(X193, .(T116, T117)), T119))), SCOPE: 48, CLAUSE: 3 | ','(head(T121, X193), ','(tail(T121, X194), rev(X194, .(X193, .(T116, T117)), T119))), SCOPE: 48, CLAUSE: 4\n\nT116 is ground\nT117 is ground\nT121 is ground\nX193 is free; \nX194 is free; \nempty(T121) !=? empty([])", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(head(T121, X193), ','(tail(T121, X194), rev(X194, .(X193, .(T116, T117)), T119))), SCOPE: 48, CLAUSE: 4\n\nT116 is ground\nT117 is ground\nT121 is ground\nX193 is free; \nX194 is free; \nX200 is free; \nempty(T121) !=? empty([])\nhead(T121, X193) !=? head([], X200)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: ','(tail(.(T122, T123), X194), rev(X194, .(T122, .(T116, T117)), T119))\n\nT116 is ground\nT117 is ground\nT122 is ground\nT123 is ground\nX193 is free; \nX194 is free; \nX200 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: \n\nX193 is free\nX200 is free; \nX203 is free; \nX204 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: ','(tail(.(T122, T123), X194), rev(X194, .(T122, .(T116, T117)), T119)), SCOPE: 49, CLAUSE: 5 | ','(tail(.(T122, T123), X194), rev(X194, .(T122, .(T116, T117)), T119)), SCOPE: 49, CLAUSE: 6\n\nT116 is ground\nT117 is ground\nT122 is ground\nT123 is ground\nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(tail(.(T122, T123), X194), rev(X194, .(T122, .(T116, T117)), T119)), SCOPE: 49, CLAUSE: 6\n\nT116 is ground\nT117 is ground\nT122 is ground\nT123 is ground\nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: rev(T125, .(T124, .(T116, T117)), T119)\n\nT116 is ground\nT117 is ground\nT124 is ground\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 189 [arrowhead = none ];
189 -> 2;

190 [label="EVAL with clause\nrev(X7, X8) :- rev(X7, [], X8).\nand substitution\nT1 -> T3\nX7 -> T3\nT2 -> T5\nX8 -> T5\nT4 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 190 [arrowhead = none ];
190 -> 3;

191 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 191 [arrowhead = none ];
191 -> 4;

192 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 192 [arrowhead = none ];
192 -> 5;

193 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 193 [arrowhead = none ];
193 -> 6;

194 [label="EVAL with clause\nrev([], X11, X11).\nand substitution\nT3 -> []\nX11 -> []\nT5 -> []", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 194 [arrowhead = none ];
194 -> 7;

195 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 195 [arrowhead = none ];
195 -> 8;

196 [label="EVAL with clause\nrev(X15, X16, X17) :- ','(no(empty(X15)), ','(head(X15, X18), ','(tail(X15, X19), rev(X19, .(X18, X16), X17)))).\nand substitution\nT3 -> T6\nX15 -> T6\nX16 -> []\nT5 -> T8\nX17 -> T8\nT7 -> T8", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 196 [arrowhead = none ];
196 -> 10;

197 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 197 [arrowhead = none ];
197 -> 9;

198 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
10 -> 198 [arrowhead = none ];
198 -> 11;

199 [label="EVAL with clause\nno(X21) :- ','(X21, ','(!, failure(a))).\nand substitution\nT6 -> T9\nX21 -> empty(T9)", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 199 [arrowhead = none ];
199 -> 12;

200 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
12 -> 200 [arrowhead = none ];
200 -> 13;

201 [label="EVAL with clause\nempty([]).\nand substitution\nT9 -> []", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 201 [arrowhead = none ];
201 -> 14;

202 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 202 [arrowhead = none ];
202 -> 15;

203 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 203 [arrowhead = none ];
203 -> 16;

204 [label="EVAL with clause\nno(X23).\nand substitution\nT9 -> T10\nX23 -> empty(T10)", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 204 [arrowhead = none ];
204 -> 19;

205 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 205 [arrowhead = none ];
205 -> 17;

206 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
17 -> 206 [arrowhead = none ];
206 -> 18;

207 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 207 [arrowhead = none ];
207 -> 20;

208 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T10), empty([]))", fontsize=14, style = filled, fillcolor = white];
20 -> 208 [arrowhead = none ];
208 -> 21;

209 [label="EVAL with clause\nhead(.(X28, X29), X28).\nand substitution\nX28 -> T11\nX29 -> T12\nT10 -> .(T11, T12)\nX18 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 209 [arrowhead = none ];
209 -> 22;

210 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 210 [arrowhead = none ];
210 -> 23;

