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

(0) Obligation:

Clauses:

rev(L, R) :- rev(L, [], R).
rev([], Y, Z) :- ','(!, eq(Y, Z)).
rev(L, S, R) :- ','(head(L, X), ','(tail(L, T), rev(T, .(X, S), R))).
head([], X1).
head(.(X, X2), X).
tail([], []).
tail(.(X3, Xs), Xs).
eq(X, X).

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 | ?_2\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(!_2, eq([], T7)) | rev([], [], T5), SCOPE: 2, CLAUSE: 2 | ?_2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: rev(T3, [], T5), SCOPE: 2, CLAUSE: 2\n\nT3 is ground\nX10 is free; \nX11 is free; \nrev(T3, [], T5) !=? rev([], X10, X11)", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: eq([], T7)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: eq([], T7), SCOPE: 3, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: \n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(head(T8, X20), ','(tail(T8, X21), rev(X21, .(X20, []), T10)))\n\nT8 is ground\nX10 is free; \nX11 is free; \nX20 is free; \nX21 is free; \nrev(T8, [], T5) !=? rev([], X10, X11)", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(head(T8, X20), ','(tail(T8, X21), rev(X21, .(X20, []), T10))), SCOPE: 4, CLAUSE: 3 | ','(head(T8, X20), ','(tail(T8, X21), rev(X21, .(X20, []), T10))), SCOPE: 4, CLAUSE: 4\n\nT8 is ground\nX10 is free; \nX11 is free; \nX20 is free; \nX21 is free; \nrev(T8, [], T5) !=? rev([], X10, X11)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ','(head(T8, X20), ','(tail(T8, X21), rev(X21, .(X20, []), T10))), SCOPE: 4, CLAUSE: 4\n\nT8 is ground\nX10 is free; \nX11 is free; \nX20 is free; \nX21 is free; \nX23 is free; \nrev(T8, [], T5) !=? rev([], X10, X11)\nhead(T8, X20) !=? head([], X23)", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(tail(.(T11, T12), X21), rev(X21, .(T11, []), T10))\n\nT11 is ground\nT12 is ground\nX10 is free; \nX11 is free; \nX20 is free; \nX21 is free; \nX23 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: \n\nX10 is free\nX11 is free; \nX20 is free; \nX23 is free; \nX26 is free; \nX27 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(tail(.(T11, T12), X21), rev(X21, .(T11, []), T10)), SCOPE: 5, CLAUSE: 5 | ','(tail(.(T11, T12), X21), rev(X21, .(T11, []), T10)), SCOPE: 5, CLAUSE: 6\n\nT11 is ground\nT12 is ground\nX21 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(tail(.(T11, T12), X21), rev(X21, .(T11, []), T10)), SCOPE: 5, CLAUSE: 6\n\nT11 is ground\nT12 is ground\nX21 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: rev(T14, .(T13, []), T10)\n\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: rev(T14, .(T13, []), T10), SCOPE: 6, CLAUSE: 1 | rev(T14, .(T13, []), T10), SCOPE: 6, CLAUSE: 2 | ?_6\n\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(!_6, eq(.(T15, []), T17)) | rev([], .(T15, []), T10), SCOPE: 6, CLAUSE: 2 | ?_6\n\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: rev(T14, .(T13, []), T10), SCOPE: 6, CLAUSE: 2\n\nT13 is ground\nT14 is ground\nX34 is free; \nX35 is free; \nrev(T14, .(T13, []), T10) !=? rev([], X34, X35)", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: eq(.(T15, []), T17)\n\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: eq(.(T15, []), T17), SCOPE: 7, CLAUSE: 7\n\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(head(T19, X44), ','(tail(T19, X45), rev(X45, .(X44, .(T20, [])), T22)))\n\nT19 is ground\nT20 is ground\nX34 is free; \nX35 is free; \nX44 is free; \nX45 is free; \nrev(T19, .(T20, []), T10) !=? rev([], X34, X35)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(head(T19, X44), ','(tail(T19, X45), rev(X45, .(X44, .(T20, [])), T22))), SCOPE: 8, CLAUSE: 3 | ','(head(T19, X44), ','(tail(T19, X45), rev(X45, .(X44, .(T20, [])), T22))), SCOPE: 8, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nX34 is free; \nX35 is free; \nX44 is free; \nX45 is free; \nrev(T19, .(T20, []), T10) !=? rev([], X34, X35)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(head(T19, X44), ','(tail(T19, X45), rev(X45, .(X44, .(T20, [])), T22))), SCOPE: 8, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nX34 is free; \nX35 is free; \nX44 is free; \nX45 is free; \nX47 is free; \nrev(T19, .(T20, []), T10) !=? rev([], X34, X35)\nhead(T19, X44) !=? head([], X47)", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(tail(.(T23, T24), X45), rev(X45, .(T23, .(T20, [])), T22))\n\nT20 is ground\nT23 is ground\nT24 is ground\nX34 is free; \nX35 is free; \nX44 is free; \nX45 is free; \nX47 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\nX34 is free\nX35 is free; \nX44 is free; \nX47 is free; \nX50 is free; \nX51 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(tail(.(T23, T24), X45), rev(X45, .(T23, .(T20, [])), T22)), SCOPE: 9, CLAUSE: 5 | ','(tail(.(T23, T24), X45), rev(X45, .(T23, .(T20, [])), T22)), SCOPE: 9, CLAUSE: 6\n\nT20 is ground\nT23 is ground\nT24 is ground\nX45 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(tail(.(T23, T24), X45), rev(X45, .(T23, .(T20, [])), T22)), SCOPE: 9, CLAUSE: 6\n\nT20 is ground\nT23 is ground\nT24 is ground\nX45 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: rev(T26, .(T25, .(T20, [])), T22)\n\nT20 is ground\nT25 is ground\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: rev(T26, .(T25, .(T20, [])), T22), SCOPE: 10, CLAUSE: 1 | rev(T26, .(T25, .(T20, [])), T22), SCOPE: 10, CLAUSE: 2 | ?_10\n\nT20 is ground\nT25 is ground\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(!_10, eq(.(T27, .(T28, [])), T30)) | rev([], .(T27, .(T28, [])), T22), SCOPE: 10, CLAUSE: 2 | ?_10\n\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: rev(T26, .(T25, .(T20, [])), T22), SCOPE: 10, CLAUSE: 2\n\nT20 is ground\nT25 is ground\nT26 is ground\nX58 is free; \nX59 is free; \nrev(T26, .(T25, .(T20, [])), T22) !=? rev([], X58, X59)", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: eq(.(T27, .(T28, [])), T30)\n\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: eq(.(T27, .(T28, [])), T30), SCOPE: 11, CLAUSE: 7\n\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\nX61 is free", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T34, .(T35, []))), T37)))\n\nT33 is ground\nT34 is ground\nT35 is ground\nX58 is free; \nX59 is free; \nX68 is free; \nX69 is free; \nrev(T33, .(T34, .(T35, [])), T22) !=? rev([], X58, X59)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T34, .(T35, []))), T37))), SCOPE: 12, CLAUSE: 3 | ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T34, .(T35, []))), T37))), SCOPE: 12, CLAUSE: 4\n\nT33 is ground\nT34 is ground\nT35 is ground\nX58 is free; \nX59 is free; \nX68 is free; \nX69 is free; \nrev(T33, .(T34, .(T35, [])), T22) !=? rev([], X58, X59)", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(head(T33, X68), ','(tail(T33, X69), rev(X69, .