Left Termination proof of /tmp/tmpxcYNRc/mergesort.pl

Left Termination of the query pattern ms_in_2(a, g) w.r.t. the given Prolog program could not be shown:

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇐)

↳2 TRIPLES

↳3 UndefinedPredicateInTriplesTransformerProof (⇐)

↳4 TRIPLES

↳5 TriplesToPiDPProof (⇐)

↳6 PiDP

↳7 DependencyGraphProof (⇔)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇐)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇐)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔)

        ↳22 YES

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔)

        ↳25 PiDP

        ↳26 PiDPToQDPProof (⇐)

        ↳27 QDP

        ↳28 NonTerminationProof (⇔)

        ↳29 NO

    ↳30 PiDP

        ↳31 UsableRulesProof (⇔)

        ↳32 PiDP

        ↳33 PiDPToQDPProof (⇐)

        ↳34 QDP

        ↳35 Narrowing (⇐)

        ↳36 QDP

        ↳37 UsableRulesProof (⇔)

        ↳38 QDP

        ↳39 QReductionProof (⇔)

        ↳40 QDP

        ↳41 Narrowing (⇐)

        ↳42 QDP

        ↳43 NonTerminationProof (⇔)

        ↳44 NO

    ↳45 PiDP

        ↳46 UsableRulesProof (⇔)

        ↳47 PiDP

        ↳48 PiDPToQDPProof (⇐)

        ↳49 QDP

        ↳50 NonTerminationProof (⇔)

        ↳51 NO

    ↳52 PiDP

        ↳53 UsableRulesProof (⇔)

        ↳54 PiDP

        ↳55 PiDPToQDPProof (⇐)

        ↳56 QDP

        ↳57 Narrowing (⇐)

        ↳58 QDP

        ↳59 Narrowing (⇐)

        ↳60 QDP

        ↳61 Narrowing (⇐)

        ↳62 QDP

        ↳63 NonTerminationProof (⇔)

        ↳64 NO

(0) Obligation:

Clauses:

ms([], []).
ms(.(X, []), .(X, [])).
ms(.(X, .(Y, Xs)), Ys) :- ','(split(.(X, .(Y, Xs)), X1s, X2s), ','(ms(X1s, Y1s), ','(ms(X2s, Y2s), merge(Y1s, Y2s, Ys)))).
split([], [], []).
split(.(X, Xs), .(X, Ys), Zs) :- split(Xs, Zs, Ys).
merge([], Xs, Xs).
merge(Xs, [], Xs).
merge(.(X, Xs), .(Y, Ys), .(X, Zs)) :- ','(less(X, s(Y)), merge(Xs, .(Y, Ys), Zs)).
merge(.(X, Xs), .(Y, Ys), .(Y, Zs)) :- ','(less(Y, X), merge(.(X, Xs), Ys, Zs)).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).

Queries:

ms(a,g).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: ms(T1, T2)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: ms(T1, T2), SCOPE: 1, CLAUSE: 0 | ms(T1, T2), SCOPE: 1, CLAUSE: 1 | ms(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | ms(T1, []), SCOPE: 1, CLAUSE: 1 | ms(T1, []), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ms(T1, T2), SCOPE: 1, CLAUSE: 1 | ms(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT2 is ground\nms(T1, T2) !=? ms([], [])", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ms(T1, []), SCOPE: 1, CLAUSE: 1 | ms(T1, []), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ms(T1, []), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(split(.(T10, .(T11, T12)), X11, X12), ','(ms(X11, X13), ','(ms(X12, X14), merge(X13, X14, []))))\n\nX11 is free\nX12 is free; \nX13 is free; \nX14 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(split(.(T10, .(T11, T12)), X11, X12), ','(ms(X11, X13), ','(ms(X12, X14), merge(X13, X14, [])))), SCOPE: 2, CLAUSE: 3 | ','(split(.(T10, .(T11, T12)), X11, X12), ','(ms(X11, X13), ','(ms(X12, X14), merge(X13, X14, [])))), SCOPE: 2, CLAUSE: 4\n\nX11 is free\nX12 is free; \nX13 is free; \nX14 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: ','(split(.(T10, .(T11, T12)), X11, X12), ','(ms(X11, X13), ','(ms(X12, X14), merge(X13, X14, [])))), SCOPE: 2, CLAUSE: 4\n\nX11 is free\nX12 is free; \nX13 is free; \nX14 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(split(.(T27, T28), X42, X41), ','(ms(.(T29, X41), X13), ','(ms(X42, X14), merge(X13, X14, []))))\n\nX13 is free\nX14 is free; \nX41 is free; \nX42 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: split(.(T27, T28), X42, X41)\n\nX41 is free\nX42 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(ms(.(T34, T33), X13), ','(ms(T32, X14), merge(X13, X14, [])))\n\nX13 is free\nX14 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: split(.(T27, T28), X42, X41), SCOPE: 3, CLAUSE: 3 | split(.(T27, T28), X42, X41), SCOPE: 3, CLAUSE: 4\n\nX41 is free\nX42 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: split(.(T27, T28), X42, X41), SCOPE: 3, CLAUSE: 4\n\nX41 is free\nX42 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: split(T44, X72, X71)\n\nX71 is free\nX72 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: split(T44, X72, X71), SCOPE: 4, CLAUSE: 3 | split(T44, X72, X71), SCOPE: 4, CLAUSE: 4\n\nX71 is free\nX72 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: split(T44, X72, X71), SCOPE: 4, CLAUSE: 3\n\nX71 is free\nX72 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: split(T44, X72, X71), SCOPE: 4, CLAUSE: 4\n\nX71 is free\nX72 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: split(T51, X90, X89)\n\nX89 is free\nX90 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ms(.(T34, T33), X13)\n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(ms(T55, X14), merge(T54, X14, []))\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 0 | ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 1 | ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 2\n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 1 | ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 2\n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 1\n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ms(.(T34, T33), X13), SCOPE: 5, CLAUSE: 2\n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(split(.(T72, .(T73, T74)), X123, X124), ','(ms(X123, X125), ','(ms(X124, X126), merge(X125, X126, X127))))\n\nX127 is free\nX123 is free; \nX124 is free; \nX125 is free; \nX126 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: split(.(T72, .(T73, T74)), X123, X124)\n\nX123 is free\nX124 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(ms(T78, X125), ','(ms(T79, X126), merge(X125, X126, X127)))\n\nX127 is free\nX125 is free; \nX126 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ms(T78, X125)\n\nX125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(ms(T84, X126), merge(T83, X126, X127))\n\nX127 is free\nX126 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ms(T78, X125), SCOPE: 6, CLAUSE: 0 | ms(T78, X125), SCOPE: 6, CLAUSE: 1 | ms(T78, X125), SCOPE: 6, CLAUSE: 2\n\nX125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ms(T78, X125), SCOPE: 6, CLAUSE: 0\n\nX125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ms(T78, X125), SCOPE: 6, CLAUSE: 1 | ms(T78, X125), SCOPE: 6, CLAUSE: 2\n\nX125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ms(T78, X125), SCOPE: 6, CLAUSE: 1\n\nX125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ms(T78, X125), SCOPE: 6, CLAUSE: 2\n\nX125 is free", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(split(.(T99, .