211 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 211 [arrowhead = none ];
211 -> 24;

212 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
24 -> 212 [arrowhead = none ];
212 -> 25;

213 [label="EVAL with clause\ntail(.(X32, X33), X33).\nand substitution\nT11 -> T13\nX32 -> T13\nT12 -> T14\nX33 -> T14\nX19 -> T14", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 213 [arrowhead = none ];
213 -> 26;

214 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
26 -> 214 [arrowhead = none ];
214 -> 27;

215 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
27 -> 215 [arrowhead = none ];
215 -> 28;

216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
27 -> 216 [arrowhead = none ];
216 -> 29;

217 [label="EVAL with clause\nrev([], X36, X36).\nand substitution\nT14 -> []\nT13 -> T15\nX36 -> .(T15, [])\nT8 -> .(T15, [])", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 217 [arrowhead = none ];
217 -> 30;

218 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 218 [arrowhead = none ];
218 -> 31;

219 [label="EVAL with clause\nrev(X40, X41, X42) :- ','(no(empty(X40)), ','(head(X40, X43), ','(tail(X40, X44), rev(X44, .(X43, X41), X42)))).\nand substitution\nT14 -> T16\nX40 -> T16\nT13 -> T17\nX41 -> .(T17, [])\nT8 -> T19\nX42 -> T19\nT18 -> T19", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 219 [arrowhead = none ];
219 -> 33;

220 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 220 [arrowhead = none ];
220 -> 32;

221 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 221 [arrowhead = none ];
221 -> 34;

222 [label="EVAL with clause\nno(X46) :- ','(X46, ','(!, failure(a))).\nand substitution\nT16 -> T20\nX46 -> empty(T20)", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 222 [arrowhead = none ];
222 -> 35;

223 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 223 [arrowhead = none ];
223 -> 36;

224 [label="EVAL with clause\nempty([]).\nand substitution\nT20 -> []", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 224 [arrowhead = none ];
224 -> 37;

225 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 225 [arrowhead = none ];
225 -> 38;

226 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 226 [arrowhead = none ];
226 -> 39;

227 [label="EVAL with clause\nno(X48).\nand substitution\nT20 -> T21\nX48 -> empty(T21)", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 227 [arrowhead = none ];
227 -> 42;

228 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 228 [arrowhead = none ];
228 -> 40;

229 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
40 -> 229 [arrowhead = none ];
229 -> 41;

230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
42 -> 230 [arrowhead = none ];
230 -> 43;

231 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T21), empty([]))", fontsize=14, style = filled, fillcolor = white];
43 -> 231 [arrowhead = none ];
231 -> 44;

232 [label="EVAL with clause\nhead(.(X53, X54), X53).\nand substitution\nX53 -> T22\nX54 -> T23\nT21 -> .(T22, T23)\nX43 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 232 [arrowhead = none ];
232 -> 45;

233 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 233 [arrowhead = none ];
233 -> 46;

234 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
45 -> 234 [arrowhead = none ];
234 -> 47;

235 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
47 -> 235 [arrowhead = none ];
235 -> 48;

236 [label="EVAL with clause\ntail(.(X57, X58), X58).\nand substitution\nT22 -> T24\nX57 -> T24\nT23 -> T25\nX58 -> T25\nX44 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 236 [arrowhead = none ];
236 -> 49;

237 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 237 [arrowhead = none ];
237 -> 50;

238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 238 [arrowhead = none ];
238 -> 51;

239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 239 [arrowhead = none ];
239 -> 52;

240 [label="EVAL with clause\nrev([], X61, X61).\nand substitution\nT25 -> []\nT24 -> T26\nT17 -> T27\nX61 -> .(T26, .(T27, []))\nT19 -> .(T26, .(T27, []))", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 240 [arrowhead = none ];
240 -> 53;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 241 [arrowhead = none ];
241 -> 54;

242 [label="EVAL with clause\nrev(X65, X66, X67) :- ','(no(empty(X65)), ','(head(X65, X68), ','(tail(X65, X69), rev(X69, .(X68, X66), X67)))).\nand substitution\nT25 -> T28\nX65 -> T28\nT24 -> T29\nT17 -> T30\nX66 -> .(T29, .(T30, []))\nT19 -> T32\nX67 -> T32\nT31 -> T32", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 242 [arrowhead = none ];
242 -> 56;

243 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 243 [arrowhead = none ];
243 -> 55;

244 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 244 [arrowhead = none ];
244 -> 57;

245 [label="EVAL with clause\nno(X71) :- ','(X71, ','(!, failure(a))).\nand substitution\nT28 -> T33\nX71 -> empty(T33)", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 245 [arrowhead = none ];
245 -> 58;