(X68, .(T34, .(T35, []))), T37))), SCOPE: 12, CLAUSE: 4\n\nT33 is ground\nT34 is ground\nT35 is ground\nX58 is free; \nX59 is free; \nX68 is free; \nX69 is free; \nX71 is free; \nrev(T33, .(T34, .(T35, [])), T22) !=? rev([], X58, X59)\nhead(T33, X68) !=? head([], X71)", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(tail(.(T38, T39), X69), rev(X69, .(T38, .(T34, .(T35, []))), T37))\n\nT34 is ground\nT35 is ground\nT38 is ground\nT39 is ground\nX58 is free; \nX59 is free; \nX68 is free; \nX69 is free; \nX71 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\nX58 is free\nX59 is free; \nX68 is free; \nX71 is free; \nX74 is free; \nX75 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(tail(.(T38, T39), X69), rev(X69, .(T38, .(T34, .(T35, []))), T37)), SCOPE: 13, CLAUSE: 5 | ','(tail(.(T38, T39), X69), rev(X69, .(T38, .(T34, .(T35, []))), T37)), SCOPE: 13, CLAUSE: 6\n\nT34 is ground\nT35 is ground\nT38 is ground\nT39 is ground\nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(tail(.(T38, T39), X69), rev(X69, .(T38, .(T34, .(T35, []))), T37)), SCOPE: 13, CLAUSE: 6\n\nT34 is ground\nT35 is ground\nT38 is ground\nT39 is ground\nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: rev(T41, .(T40, .(T34, .(T35, []))), T37)\n\nT34 is ground\nT35 is ground\nT40 is ground\nT41 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: rev(T41, .(T40, .(T34, .(T35, []))), T37), SCOPE: 14, CLAUSE: 1 | rev(T41, .(T40, .(T34, .(T35, []))), T37), SCOPE: 14, CLAUSE: 2 | ?_14\n\nT34 is ground\nT35 is ground\nT40 is ground\nT41 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(!_14, eq(.(T42, .(T43, .(T44, []))), T46)) | rev([], .(T42, .(T43, .(T44, []))), T37), SCOPE: 14, CLAUSE: 2 | ?_14\n\nT42 is ground\nT43 is ground\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: rev(T41, .(T40, .(T34, .(T35, []))), T37), SCOPE: 14, CLAUSE: 2\n\nT34 is ground\nT35 is ground\nT40 is ground\nT41 is ground\nX82 is free; \nX83 is free; \nrev(T41, .(T40, .(T34, .(T35, []))), T37) !=? rev([], X82, X83)", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: eq(.(T42, .(T43, .(T44, []))), T46)\n\nT42 is ground\nT43 is ground\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: eq(.(T42, .(T43, .(T44, []))), T46), SCOPE: 15, CLAUSE: 7\n\nT42 is ground\nT43 is ground\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\nX85 is free", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(head(T50, X92), ','(tail(T50, X93), rev(X93, .(X92, .(T51, .(T52, .(T53, [])))), T55)))\n\nT50 is ground\nT51 is ground\nT52 is ground\nT53 is ground\nX82 is free; \nX83 is free; \nX92 is free; \nX93 is free; \nrev(T50, .(T51, .(T52, .(T53, []))), T37) !=? rev([], X82, X83)", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(head(T50, X92), ','(tail(T50, X93), rev(X93, .(X92, .(T51, .(T52, .(T53, [])))), T55))), SCOPE: 16, CLAUSE: 3 | ','(head(T50, X92), ','(tail(T50, X93), rev(X93, .(X92, .(T51, .(T52, .(T53, [])))), T55))), SCOPE: 16, CLAUSE: 4\n\nT50 is ground\nT51 is ground\nT52 is ground\nT53 is ground\nX82 is free; \nX83 is free; \nX92 is free; \nX93 is free; \nrev(T50, .(T51, .(T52, .(T53, []))), T37) !=? rev([], X82, X83)", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(head(T50, X92), ','(tail(T50, X93), rev(X93, .(X92, .(T51, .(T52, .(T53, [])))), T55))), SCOPE: 16, CLAUSE: 4\n\nT50 is ground\nT51 is ground\nT52 is ground\nT53 is ground\nX82 is free; \nX83 is free; \nX92 is free; \nX93 is free; \nX95 is free; \nrev(T50, .(T51, .(T52, .(T53, []))), T37) !=? rev([], X82, X83)\nhead(T50, X92) !=? head([], X95)", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(tail(.(T56, T57), X93), rev(X93, .(T56, .(T51, .(T52, .(T53, [])))), T55))\n\nT51 is ground\nT52 is ground\nT53 is ground\nT56 is ground\nT57 is ground\nX82 is free; \nX83 is free; \nX92 is free; \nX93 is free; \nX95 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\nX82 is free\nX83 is free; \nX92 is free; \nX95 is free; \nX98 is free; \nX99 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(tail(.(T56, T57), X93), rev(X93, .(T56, .(T51, .(T52, .(T53, [])))), T55)), SCOPE: 17, CLAUSE: 5 | ','(tail(.(T56, T57), X93), rev(X93, .(T56, .(T51, .(T52, .(T53, [])))), T55)), SCOPE: 17, CLAUSE: 6\n\nT51 is ground\nT52 is ground\nT53 is ground\nT56 is ground\nT57 is ground\nX93 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(tail(.(T56, T57), X93), rev(X93, .(T56, .(T51, .(T52, .(T53, [])))), T55)), SCOPE: 17, CLAUSE: 6\n\nT51 is ground\nT52 is ground\nT53 is ground\nT56 is ground\nT57 is ground\nX93 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: rev(T59, .(T58, .(T51, .(T52, .(T53, [])))), T55)\n\nT51 is ground\nT52 is ground\nT53 is ground\nT58 is ground\nT59 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: rev(T59, .(T58, .(T51, .(T52, .(T53, [])))), T55), SCOPE: 18, CLAUSE: 1 | rev(T59, .(T58, .(T51, .(T52, .(T53, [])))), T55), SCOPE: 18, CLAUSE: 2 | ?_18\n\nT51 is ground\nT52 is ground\nT53 is ground\nT58 is ground\nT59 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(!_18, eq(.(T60, .(T61, .(T62, .(T63, [])))), T65)) | rev([], .(T60, .(T61, .(T62, .(T63, [])))), T55), SCOPE: 18, CLAUSE: 2 | ?_18\n\nT60 is ground\nT61 is ground\nT62 is ground\nT63 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: rev(T59, .(T58, .(T51, .(T52, .(T53, [])))), T55), SCOPE: 18, CLAUSE: 2\n\nT51 is ground\nT52 is ground\nT53 is ground\nT58 is ground\nT59 is ground\nX106 is free; \nX107 is free; \nrev(T59, .(T58, .(T51, .(T52, .(T53, [])))), T55) !=? rev([], X106, X107)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: eq(.(T60, .(T61, .(T62, .(T63, [])))), T65)\n\nT60 is ground\nT61 is ground\nT62 is ground\nT63 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: eq(.(T60, .(T61, .(T62, .(T63, [])))), T65), SCOPE: 19, CLAUSE: 7\n\nT60 is ground\nT61 is ground\nT62 is ground\nT63 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\nX109 is free", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(head(T70, X116), ','(tail(T70, X117), rev(X117, .(X116, .(T71, .(T72, .(T73, .(T74, []))))), T76)))\n\nT70 is ground\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nX106 is free; \nX107 is free; \nX116 is free; \nX117 is free; \nrev(T70, .(T71, .(T72, .(T73, .(T74, [])))), T55) !=? rev([], X106, X107)", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(head(T70, X116), ','(tail(T70, X117), rev(X117, .(X116, .(T71, .(T72, .(T73, .(T74, []))))), T76))), SCOPE: 20, CLAUSE: 3 | ','(head(T70, X116), ','(tail(T70, X117), rev(X117, .(X116, .(T71, .(T72, .(T73, .(T74, []))))), T76))), SCOPE: 20, CLAUSE: 4\n\nT70 is ground\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nX106 is free; \nX107 is free; \nX116 is free; \nX117 is free; \nrev(T70, .(T71, .