(T100, T101)), X168, X169), ','(ms(X168, X170), ','(ms(X169, X171), merge(X170, X171, X172))))\n\nX172 is free\nX168 is free; \nX169 is free; \nX170 is free; \nX171 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ms(T84, X126)\n\nX126 is free", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: merge(T106, T105, X127)\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 5 | merge(T106, T105, X127), SCOPE: 7, CLAUSE: 6 | merge(T106, T105, X127), SCOPE: 7, CLAUSE: 7 | merge(T106, T105, X127), SCOPE: 7, CLAUSE: 8\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 5\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 6 | merge(T106, T105, X127), SCOPE: 7, CLAUSE: 7 | merge(T106, T105, X127), SCOPE: 7, CLAUSE: 8\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 6\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 7 | merge(T106, T105, X127), SCOPE: 7, CLAUSE: 8\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 7\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: merge(T106, T105, X127), SCOPE: 7, CLAUSE: 8\n\nX127 is free", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(less(T139, s(T140)), merge(T141, .(T140, T142), X226))\n\nX226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: less(T139, s(T140))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: merge(T145, .(T146, T147), X226)\n\nX226 is free", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: less(T139, s(T140)), SCOPE: 8, CLAUSE: 9 | less(T139, s(T140)), SCOPE: 8, CLAUSE: 10\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: less(T139, s(T140)), SCOPE: 8, CLAUSE: 9\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: less(T139, s(T140)), SCOPE: 8, CLAUSE: 10\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: less(T161, T162)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: less(T161, T162), SCOPE: 9, CLAUSE: 9 | less(T161, T162), SCOPE: 9, CLAUSE: 10\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: less(T161, T162), SCOPE: 9, CLAUSE: 9\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: less(T161, T162), SCOPE: 9, CLAUSE: 10\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: less(T176, T177)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ','(less(T196, T197), merge(.(T197, T199), T198, X287))\n\nX287 is free", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: less(T196, T197)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: merge(.(T202, T203), T204, X287)\n\nX287 is free", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ms(T55, X14)\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: merge(T212, T211, [])\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: merge(T212, T211, []), SCOPE: 10, CLAUSE: 5 | merge(T212, T211, []), SCOPE: 10, CLAUSE: 6 | merge(T212, T211, []), SCOPE: 10, CLAUSE: 7 | merge(T212, T211, []), SCOPE: 10, CLAUSE: 8\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: merge(T212, T211, []), SCOPE: 10, CLAUSE: 5\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: merge(T212, T211, []), SCOPE: 10, CLAUSE: 6 | merge(T212, T211, []), SCOPE: 10, CLAUSE: 7 | merge(T212, T211, []), SCOPE: 10, CLAUSE: 8\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: merge(T212, T211, []), SCOPE: 10, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: merge(T212, T211, []), SCOPE: 10, CLAUSE: 7 | merge(T212, T211, []), SCOPE: 10, CLAUSE: 8\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: merge(T212, T211, []), SCOPE: 10, CLAUSE: 8\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: true | ms(T1, .(T234, [])), SCOPE: 1, CLAUSE: 2\n\nT234 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ms(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT2 is ground\nms(T1, T2) !=? ms([], [])\nms(T1, T2) !=? ms(.(X326, []), .(X326, []))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ms(T1, .(T234, [])), SCOPE: 1, CLAUSE: 2\n\nT234 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(split(.(T243, .(T244, T245)), X336, X337), ','(ms(X336, X338), ','(ms(X337, X339), merge(X338, X339, .(T242, [])))))\n\nT242 is ground\nX336 is free; \nX337 is free; \nX338 is free; \nX339 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(split(.(T243, .(T244, T245)), X336, X337), ','(ms(X336, X338), ','(ms(X337, X339), merge(X338, X339, .(T242, []))))), SCOPE: 11, CLAUSE: 3 | ','(split(.(T243, .(T244, T245)), X336, X337), ','(ms(X336, X338), ','(ms(X337, X339), merge(X338, X339, .(T242, []))))), SCOPE: 11, CLAUSE: 4\n\nT242 is ground\nX336 is free; \nX337 is free; \nX338 is free; \nX339 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(split(.(T243, .(T244, T245)), X336, X337), ','(ms(X336, X338), ','(ms(X337, X339), merge(X338, X339, .(T242, []))))), SCOPE: 11, CLAUSE: 4\n\nT242 is ground\nX336 is free; \nX337 is free; \nX338 is free; \nX339 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(split(.(T260, T261), X367, X366), ','(ms(.(T262, X366), X338), ','(ms(X367, X339), merge(X338, X339, .(T242, [])))))\n\nT242 is ground\nX338 is free; \nX339 is free; \nX366 is free; \nX367 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: split(.(T260, T261), X367, X366)\n\nX366 is free\nX367 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(ms(.(T267, T266), X338), ','(ms(T265, X339), merge(X338, X339, .