246 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
58 -> 246 [arrowhead = none ];
246 -> 59;

247 [label="EVAL with clause\nempty([]).\nand substitution\nT33 -> []", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 247 [arrowhead = none ];
247 -> 60;

248 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 248 [arrowhead = none ];
248 -> 61;

249 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 249 [arrowhead = none ];
249 -> 62;

250 [label="EVAL with clause\nno(X73).\nand substitution\nT33 -> T34\nX73 -> empty(T34)", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 250 [arrowhead = none ];
250 -> 65;

251 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
62 -> 251 [arrowhead = none ];
251 -> 63;

252 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
63 -> 252 [arrowhead = none ];
252 -> 64;

253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
65 -> 253 [arrowhead = none ];
253 -> 66;

254 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T34), empty([]))", fontsize=14, style = filled, fillcolor = white];
66 -> 254 [arrowhead = none ];
254 -> 67;

255 [label="EVAL with clause\nhead(.(X78, X79), X78).\nand substitution\nX78 -> T35\nX79 -> T36\nT34 -> .(T35, T36)\nX68 -> T35", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 255 [arrowhead = none ];
255 -> 68;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 256 [arrowhead = none ];
256 -> 69;

257 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 257 [arrowhead = none ];
257 -> 70;

258 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
70 -> 258 [arrowhead = none ];
258 -> 71;

259 [label="EVAL with clause\ntail(.(X82, X83), X83).\nand substitution\nT35 -> T37\nX82 -> T37\nT36 -> T38\nX83 -> T38\nX69 -> T38", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 259 [arrowhead = none ];
259 -> 72;

260 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
72 -> 260 [arrowhead = none ];
260 -> 73;

261 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
73 -> 261 [arrowhead = none ];
261 -> 74;

262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
73 -> 262 [arrowhead = none ];
262 -> 75;

263 [label="EVAL with clause\nrev([], X86, X86).\nand substitution\nT38 -> []\nT37 -> T39\nT29 -> T40\nT30 -> T41\nX86 -> .(T39, .(T40, .(T41, [])))\nT32 -> .(T39, .(T40, .(T41, [])))", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 263 [arrowhead = none ];
263 -> 76;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 264 [arrowhead = none ];
264 -> 77;

265 [label="EVAL with clause\nrev(X90, X91, X92) :- ','(no(empty(X90)), ','(head(X90, X93), ','(tail(X90, X94), rev(X94, .(X93, X91), X92)))).\nand substitution\nT38 -> T42\nX90 -> T42\nT37 -> T43\nT29 -> T44\nT30 -> T45\nX91 -> .(T43, .(T44, .(T45, [])))\nT32 -> T47\nX92 -> T47\nT46 -> T47", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 265 [arrowhead = none ];
265 -> 79;

266 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 266 [arrowhead = none ];
266 -> 78;

267 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
79 -> 267 [arrowhead = none ];
267 -> 80;

268 [label="EVAL with clause\nno(X96) :- ','(X96, ','(!, failure(a))).\nand substitution\nT42 -> T48\nX96 -> empty(T48)", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 268 [arrowhead = none ];
268 -> 81;

269 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
81 -> 269 [arrowhead = none ];
269 -> 82;

270 [label="EVAL with clause\nempty([]).\nand substitution\nT48 -> []", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 270 [arrowhead = none ];
270 -> 83;

271 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 271 [arrowhead = none ];
271 -> 84;

272 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 272 [arrowhead = none ];
272 -> 85;

273 [label="EVAL with clause\nno(X98).\nand substitution\nT48 -> T49\nX98 -> empty(T49)", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 273 [arrowhead = none ];
273 -> 88;

274 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
85 -> 274 [arrowhead = none ];
274 -> 86;

275 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
86 -> 275 [arrowhead = none ];
275 -> 87;

276 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
88 -> 276 [arrowhead = none ];
276 -> 89;

277 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T49), empty([]))", fontsize=14, style = filled, fillcolor = white];
89 -> 277 [arrowhead = none ];
277 -> 90;

278 [label="EVAL with clause\nhead(.(X103, X104), X103).\nand substitution\nX103 -> T50\nX104 -> T51\nT49 -> .(T50, T51)\nX93 -> T50", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 278 [arrowhead = none ];
278 -> 91;

279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 279 [arrowhead = none ];
279 -> 92;

280 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 280 [arrowhead = none ];
280 -> 93;

281 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
93 -> 281 [arrowhead = none ];
281 -> 94;