(T72, .(T73, .(T74, [])))), T55) !=? rev([], X106, X107)", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(head(T70, X116), ','(tail(T70, X117), rev(X117, .(X116, .(T71, .(T72, .(T73, .(T74, []))))), T76))), SCOPE: 20, CLAUSE: 4\n\nT70 is ground\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nX106 is free; \nX107 is free; \nX116 is free; \nX117 is free; \nX119 is free; \nrev(T70, .(T71, .(T72, .(T73, .(T74, [])))), T55) !=? rev([], X106, X107)\nhead(T70, X116) !=? head([], X119)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(tail(.(T77, T78), X117), rev(X117, .(T77, .(T71, .(T72, .(T73, .(T74, []))))), T76))\n\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nT77 is ground\nT78 is ground\nX106 is free; \nX107 is free; \nX116 is free; \nX117 is free; \nX119 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: \n\nX106 is free\nX107 is free; \nX116 is free; \nX119 is free; \nX122 is free; \nX123 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(tail(.(T77, T78), X117), rev(X117, .(T77, .(T71, .(T72, .(T73, .(T74, []))))), T76)), SCOPE: 21, CLAUSE: 5 | ','(tail(.(T77, T78), X117), rev(X117, .(T77, .(T71, .(T72, .(T73, .(T74, []))))), T76)), SCOPE: 21, CLAUSE: 6\n\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nT77 is ground\nT78 is ground\nX117 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(tail(.(T77, T78), X117), rev(X117, .(T77, .(T71, .(T72, .(T73, .(T74, []))))), T76)), SCOPE: 21, CLAUSE: 6\n\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nT77 is ground\nT78 is ground\nX117 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: rev(T80, .(T79, .(T71, .(T72, .(T73, .(T74, []))))), T76)\n\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nT79 is ground\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: rev(T80, .(T79, .(T71, .(T72, .(T73, .(T74, []))))), T76), SCOPE: 22, CLAUSE: 1 | rev(T80, .(T79, .(T71, .(T72, .(T73, .(T74, []))))), T76), SCOPE: 22, CLAUSE: 2 | ?_22\n\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nT79 is ground\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(!_22, eq(.(T81, .(T82, .(T83, .(T84, .(T85, []))))), T87)) | rev([], .(T81, .(T82, .(T83, .(T84, .(T85, []))))), T76), SCOPE: 22, CLAUSE: 2 | ?_22\n\nT81 is ground\nT82 is ground\nT83 is ground\nT84 is ground\nT85 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: rev(T80, .(T79, .(T71, .(T72, .(T73, .(T74, []))))), T76), SCOPE: 22, CLAUSE: 2\n\nT71 is ground\nT72 is ground\nT73 is ground\nT74 is ground\nT79 is ground\nT80 is ground\nX130 is free; \nX131 is free; \nrev(T80, .(T79, .(T71, .(T72, .(T73, .(T74, []))))), T76) !=? rev([], X130, X131)", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: eq(.(T81, .(T82, .(T83, .(T84, .(T85, []))))), T87)\n\nT81 is ground\nT82 is ground\nT83 is ground\nT84 is ground\nT85 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: eq(.(T81, .(T82, .(T83, .(T84, .(T85, []))))), T87), SCOPE: 23, CLAUSE: 7\n\nT81 is ground\nT82 is ground\nT83 is ground\nT84 is ground\nT85 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\nX133 is free", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(head(T93, X140), ','(tail(T93, X141), rev(X141, .(X140, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100)))\n\nT93 is ground\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nX130 is free; \nX131 is free; \nX140 is free; \nX141 is free; \nrev(T93, .(T94, .(T95, .(T96, .(T97, .(T98, []))))), T76) !=? rev([], X130, X131)", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(head(T93, X140), ','(tail(T93, X141), rev(X141, .(X140, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100))), SCOPE: 24, CLAUSE: 3 | ','(head(T93, X140), ','(tail(T93, X141), rev(X141, .(X140, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100))), SCOPE: 24, CLAUSE: 4\n\nT93 is ground\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nX130 is free; \nX131 is free; \nX140 is free; \nX141 is free; \nrev(T93, .(T94, .(T95, .(T96, .(T97, .(T98, []))))), T76) !=? rev([], X130, X131)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(head(T93, X140), ','(tail(T93, X141), rev(X141, .(X140, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100))), SCOPE: 24, CLAUSE: 4\n\nT93 is ground\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nX130 is free; \nX131 is free; \nX140 is free; \nX141 is free; \nX143 is free; \nrev(T93, .(T94, .(T95, .(T96, .(T97, .(T98, []))))), T76) !=? rev([], X130, X131)\nhead(T93, X140) !=? head([], X143)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: ','(tail(.(T101, T102), X141), rev(X141, .(T101, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100))\n\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nT101 is ground\nT102 is ground\nX130 is free; \nX131 is free; \nX140 is free; \nX141 is free; \nX143 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\nX130 is free\nX131 is free; \nX140 is free; \nX143 is free; \nX146 is free; \nX147 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(tail(.(T101, T102), X141), rev(X141, .(T101, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100)), SCOPE: 25, CLAUSE: 5 | ','(tail(.(T101, T102), X141), rev(X141, .(T101, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100)), SCOPE: 25, CLAUSE: 6\n\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nT101 is ground\nT102 is ground\nX141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(tail(.(T101, T102), X141), rev(X141, .(T101, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100)), SCOPE: 25, CLAUSE: 6\n\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nT101 is ground\nT102 is ground\nX141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: rev(T104, .(T103, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100)\n\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nT103 is ground\nT104 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: rev(T104, .(T103, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100), SCOPE: 26, CLAUSE: 1 | rev(T104, .(T103, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100), SCOPE: 26, CLAUSE: 2 | ?_26\n\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nT103 is ground\nT104 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(!_26, eq(.(T105, .(T106, .(T107, .(T108, .(T109, .(T110, [])))))), T112)) | rev([], .(T105, .(T106, .(T107, .(T108, .(T109, .(T110, [])))))), T100), SCOPE: 26, CLAUSE: 2 | ?_26\n\nT105 is ground\nT106 is ground\nT107 is ground\nT108 is ground\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: rev(T104, .(T103, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100), SCOPE: 26, CLAUSE: 2\n\nT94 is ground\nT95 is ground\nT96 is ground\nT97 is ground\nT98 is ground\nT103 is ground\nT104 is ground\nX154 is free; \nX155 is free; \nrev(T104, .(T103, .(T94, .(T95, .(T96, .(T97, .(T98, [])))))), T100) !=? rev([], X154, X155)", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: eq(.(T105, .(T106, .(T107, .(T108, .(T109, .(T110, [])))))), T112)\n\nT105 is ground\nT106 is ground\nT107 is ground\nT108 is ground\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: eq(.(T105, .(T106, .(T107, .(T108, .(T109, .(T110, [])))))), T112), SCOPE: 27, CLAUSE: 7\n\nT105 is ground\nT106 is ground\nT107 is ground\nT108 is ground\nT109 is ground\nT110 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\nX157 is free", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(head(T119, X164), ','(tail(T119, X165), rev(X165, .(X164, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127)))\n\nT119 is ground\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nX154 is free; \nX155 is free; \nX164 is free; \nX165 is free; \nrev(T119, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, [])))))), T100) !=? rev([], X154, X155)", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(head(T119, X164), ','(tail(T119, X165), rev(X165, .(X164, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127))), SCOPE: 28, CLAUSE: 3 | ','(head(T119, X164), ','(tail(T119, X165), rev(X165, .(X164, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127))), SCOPE: 28, CLAUSE: 4\n\nT119 is ground\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nX154 is free; \nX155 is free; \nX164 is free; \nX165 is free; \nrev(T119, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, [])))))), T100) !=? rev([], X154, X155)", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(head(T119, X164), ','(tail(T119, X165), rev(X165, .(X164, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127))), SCOPE: 28, CLAUSE: 4\n\nT119 is ground\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nX154 is free; \nX155 is free; \nX164 is free; \nX165 is free; \nX167 is free; \nrev(T119, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, [])))))), T100) !=? rev([], X154, X155)\nhead(T119, X164) !=? head([], X167)", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(tail(.(T128, T129), X165), rev(X165, .(T128, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127))\n\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nT128 is ground\nT129 is ground\nX154 is free; \nX155 is free; \nX164 is free; \nX165 is free; \nX167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\nX154 is free\nX155 is free; \nX164 is free; \nX167 is free; \nX170 is free; \nX171 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(tail(.(T128, T129), X165), rev(X165, .(T128, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127)), SCOPE: 29, CLAUSE: 5 | ','(tail(.(T128, T129), X165), rev(X165, .(T128, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127)), SCOPE: 29, CLAUSE: 6\n\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nT128 is ground\nT129 is ground\nX165 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(tail(.(T128, T129), X165), rev(X165, .(T128, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127)), SCOPE: 29, CLAUSE: 6\n\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nT128 is ground\nT129 is ground\nX165 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: rev(T131, .(T130, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))), T127)\n\nT120 is ground\nT121 is ground\nT122 is ground\nT123 is ground\nT124 is ground\nT125 is ground\nT130 is ground\nT131 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: rev(T131, .(T132, T133), T127)\n\nT131 is ground\nT132 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: rev(T131, .(T132, T133), T127), SCOPE: 30, CLAUSE: 1 | rev(T131, .(T132, T133), T127), SCOPE: 30, CLAUSE: 2 | ?_30\n\nT131 is ground\nT132 is ground\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(!_30, eq(.(T134, T135), T137)) | rev([], .(T134, T135), T127), SCOPE: 30, CLAUSE: 2 | ?_30\n\nT134 is ground\nT135 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: rev(T131, .(T132, T133), T127), SCOPE: 30, CLAUSE: 2\n\nT131 is ground\nT132 is ground\nT133 is ground\nX178 is free; \nX179 is free; \nrev(T131, .(T132, T133), T127) !=? rev([], X178, X179)", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: eq(.(T134, T135), T137)\n\nT134 is ground\nT135 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: eq(.(T134, T135), T137), SCOPE: 31, CLAUSE: 7\n\nT134 is ground\nT135 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\nX181 is free", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(head(T140, X188), ','(tail(T140, X189), rev(X189, .(X188, .(T141, T142)), T144)))\n\nT140 is ground\nT141 is ground\nT142 is ground\nX178 is free; \nX179 is free; \nX188 is free; \nX189 is free; \nrev(T140, .(T141, T142), T127) !=? rev([], X178, X179)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ','(head(T140, X188), ','(tail(T140, X189), rev(X189, .(X188, .(T141, T142)), T144))), SCOPE: 32, CLAUSE: 3 | ','(head(T140, X188), ','(tail(T140, X189), rev(X189, .(X188, .(T141, T142)), T144))), SCOPE: 32, CLAUSE: 4\n\nT140 is ground\nT141 is ground\nT142 is ground\nX178 is free; \nX179 is free; \nX188 is free; \nX189 is free; \nrev(T140, .(T141, T142), T127) !=? rev([], X178, X179)", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(head(T140, X188), ','(tail(T140, X189), rev(X189, .(X188, .(T141, T142)), T144))), SCOPE: 32, CLAUSE: 4\n\nT140 is ground\nT141 is ground\nT142 is ground\nX178 is free; \nX179 is free; \nX188 is free; \nX189 is free; \nX191 is free; \nrev(T140, .(T141, T142), T127) !=? rev([], X178, X179)\nhead(T140, X188) !=? head([], X191)", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(tail(.(T145, T146), X189), rev(X189, .(T145, .(T141, T142)), T144))\n\nT141 is ground\nT142 is ground\nT145 is ground\nT146 is ground\nX178 is free; \nX179 is free; \nX188 is free; \nX189 is free; \nX191 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\nX178 is free\nX179 is free; \nX188 is free; \nX191 is free; \nX194 is free; \nX195 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: ','(tail(.(T145, T146), X189), rev(X189, .(T145, .(T141, T142)), T144)), SCOPE: 33, CLAUSE: 5 | ','(tail(.(T145, T146), X189), rev(X189, .(T145, .(T141, T142)), T144)), SCOPE: 33, CLAUSE: 6\n\nT141 is ground\nT142 is ground\nT145 is ground\nT146 is ground\nX189 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(tail(.(T145, T146), X189), rev(X189, .(T145, .(T141, T142)), T144)), SCOPE: 33, CLAUSE: 6\n\nT141 is ground\nT142 is ground\nT145 is ground\nT146 is ground\nX189 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: rev(T148, .(T147, .(T141, T142)), T144)\n\nT141 is ground\nT142 is ground\nT147 is ground\nT148 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 133 [arrowhead = none ];
133 -> 2;