282 [label="EVAL with clause\ntail(.(X107, X108), X108).\nand substitution\nT50 -> T52\nX107 -> T52\nT51 -> T53\nX108 -> T53\nX94 -> T53", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 282 [arrowhead = none ];
282 -> 95;

283 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
95 -> 283 [arrowhead = none ];
283 -> 96;

284 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 284 [arrowhead = none ];
284 -> 97;

285 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 285 [arrowhead = none ];
285 -> 98;

286 [label="EVAL with clause\nrev([], X111, X111).\nand substitution\nT53 -> []\nT52 -> T54\nT43 -> T55\nT44 -> T56\nT45 -> T57\nX111 -> .(T54, .(T55, .(T56, .(T57, []))))\nT47 -> .(T54, .(T55, .(T56, .(T57, []))))", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 286 [arrowhead = none ];
286 -> 99;

287 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 287 [arrowhead = none ];
287 -> 100;

288 [label="EVAL with clause\nrev(X115, X116, X117) :- ','(no(empty(X115)), ','(head(X115, X118), ','(tail(X115, X119), rev(X119, .(X118, X116), X117)))).\nand substitution\nT53 -> T58\nX115 -> T58\nT52 -> T59\nT43 -> T60\nT44 -> T61\nT45 -> T62\nX116 -> .(T59, .(T60, .(T61, .(T62, []))))\nT47 -> T64\nX117 -> T64\nT63 -> T64", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 288 [arrowhead = none ];
288 -> 102;

289 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 289 [arrowhead = none ];
289 -> 101;

290 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
102 -> 290 [arrowhead = none ];
290 -> 103;

291 [label="EVAL with clause\nno(X121) :- ','(X121, ','(!, failure(a))).\nand substitution\nT58 -> T65\nX121 -> empty(T65)", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 291 [arrowhead = none ];
291 -> 104;

292 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
104 -> 292 [arrowhead = none ];
292 -> 105;

293 [label="EVAL with clause\nempty([]).\nand substitution\nT65 -> []", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 293 [arrowhead = none ];
293 -> 106;

294 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 294 [arrowhead = none ];
294 -> 107;

295 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
106 -> 295 [arrowhead = none ];
295 -> 108;

296 [label="EVAL with clause\nno(X123).\nand substitution\nT65 -> T66\nX123 -> empty(T66)", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 296 [arrowhead = none ];
296 -> 111;

297 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
108 -> 297 [arrowhead = none ];
297 -> 109;

298 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
109 -> 298 [arrowhead = none ];
298 -> 110;

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 299 [arrowhead = none ];
299 -> 112;

300 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T66), empty([]))", fontsize=14, style = filled, fillcolor = white];
112 -> 300 [arrowhead = none ];
300 -> 113;

301 [label="EVAL with clause\nhead(.(X128, X129), X128).\nand substitution\nX128 -> T67\nX129 -> T68\nT66 -> .(T67, T68)\nX118 -> T67", fontsize=14, style = filled, fillcolor = lightblue];
113 -> 301 [arrowhead = none ];
301 -> 114;

302 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
113 -> 302 [arrowhead = none ];
302 -> 115;

303 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
114 -> 303 [arrowhead = none ];
303 -> 116;

304 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
116 -> 304 [arrowhead = none ];
304 -> 117;

305 [label="EVAL with clause\ntail(.(X132, X133), X133).\nand substitution\nT67 -> T69\nX132 -> T69\nT68 -> T70\nX133 -> T70\nX119 -> T70", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 305 [arrowhead = none ];
305 -> 118;

306 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 306 [arrowhead = none ];
306 -> 119;

307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
119 -> 307 [arrowhead = none ];
307 -> 120;

308 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
119 -> 308 [arrowhead = none ];
308 -> 121;

309 [label="EVAL with clause\nrev([], X136, X136).\nand substitution\nT70 -> []\nT69 -> T71\nT59 -> T72\nT60 -> T73\nT61 -> T74\nT62 -> T75\nX136 -> .(T71, .(T72, .(T73, .(T74, .(T75, [])))))\nT64 -> .(T71, .(T72, .(T73, .(T74, .(T75, [])))))", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 309 [arrowhead = none ];
309 -> 122;

310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 310 [arrowhead = none ];
310 -> 123;

311 [label="EVAL with clause\nrev(X140, X141, X142) :- ','(no(empty(X140)), ','(head(X140, X143), ','(tail(X140, X144), rev(X144, .(X143, X141), X142)))).\nand substitution\nT70 -> T76\nX140 -> T76\nT69 -> T77\nT59 -> T78\nT60 -> T79\nT61 -> T80\nT62 -> T81\nX141 -> .(T77, .(T78, .(T79, .(T80, .(T81, [])))))\nT64 -> T83\nX142 -> T83\nT82 -> T83", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 311 [arrowhead = none ];
311 -> 125;