134 [label="EVAL with clause\nrev(X6, X7) :- rev(X6, [], X7).\nand substitution\nT1 -> T3\nX6 -> T3\nT2 -> T5\nX7 -> T5\nT4 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 134 [arrowhead = none ];
134 -> 3;

135 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 135 [arrowhead = none ];
135 -> 4;

136 [label="EVAL with clause\nrev([], X10, X11) :- ','(!, eq(X10, X11)).\nand substitution\nT3 -> []\nX10 -> []\nT5 -> T7\nX11 -> T7\nT6 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 136 [arrowhead = none ];
136 -> 5;

137 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 137 [arrowhead = none ];
137 -> 6;

138 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 138 [arrowhead = none ];
138 -> 7;

139 [label="EVAL with clause\nrev(X17, X18, X19) :- ','(head(X17, X20), ','(tail(X17, X21), rev(X21, .(X20, X18), X19))).\nand substitution\nT3 -> T8\nX17 -> T8\nX18 -> []\nT5 -> T10\nX19 -> T10\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 139 [arrowhead = none ];
139 -> 12;

140 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 140 [arrowhead = none ];
140 -> 8;

141 [label="EVAL with clause\neq(X13, X13).\nand substitution\nX13 -> []\nT7 -> []", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 141 [arrowhead = none ];
141 -> 9;

142 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 142 [arrowhead = none ];
142 -> 10;

143 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 143 [arrowhead = none ];
143 -> 11;

144 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
12 -> 144 [arrowhead = none ];
144 -> 13;

145 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T8, [], T5), rev([], X10, X11))", fontsize=14, style = filled, fillcolor = white];
13 -> 145 [arrowhead = none ];
145 -> 14;

146 [label="EVAL with clause\nhead(.(X26, X27), X26).\nand substitution\nX26 -> T11\nX27 -> T12\nT8 -> .(T11, T12)\nX20 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 146 [arrowhead = none ];
146 -> 15;

147 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 147 [arrowhead = none ];
147 -> 16;

148 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 148 [arrowhead = none ];
148 -> 17;

149 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
17 -> 149 [arrowhead = none ];
149 -> 18;

150 [label="EVAL with clause\ntail(.(X30, X31), X31).\nand substitution\nT11 -> T13\nX30 -> T13\nT12 -> T14\nX31 -> T14\nX21 -> T14", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 150 [arrowhead = none ];
150 -> 19;

151 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 151 [arrowhead = none ];
151 -> 20;

152 [label="EVAL with clause\nrev([], X34, X35) :- ','(!, eq(X34, X35)).\nand substitution\nT14 -> []\nT13 -> T15\nX34 -> .(T15, [])\nT10 -> T17\nX35 -> T17\nT16 -> T17", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 152 [arrowhead = none ];
152 -> 21;

153 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 153 [arrowhead = none ];
153 -> 22;

154 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 154 [arrowhead = none ];
154 -> 23;

155 [label="EVAL with clause\nrev(X41, X42, X43) :- ','(head(X41, X44), ','(tail(X41, X45), rev(X45, .(X44, X42), X43))).\nand substitution\nT14 -> T19\nX41 -> T19\nT13 -> T20\nX42 -> .(T20, [])\nT10 -> T22\nX43 -> T22\nT21 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 155 [arrowhead = none ];
155 -> 28;

156 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 156 [arrowhead = none ];
156 -> 24;

157 [label="EVAL with clause\neq(X37, X37).\nand substitution\nT15 -> T18\nX37 -> .(T18, [])\nT17 -> .(T18, [])", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 157 [arrowhead = none ];
157 -> 25;

158 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 158 [arrowhead = none ];
158 -> 26;

159 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 159 [arrowhead = none ];
159 -> 27;

160 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
28 -> 160 [arrowhead = none ];
160 -> 29;

161 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T19, .(T20, []), T10), rev([], X34, X35))", fontsize=14, style = filled, fillcolor = white];
29 -> 161 [arrowhead = none ];
161 -> 30;

162 [label="EVAL with clause\nhead(.(X50, X51), X50).\nand substitution\nX50 -> T23\nX51 -> T24\nT19 -> .(T23, T24)\nX44 -> T23", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 162 [arrowhead = none ];
162 -> 31;

163 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 163 [arrowhead = none ];
163 -> 32;

164 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
31 -> 164 [arrowhead = none ];
164 -> 33;

165 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
33 -> 165 [arrowhead = none ];
165 -> 34;

166 [label="EVAL with clause\ntail(.(X54, X55), X55).\nand substitution\nT23 -> T25\nX54 -> T25\nT24 -> T26\nX55 -> T26\nX45 -> T26", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 166 [arrowhead = none ];
166 -> 35;

167 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 167 [arrowhead = none ];
167 -> 36;

168 [label="EVAL with clause\nrev([], X58, X59) :- ','(!, eq(X58, X59)).\nand substitution\nT26 -> []\nT25 -> T27\nT20 -> T28\nX58 -> .(T27, .(T28, []))\nT22 -> T30\nX59 -> T30\nT29 -> T30", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 168 [arrowhead = none ];
168 -> 37;

169 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 169 [arrowhead = none ];
169 -> 38;

170 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 170 [arrowhead = none ];
170 -> 39;

171 [label="EVAL with clause\nrev(X65, X66, X67) :- ','(head(X65, X68), ','(tail(X65, X69), rev(X69, .(X68, X66), X67))).\nand substitution\nT26 -> T33\nX65 -> T33\nT25 -> T34\nT20 -> T35\nX66 -> .(T34, .(T35, []))\nT22 -> T37\nX67 -> T37\nT36 -> T37", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 171 [arrowhead = none ];
171 -> 44;

172 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 172 [arrowhead = none ];
172 -> 40;

173 [label="EVAL with clause\neq(X61, X61).\nand substitution\nT27 -> T31\nT28 -> T32\nX61 -> .(T31, .(T32, []))\nT30 -> .(T31, .(T32, []))", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 173 [arrowhead = none ];
173 -> 41;

174 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 174 [arrowhead = none ];
174 -> 42;

175 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 175 [arrowhead = none ];
175 -> 43;

176 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
44 -> 176 [arrowhead = none ];
176 -> 45;

177 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T33, .(T34, .(T35, [])), T22), rev([], X58, X59))", fontsize=14, style = filled, fillcolor = white];
45 -> 177 [arrowhead = none ];
177 -> 46;

178 [label="EVAL with clause\nhead(.(X74, X75), X74).\nand substitution\nX74 -> T38\nX75 -> T39\nT33 -> .(T38, T39)\nX68 -> T38", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 178 [arrowhead = none ];
178 -> 47;

179 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 179 [arrowhead = none ];
179 -> 48;

180 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 180 [arrowhead = none ];
180 -> 49;

181 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
49 -> 181 [arrowhead = none ];
181 -> 50;

182 [label="EVAL with clause\ntail(.(X78, X79), X79).\nand substitution\nT38 -> T40\nX78 -> T40\nT39 -> T41\nX79 -> T41\nX69 -> T41", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 182 [arrowhead = none ];
182 -> 51;

183 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
51 -> 183 [arrowhead = none ];
183 -> 52;

184 [label="EVAL with clause\nrev([], X82, X83) :- ','(!, eq(X82, X83)).\nand substitution\nT41 -> []\nT40 -> T42\nT34 -> T43\nT35 -> T44\nX82 -> .(T42, .(T43, .(T44, [])))\nT37 -> T46\nX83 -> T46\nT45 -> T46", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 184 [arrowhead = none ];
184 -> 53;

185 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 185 [arrowhead = none ];
185 -> 54;

186 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 186 [arrowhead = none ];
186 -> 55;

187 [label="EVAL with clause\nrev(X89, X90, X91) :- ','(head(X89, X92), ','(tail(X89, X93), rev(X93, .(X92, X90), X91))).\nand substitution\nT41 -> T50\nX89 -> T50\nT40 -> T51\nT34 -> T52\nT35 -> T53\nX90 -> .(T51, .(T52, .(T53, [])))\nT37 -> T55\nX91 -> T55\nT54 -> T55", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 187 [arrowhead = none ];
187 -> 60;

188 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
55 -> 188 [arrowhead = none ];
188 -> 56;

189 [label="EVAL with clause\neq(X85, X85).\nand substitution\nT42 -> T47\nT43 -> T48\nT44 -> T49\nX85 -> .(T47, .(T48, .(T49, [])))\nT46 -> .(T47, .(T48, .(T49, [])))", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 189 [arrowhead = none ];
189 -> 57;

190 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 190 [arrowhead = none ];
190 -> 58;

191 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
57 -> 191 [arrowhead = none ];
191 -> 59;

192 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
60 -> 192 [arrowhead = none ];
192 -> 61;

193 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T50, .(T51, .(T52, .(T53, []))), T37), rev([], X82, X83))", fontsize=14, style = filled, fillcolor = white];
61 -> 193 [arrowhead = none ];
193 -> 62;

194 [label="EVAL with clause\nhead(.(X98, X99), X98).\nand substitution\nX98 -> T56\nX99 -> T57\nT50 -> .(T56, T57)\nX92 -> T56", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 194 [arrowhead = none ];
194 -> 63;

195 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 195 [arrowhead = none ];
195 -> 64;

196 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
63 -> 196 [arrowhead = none ];
196 -> 65;

197 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
65 -> 197 [arrowhead = none ];
197 -> 66;

198 [label="EVAL with clause\ntail(.(X102, X103), X103).\nand substitution\nT56 -> T58\nX102 -> T58\nT57 -> T59\nX103 -> T59\nX93 -> T59", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 198 [arrowhead = none ];
198 -> 67;

199 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
67 -> 199 [arrowhead = none ];
199 -> 68;