312 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 312 [arrowhead = none ];
312 -> 124;

313 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 313 [arrowhead = none ];
313 -> 126;

314 [label="EVAL with clause\nno(X146) :- ','(X146, ','(!, failure(a))).\nand substitution\nT76 -> T84\nX146 -> empty(T84)", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 314 [arrowhead = none ];
314 -> 127;

315 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 315 [arrowhead = none ];
315 -> 128;

316 [label="EVAL with clause\nempty([]).\nand substitution\nT84 -> []", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 316 [arrowhead = none ];
316 -> 129;

317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 317 [arrowhead = none ];
317 -> 130;

318 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 318 [arrowhead = none ];
318 -> 131;

319 [label="EVAL with clause\nno(X148).\nand substitution\nT84 -> T85\nX148 -> empty(T85)", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 319 [arrowhead = none ];
319 -> 134;

320 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
131 -> 320 [arrowhead = none ];
320 -> 132;

321 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
132 -> 321 [arrowhead = none ];
321 -> 133;

322 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 322 [arrowhead = none ];
322 -> 135;

323 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T85), empty([]))", fontsize=14, style = filled, fillcolor = white];
135 -> 323 [arrowhead = none ];
323 -> 136;

324 [label="EVAL with clause\nhead(.(X153, X154), X153).\nand substitution\nX153 -> T86\nX154 -> T87\nT85 -> .(T86, T87)\nX143 -> T86", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 324 [arrowhead = none ];
324 -> 137;

325 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 325 [arrowhead = none ];
325 -> 138;

326 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
137 -> 326 [arrowhead = none ];
326 -> 139;

327 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
139 -> 327 [arrowhead = none ];
327 -> 140;

328 [label="EVAL with clause\ntail(.(X157, X158), X158).\nand substitution\nT86 -> T88\nX157 -> T88\nT87 -> T89\nX158 -> T89\nX144 -> T89", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 328 [arrowhead = none ];
328 -> 141;

329 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
141 -> 329 [arrowhead = none ];
329 -> 142;

330 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 330 [arrowhead = none ];
330 -> 143;

331 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 331 [arrowhead = none ];
331 -> 144;

332 [label="EVAL with clause\nrev([], X161, X161).\nand substitution\nT89 -> []\nT88 -> T90\nT77 -> T91\nT78 -> T92\nT79 -> T93\nT80 -> T94\nT81 -> T95\nX161 -> .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))\nT83 -> .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 332 [arrowhead = none ];
332 -> 145;

333 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 333 [arrowhead = none ];
333 -> 146;

334 [label="EVAL with clause\nrev(X165, X166, X167) :- ','(no(empty(X165)), ','(head(X165, X168), ','(tail(X165, X169), rev(X169, .(X168, X166), X167)))).\nand substitution\nT89 -> T96\nX165 -> T96\nT88 -> T97\nT77 -> T98\nT78 -> T99\nT79 -> T100\nT80 -> T101\nT81 -> T102\nX166 -> .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))\nT83 -> T104\nX167 -> T104\nT103 -> T104", fontsize=14, style = filled, fillcolor = lightblue];
144 -> 334 [arrowhead = none ];
334 -> 148;

335 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
145 -> 335 [arrowhead = none ];
335 -> 147;

336 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
148 -> 336 [arrowhead = none ];
336 -> 149;

337 [label="EVAL with clause\nno(X171) :- ','(X171, ','(!, failure(a))).\nand substitution\nT96 -> T105\nX171 -> empty(T105)", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 337 [arrowhead = none ];
337 -> 150;

338 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
150 -> 338 [arrowhead = none ];
338 -> 151;

339 [label="EVAL with clause\nempty([]).\nand substitution\nT105 -> []", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 339 [arrowhead = none ];
339 -> 152;

340 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 340 [arrowhead = none ];
340 -> 153;

341 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
152 -> 341 [arrowhead = none ];
341 -> 154;

342 [label="EVAL with clause\nno(X173).\nand substitution\nT105 -> T106\nX173 -> empty(T106)", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 342 [arrowhead = none ];
342 -> 157;

343 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
154 -> 343 [arrowhead = none ];
343 -> 155;

344 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
155 -> 344 [arrowhead = none ];
344 -> 156;

345 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
157 -> 345 [arrowhead = none ];
345 -> 158;

346 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T106), empty([]))", fontsize=14, style = filled, fillcolor = white];
158 -> 346 [arrowhead = none ];
346 -> 159;