200 [label="EVAL with clause\nrev([], X106, X107) :- ','(!, eq(X106, X107)).\nand substitution\nT59 -> []\nT58 -> T60\nT51 -> T61\nT52 -> T62\nT53 -> T63\nX106 -> .(T60, .(T61, .(T62, .(T63, []))))\nT55 -> T65\nX107 -> T65\nT64 -> T65", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 200 [arrowhead = none ];
200 -> 69;

201 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 201 [arrowhead = none ];
201 -> 70;

202 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 202 [arrowhead = none ];
202 -> 71;

203 [label="EVAL with clause\nrev(X113, X114, X115) :- ','(head(X113, X116), ','(tail(X113, X117), rev(X117, .(X116, X114), X115))).\nand substitution\nT59 -> T70\nX113 -> T70\nT58 -> T71\nT51 -> T72\nT52 -> T73\nT53 -> T74\nX114 -> .(T71, .(T72, .(T73, .(T74, []))))\nT55 -> T76\nX115 -> T76\nT75 -> T76", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 203 [arrowhead = none ];
203 -> 76;

204 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
71 -> 204 [arrowhead = none ];
204 -> 72;

205 [label="EVAL with clause\neq(X109, X109).\nand substitution\nT60 -> T66\nT61 -> T67\nT62 -> T68\nT63 -> T69\nX109 -> .(T66, .(T67, .(T68, .(T69, []))))\nT65 -> .(T66, .(T67, .(T68, .(T69, []))))", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 205 [arrowhead = none ];
205 -> 73;

206 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 206 [arrowhead = none ];
206 -> 74;

207 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 207 [arrowhead = none ];
207 -> 75;

208 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
76 -> 208 [arrowhead = none ];
208 -> 77;

209 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T70, .(T71, .(T72, .(T73, .(T74, [])))), T55), rev([], X106, X107))", fontsize=14, style = filled, fillcolor = white];
77 -> 209 [arrowhead = none ];
209 -> 78;

210 [label="EVAL with clause\nhead(.(X122, X123), X122).\nand substitution\nX122 -> T77\nX123 -> T78\nT70 -> .(T77, T78)\nX116 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 210 [arrowhead = none ];
210 -> 79;

211 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 211 [arrowhead = none ];
211 -> 80;

212 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
79 -> 212 [arrowhead = none ];
212 -> 81;

213 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
81 -> 213 [arrowhead = none ];
213 -> 82;

214 [label="EVAL with clause\ntail(.(X126, X127), X127).\nand substitution\nT77 -> T79\nX126 -> T79\nT78 -> T80\nX127 -> T80\nX117 -> T80", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 214 [arrowhead = none ];
214 -> 83;

215 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
83 -> 215 [arrowhead = none ];
215 -> 84;

216 [label="EVAL with clause\nrev([], X130, X131) :- ','(!, eq(X130, X131)).\nand substitution\nT80 -> []\nT79 -> T81\nT71 -> T82\nT72 -> T83\nT73 -> T84\nT74 -> T85\nX130 -> .(T81, .(T82, .(T83, .(T84, .(T85, [])))))\nT76 -> T87\nX131 -> T87\nT86 -> T87", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 216 [arrowhead = none ];
216 -> 85;

217 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 217 [arrowhead = none ];
217 -> 86;

218 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
85 -> 218 [arrowhead = none ];
218 -> 87;

219 [label="EVAL with clause\nrev(X137, X138, X139) :- ','(head(X137, X140), ','(tail(X137, X141), rev(X141, .(X140, X138), X139))).\nand substitution\nT80 -> T93\nX137 -> T93\nT79 -> T94\nT71 -> T95\nT72 -> T96\nT73 -> T97\nT74 -> T98\nX138 -> .(T94, .(T95, .(T96, .(T97, .(T98, [])))))\nT76 -> T100\nX139 -> T100\nT99 -> T100", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 219 [arrowhead = none ];
219 -> 92;

220 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
87 -> 220 [arrowhead = none ];
220 -> 88;

221 [label="EVAL with clause\neq(X133, X133).\nand substitution\nT81 -> T88\nT82 -> T89\nT83 -> T90\nT84 -> T91\nT85 -> T92\nX133 -> .(T88, .(T89, .(T90, .(T91, .(T92, [])))))\nT87 -> .(T88, .(T89, .(T90, .(T91, .(T92, [])))))", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 221 [arrowhead = none ];
221 -> 89;

222 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 222 [arrowhead = none ];
222 -> 90;

223 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 223 [arrowhead = none ];
223 -> 91;

224 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
92 -> 224 [arrowhead = none ];
224 -> 93;

225 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T93, .(T94, .(T95, .(T96, .(T97, .(T98, []))))), T76), rev([], X130, X131))", fontsize=14, style = filled, fillcolor = white];
93 -> 225 [arrowhead = none ];
225 -> 94;

226 [label="EVAL with clause\nhead(.(X146, X147), X146).\nand substitution\nX146 -> T101\nX147 -> T102\nT93 -> .(T101, T102)\nX140 -> T101", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 226 [arrowhead = none ];
226 -> 95;

227 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 227 [arrowhead = none ];
227 -> 96;

228 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
95 -> 228 [arrowhead = none ];
228 -> 97;

229 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
97 -> 229 [arrowhead = none ];
229 -> 98;

230 [label="EVAL with clause\ntail(.(X150, X151), X151).\nand substitution\nT101 -> T103\nX150 -> T103\nT102 -> T104\nX151 -> T104\nX141 -> T104", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 230 [arrowhead = none ];
230 -> 99;

231 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
99 -> 231 [arrowhead = none ];
231 -> 100;

232 [label="EVAL with clause\nrev([], X154, X155) :- ','(!, eq(X154, X155)).\nand substitution\nT104 -> []\nT103 -> T105\nT94 -> T106\nT95 -> T107\nT96 -> T108\nT97 -> T109\nT98 -> T110\nX154 -> .(T105, .(T106, .(T107, .(T108, .(T109, .(T110, []))))))\nT100 -> T112\nX155 -> T112\nT111 -> T112", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 232 [arrowhead = none ];
232 -> 101;

233 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 233 [arrowhead = none ];
233 -> 102;

234 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 234 [arrowhead = none ];
234 -> 103;