347 [label="EVAL with clause\nhead(.(X178, X179), X178).\nand substitution\nX178 -> T107\nX179 -> T108\nT106 -> .(T107, T108)\nX168 -> T107", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 347 [arrowhead = none ];
347 -> 160;

348 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 348 [arrowhead = none ];
348 -> 161;

349 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
160 -> 349 [arrowhead = none ];
349 -> 162;

350 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
162 -> 350 [arrowhead = none ];
350 -> 163;

351 [label="EVAL with clause\ntail(.(X182, X183), X183).\nand substitution\nT107 -> T109\nX182 -> T109\nT108 -> T110\nX183 -> T110\nX169 -> T110", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 351 [arrowhead = none ];
351 -> 164;

352 [label="GENERALIZATION\nT111 <-- T109\nT112 <-- .(T97, .(T98, .(T99, .(T100, .(T101, .(T102, []))))))\n\nNew Knowledge:\nT111 is ground\nT112 is ground", fontsize=14, style = filled, fillcolor = violet];
164 -> 352 [arrowhead = none ];
352 -> 165;

353 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
165 -> 353 [arrowhead = none ];
353 -> 166;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 354 [arrowhead = none ];
354 -> 167;

355 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 355 [arrowhead = none ];
355 -> 168;

356 [label="EVAL with clause\nrev([], X186, X186).\nand substitution\nT110 -> []\nT111 -> T113\nT112 -> T114\nX186 -> .(T113, T114)\nT104 -> .(T113, T114)", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 356 [arrowhead = none ];
356 -> 169;

357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 357 [arrowhead = none ];
357 -> 170;

358 [label="EVAL with clause\nrev(X190, X191, X192) :- ','(no(empty(X190)), ','(head(X190, X193), ','(tail(X190, X194), rev(X194, .(X193, X191), X192)))).\nand substitution\nT110 -> T115\nX190 -> T115\nT111 -> T116\nT112 -> T117\nX191 -> .(T116, T117)\nT104 -> T119\nX192 -> T119\nT118 -> T119", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 358 [arrowhead = none ];
358 -> 172;

359 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 359 [arrowhead = none ];
359 -> 171;

360 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
172 -> 360 [arrowhead = none ];
360 -> 173;

361 [label="EVAL with clause\nno(X196) :- ','(X196, ','(!, failure(a))).\nand substitution\nT115 -> T120\nX196 -> empty(T120)", fontsize=14, style = filled, fillcolor = lightblue];
173 -> 361 [arrowhead = none ];
361 -> 174;

362 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
174 -> 362 [arrowhead = none ];
362 -> 175;

363 [label="EVAL with clause\nempty([]).\nand substitution\nT120 -> []", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 363 [arrowhead = none ];
363 -> 176;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 364 [arrowhead = none ];
364 -> 177;

365 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
176 -> 365 [arrowhead = none ];
365 -> 178;

366 [label="EVAL with clause\nno(X198).\nand substitution\nT120 -> T121\nX198 -> empty(T121)", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 366 [arrowhead = none ];
366 -> 181;

367 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 367 [arrowhead = none ];
367 -> 179;

368 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
179 -> 368 [arrowhead = none ];
368 -> 180;

369 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
181 -> 369 [arrowhead = none ];
369 -> 182;

370 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (empty(T121), empty([]))", fontsize=14, style = filled, fillcolor = white];
182 -> 370 [arrowhead = none ];
370 -> 183;

371 [label="EVAL with clause\nhead(.(X203, X204), X203).\nand substitution\nX203 -> T122\nX204 -> T123\nT121 -> .(T122, T123)\nX193 -> T122", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 371 [arrowhead = none ];
371 -> 184;

372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 372 [arrowhead = none ];
372 -> 185;

373 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
184 -> 373 [arrowhead = none ];
373 -> 186;

374 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
186 -> 374 [arrowhead = none ];
374 -> 187;

375 [label="EVAL with clause\ntail(.(X207, X208), X208).\nand substitution\nT122 -> T124\nX207 -> T124\nT123 -> T125\nX208 -> T125\nX194 -> T125", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 375 [arrowhead = none ];
375 -> 188;

376 [label="INSTANCE with matching:\nT110 -> T125\nT111 -> T124\nT112 -> .(T116, T117)\nT104 -> T119", fontsize=14, style = filled, fillcolor = lightgrey];
188 -> 376 [arrowhead = none , style=dashed];
376 -> 165[style=dashed];

}

(2) Obligation:

Clauses:

rev165([], T113, T114, .(T113, T114)).
rev165(.(T124, T125), T116, T117, T119) :- rev165(T125, T124, .(T116, T117), T119).
rev1([], []).
rev1(.(T15, []), .(T15, [])).
rev1(.(T27, .(T26, [])), .(T26, .(T27, []))).
rev1(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, [])))).
rev1(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, []))))).
rev1(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, [])))))).
rev1(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))).
rev1(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114)).
rev1(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) :- rev165(T125, T124, .(T116, T117), T119).

Queries:

rev1(g,a).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
rev1_in: (b,f)
rev165_in: (b,f,f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T15, []), .(T15, [])) → rev1_out_ga(.(T15, []), .(T15, []))
rev1_in_ga(.(T27, .(T26, [])), .(T26, .(T27, []))) → rev1_out_ga(.(T27, .(T26, [])), .(T26, .(T27, [])))
rev1_in_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, [])))) → rev1_out_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, []))))
rev1_in_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, []))))) → rev1_out_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, [])))))
rev1_in_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, [])))))) → rev1_out_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, []))))))
rev1_in_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))) → rev1_out_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, [])))))))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
rev165_in_gaaa([], T113, T114, .(T113, T114)) → rev165_out_gaaa([], T113, T114, .(T113, T114))
rev165_in_gaaa(.(T124, T125), T116, T117, T119) → U1_gaaa(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
U1_gaaa(T124, T125, T116, T117, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev165_out_gaaa(.(T124, T125), T116, T117, T119)
U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T15, []), .(T15, [])) → rev1_out_ga(.(T15, []), .(T15, []))
rev1_in_ga(.(T27, .(T26, [])), .(T26, .(T27, []))) → rev1_out_ga(.(T27, .(T26, [])), .(T26, .(T27, [])))
rev1_in_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, [])))) → rev1_out_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, []))))
rev1_in_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, []))))) → rev1_out_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, [])))))
rev1_in_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, [])))))) → rev1_out_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, []))))))
rev1_in_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))) → rev1_out_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, [])))))))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
rev165_in_gaaa([], T113, T114, .(T113, T114)) → rev165_out_gaaa([], T113, T114, .(T113, T114))
rev165_in_gaaa(.(T124, T125), T116, T117, T119) → U1_gaaa(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
U1_gaaa(T124, T125, T116, T117, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev165_out_gaaa(.(T124, T125), T116, T117, T119)
U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119)

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

REV1_IN_GA(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_GA(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
REV1_IN_GA(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → REV165_IN_GAAA(T125, T124, .(T116, T117), T119)
REV165_IN_GAAA(.(T124, T125), T116, T117, T119) → U1_GAAA(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
REV165_IN_GAAA(.(T124, T125), T116, T117, T119) → REV165_IN_GAAA(T125, T124, .(T116, T117), T119)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T15, []), .(T15, [])) → rev1_out_ga(.(T15, []), .(T15, []))
rev1_in_ga(.(T27, .(T26, [])), .(T26, .(T27, []))) → rev1_out_ga(.(T27, .(T26, [])), .(T26, .(T27, [])))
rev1_in_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, [])))) → rev1_out_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, []))))
rev1_in_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, []))))) → rev1_out_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, [])))))
rev1_in_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, [])))))) → rev1_out_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, []))))))
rev1_in_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))) → rev1_out_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, [])))))))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
rev165_in_gaaa([], T113, T114, .(T113, T114)) → rev165_out_gaaa([], T113, T114, .(T113, T114))
rev165_in_gaaa(.(T124, T125), T116, T117, T119) → U1_gaaa(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
U1_gaaa(T124, T125, T116, T117, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev165_out_gaaa(.(T124, T125), T116, T117, T119)
U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2) = rev1_in_ga(x1)
[] = []
rev1_out_ga(x1, x2) = rev1_out_ga
.(x1, x2) = .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U2_ga(x11)
rev165_in_gaaa(x1, x2, x3, x4) = rev165_in_gaaa(x1)
rev165_out_gaaa(x1, x2, x3, x4) = rev165_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6) = U1_gaaa(x6)
REV1_IN_GA(x1, x2) = REV1_IN_GA(x1)
U2_GA(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U2_GA(x11)
REV165_IN_GAAA(x1, x2, x3, x4) = REV165_IN_GAAA(x1)
U1_GAAA(x1, x2, x3, x4, x5, x6) = U1_GAAA(x6)