235 [label="EVAL with clause\nrev(X161, X162, X163) :- ','(head(X161, X164), ','(tail(X161, X165), rev(X165, .(X164, X162), X163))).\nand substitution\nT104 -> T119\nX161 -> T119\nT103 -> T120\nT94 -> T121\nT95 -> T122\nT96 -> T123\nT97 -> T124\nT98 -> T125\nX162 -> .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))\nT100 -> T127\nX163 -> T127\nT126 -> T127", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 235 [arrowhead = none ];
235 -> 108;

236 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
103 -> 236 [arrowhead = none ];
236 -> 104;

237 [label="EVAL with clause\neq(X157, X157).\nand substitution\nT105 -> T113\nT106 -> T114\nT107 -> T115\nT108 -> T116\nT109 -> T117\nT110 -> T118\nX157 -> .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))\nT112 -> .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 237 [arrowhead = none ];
237 -> 105;

238 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 238 [arrowhead = none ];
238 -> 106;

239 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 239 [arrowhead = none ];
239 -> 107;

240 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
108 -> 240 [arrowhead = none ];
240 -> 109;

241 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T119, .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, [])))))), T100), rev([], X154, X155))", fontsize=14, style = filled, fillcolor = white];
109 -> 241 [arrowhead = none ];
241 -> 110;

242 [label="EVAL with clause\nhead(.(X170, X171), X170).\nand substitution\nX170 -> T128\nX171 -> T129\nT119 -> .(T128, T129)\nX164 -> T128", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 242 [arrowhead = none ];
242 -> 111;

243 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 243 [arrowhead = none ];
243 -> 112;

244 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 244 [arrowhead = none ];
244 -> 113;

245 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
113 -> 245 [arrowhead = none ];
245 -> 114;

246 [label="EVAL with clause\ntail(.(X174, X175), X175).\nand substitution\nT128 -> T130\nX174 -> T130\nT129 -> T131\nX175 -> T131\nX165 -> T131", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 246 [arrowhead = none ];
246 -> 115;

247 [label="GENERALIZATION\nT132 <-- T130\nT133 <-- .(T120, .(T121, .(T122, .(T123, .(T124, .(T125, []))))))\n\nNew Knowledge:\nT132 is ground\nT133 is ground", fontsize=14, style = filled, fillcolor = violet];
115 -> 247 [arrowhead = none ];
247 -> 116;

248 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
116 -> 248 [arrowhead = none ];
248 -> 117;

249 [label="EVAL with clause\nrev([], X178, X179) :- ','(!, eq(X178, X179)).\nand substitution\nT131 -> []\nT132 -> T134\nT133 -> T135\nX178 -> .(T134, T135)\nT127 -> T137\nX179 -> T137\nT136 -> T137", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 249 [arrowhead = none ];
249 -> 118;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 250 [arrowhead = none ];
250 -> 119;

251 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
118 -> 251 [arrowhead = none ];
251 -> 120;

252 [label="EVAL with clause\nrev(X185, X186, X187) :- ','(head(X185, X188), ','(tail(X185, X189), rev(X189, .(X188, X186), X187))).\nand substitution\nT131 -> T140\nX185 -> T140\nT132 -> T141\nT133 -> T142\nX186 -> .(T141, T142)\nT127 -> T144\nX187 -> T144\nT143 -> T144", fontsize=14, style = filled, fillcolor = lightblue];
119 -> 252 [arrowhead = none ];
252 -> 125;

253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
120 -> 253 [arrowhead = none ];
253 -> 121;

254 [label="EVAL with clause\neq(X181, X181).\nand substitution\nT134 -> T138\nT135 -> T139\nX181 -> .(T138, T139)\nT137 -> .(T138, T139)", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 254 [arrowhead = none ];
254 -> 122;

255 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 255 [arrowhead = none ];
255 -> 123;

256 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 256 [arrowhead = none ];
256 -> 124;

257 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 257 [arrowhead = none ];
257 -> 126;

258 [label="BACKTRACK\nfor clause: head([], X1)\nwith clash: (rev(T140, .(T141, T142), T127), rev([], X178, X179))", fontsize=14, style = filled, fillcolor = white];
126 -> 258 [arrowhead = none ];
258 -> 127;

259 [label="EVAL with clause\nhead(.(X194, X195), X194).\nand substitution\nX194 -> T145\nX195 -> T146\nT140 -> .(T145, T146)\nX188 -> T145", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 259 [arrowhead = none ];
259 -> 128;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 260 [arrowhead = none ];
260 -> 129;

261 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
128 -> 261 [arrowhead = none ];
261 -> 130;

262 [label="BACKTRACK\nfor clause: tail([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
130 -> 262 [arrowhead = none ];
262 -> 131;

263 [label="EVAL with clause\ntail(.(X198, X199), X199).\nand substitution\nT145 -> T147\nX198 -> T147\nT146 -> T148\nX199 -> T148\nX189 -> T148", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 263 [arrowhead = none ];
263 -> 132;

264 [label="INSTANCE with matching:\nT131 -> T148\nT132 -> T147\nT133 -> .(T141, T142)\nT127 -> T144", fontsize=14, style = filled, fillcolor = lightgrey];
132 -> 264 [arrowhead = none , style=dashed];
264 -> 116[style=dashed];

}

(2) Obligation:

Clauses:

rev116([], T138, T139, .(T138, T139)).
rev116(.(T147, T148), T141, T142, T144) :- rev116(T148, T147, .(T141, T142), T144).
rev1([], []).
rev1(.(T18, []), .(T18, [])).
rev1(.(T32, .(T31, [])), .(T31, .(T32, []))).
rev1(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))).
rev1(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))).
rev1(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))).
rev1(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))).
rev1(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)).
rev1(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) :- rev116(T148, T147, .(T141, T142), T144).

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)
rev116_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(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

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)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)

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(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

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)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)

(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(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_GA(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV1_IN_GA(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → U1_GAAA(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

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)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_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)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_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(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_GA(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV1_IN_GA(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → U1_GAAA(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

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)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_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)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_IN_GAAA(x1)
U1_GAAA(x1, x2, x3, x4, x5, x6)  =  U1_GAAA(x6)

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

(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:

REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

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)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_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:

REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x2)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_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:

REV116_IN_GAAA(.(T148)) → REV116_IN_GAAA(T148)

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:

• REV116_IN_GAAA(.(T148)) → REV116_IN_GAAA(T148)
  The graph contains the following edges 1 > 1

(14) TRUE