We have to consider all (P,R,Pi)-chains

(6) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

REV1_IN_GA(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_GA(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
REV1_IN_GA(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → REV165_IN_GAAA(T125, T124, .(T116, T117), T119)
REV165_IN_GAAA(.(T124, T125), T116, T117, T119) → U1_GAAA(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
REV165_IN_GAAA(.(T124, T125), T116, T117, T119) → REV165_IN_GAAA(T125, T124, .(T116, T117), T119)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T15, []), .(T15, [])) → rev1_out_ga(.(T15, []), .(T15, []))
rev1_in_ga(.(T27, .(T26, [])), .(T26, .(T27, []))) → rev1_out_ga(.(T27, .(T26, [])), .(T26, .(T27, [])))
rev1_in_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, [])))) → rev1_out_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, []))))
rev1_in_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, []))))) → rev1_out_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, [])))))
rev1_in_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, [])))))) → rev1_out_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, []))))))
rev1_in_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))) → rev1_out_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, [])))))))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
rev165_in_gaaa([], T113, T114, .(T113, T114)) → rev165_out_gaaa([], T113, T114, .(T113, T114))
rev165_in_gaaa(.(T124, T125), T116, T117, T119) → U1_gaaa(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
U1_gaaa(T124, T125, T116, T117, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev165_out_gaaa(.(T124, T125), T116, T117, T119)
U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119)

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 3 less nodes.

(8) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

REV165_IN_GAAA(.(T124, T125), T116, T117, T119) → REV165_IN_GAAA(T125, T124, .(T116, T117), T119)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T15, []), .(T15, [])) → rev1_out_ga(.(T15, []), .(T15, []))
rev1_in_ga(.(T27, .(T26, [])), .(T26, .(T27, []))) → rev1_out_ga(.(T27, .(T26, [])), .(T26, .(T27, [])))
rev1_in_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, [])))) → rev1_out_ga(.(T41, .(T40, .(T39, []))), .(T39, .(T40, .(T41, []))))
rev1_in_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, []))))) → rev1_out_ga(.(T57, .(T56, .(T55, .(T54, [])))), .(T54, .(T55, .(T56, .(T57, [])))))
rev1_in_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, [])))))) → rev1_out_ga(.(T75, .(T74, .(T73, .(T72, .(T71, []))))), .(T71, .(T72, .(T73, .(T74, .(T75, []))))))
rev1_in_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, []))))))) → rev1_out_ga(.(T95, .(T94, .(T93, .(T92, .(T91, .(T90, [])))))), .(T90, .(T91, .(T92, .(T93, .(T94, .(T95, [])))))))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, []))))))), .(T113, T114))
rev1_in_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119) → U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
rev165_in_gaaa([], T113, T114, .(T113, T114)) → rev165_out_gaaa([], T113, T114, .(T113, T114))
rev165_in_gaaa(.(T124, T125), T116, T117, T119) → U1_gaaa(T124, T125, T116, T117, T119, rev165_in_gaaa(T125, T124, .(T116, T117), T119))
U1_gaaa(T124, T125, T116, T117, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev165_out_gaaa(.(T124, T125), T116, T117, T119)
U2_ga(T102, T101, T100, T99, T98, T97, T109, T124, T125, T119, rev165_out_gaaa(T125, T124, .(T116, T117), T119)) → rev1_out_ga(.(T102, .(T101, .(T100, .(T99, .(T98, .(T97, .(T109, .(T124, T125)))))))), T119)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2) = rev1_in_ga(x1)
[] = []
rev1_out_ga(x1, x2) = rev1_out_ga
.(x1, x2) = .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U2_ga(x11)
rev165_in_gaaa(x1, x2, x3, x4) = rev165_in_gaaa(x1)
rev165_out_gaaa(x1, x2, x3, x4) = rev165_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6) = U1_gaaa(x6)
REV165_IN_GAAA(x1, x2, x3, x4) = REV165_IN_GAAA(x1)

We have to consider all (P,R,Pi)-chains

(9) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(10) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

REV165_IN_GAAA(.(T124, T125), T116, T117, T119) → REV165_IN_GAAA(T125, T124, .(T116, T117), T119)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x2)
REV165_IN_GAAA(x1, x2, x3, x4) = REV165_IN_GAAA(x1)

We have to consider all (P,R,Pi)-chains

(11) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(12) Obligation:

Q DP problem:
The TRS P consists of the following rules:

REV165_IN_GAAA(.(T125)) → REV165_IN_GAAA(T125)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(13) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

REV165_IN_GAAA(.(T125)) → REV165_IN_GAAA(T125)
The graph contains the following edges 1 > 1

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Obligation:

(9) UsableRulesProof (EQUIVALENT transformation)

(10) Obligation:

(11) PiDPToQDPProof (SOUND transformation)

(12) Obligation:

(13) QDPSizeChangeProof (EQUIVALENT transformation)

(14) TRUE