(T242, []))))\n\nT242 is ground\nX338 is free; \nX339 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ms(.(T267, T266), X338)\n\nX338 is free", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(ms(T273, X339), merge(T272, X339, .(T242, [])))\n\nT242 is ground\nX339 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ms(T273, X339)\n\nX339 is free", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: merge(T277, T276, .(T242, []))\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 5 | merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 6 | merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 7 | merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 8\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 5\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 6 | merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 7 | merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 8\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 6\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 7 | merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 8\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 7\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: merge(T277, T276, .(T242, [])), SCOPE: 12, CLAUSE: 8\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(less(T318, s(T322)), merge(T323, .(T322, T324), []))\n\nT318 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: less(T318, s(T322))\n\nT318 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: merge(T327, .(T328, T329), [])\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(less(T356, T358), merge(.(T358, T360), T359, []))\n\nT356 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: less(T356, T358)\n\nT356 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: merge(.(T363, T364), T365, [])\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(split(.(T388, .(T389, T390)), X492, X493), ','(ms(X492, X494), ','(ms(X493, X495), merge(X494, X495, T387))))\n\nT387 is ground\nX492 is free; \nX493 is free; \nX494 is free; \nX495 is free; \nms(T1, T387) !=? ms([], [])\nms(T1, T387) !=? ms(.(X326, []), .(X326, []))", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(split(.(T388, .(T389, T390)), X492, X493), ','(ms(X492, X494), ','(ms(X493, X495), merge(X494, X495, T387)))), SCOPE: 13, CLAUSE: 3 | ','(split(.(T388, .(T389, T390)), X492, X493), ','(ms(X492, X494), ','(ms(X493, X495), merge(X494, X495, T387)))), SCOPE: 13, CLAUSE: 4\n\nT387 is ground\nX492 is free; \nX493 is free; \nX494 is free; \nX495 is free; \nms(T1, T387) !=? ms([], [])\nms(T1, T387) !=? ms(.(X326, []), .(X326, []))", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(split(.(T388, .(T389, T390)), X492, X493), ','(ms(X492, X494), ','(ms(X493, X495), merge(X494, X495, T387)))), SCOPE: 13, CLAUSE: 4\n\nT387 is ground\nX492 is free; \nX493 is free; \nX494 is free; \nX495 is free; \nms(T1, T387) !=? ms([], [])\nms(T1, T387) !=? ms(.(X326, []), .(X326, []))", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(split(.(T405, T406), X523, X522), ','(ms(.(T407, X522), X494), ','(ms(X523, X495), merge(X494, X495, T387))))\n\nT387 is ground\nX494 is free; \nX495 is free; \nX522 is free; \nX523 is free; \nms(T1, T387) !=? ms([], [])\nms(T1, T387) !=? ms(.(X326, []), .(X326, []))", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: split(.(T405, T406), X523, X522)\n\nX522 is free\nX523 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(ms(.(T412, T411), X494), ','(ms(T410, X495), merge(X494, X495, T387)))\n\nT387 is ground\nX494 is free; \nX495 is free; \nms(T413, T387) !=? ms([], [])\nms(T413, T387) !=? ms(.(T414, []), .(T414, []))", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ms(.(T412, T411), X494)\n\nX494 is free", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(ms(T420, X495), merge(T419, X495, T387))\n\nT387 is ground\nX495 is free; \nms(T421, T387) !=? ms([], [])\nms(T421, T387) !=? ms(.(T422, []), .(T422, []))", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: ms(T420, X495)\n\nX495 is free", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: merge(T426, T425, T387)\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 5 | merge(T426, T425, T387), SCOPE: 14, CLAUSE: 6 | merge(T426, T425, T387), SCOPE: 14, CLAUSE: 7 | merge(T426, T425, T387), SCOPE: 14, CLAUSE: 8\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 5\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 6 | merge(T426, T425, T387), SCOPE: 14, CLAUSE: 7 | merge(T426, T425, T387), SCOPE: 14, CLAUSE: 8\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 6\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 7 | merge(T426, T425, T387), SCOPE: 14, CLAUSE: 8\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 7\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: merge(T426, T425, T387), SCOPE: 14, CLAUSE: 8\n\nT387 is ground\nms(T427, T387) !=? ms([], [])\nms(T427, T387) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: ','(less(T461, s(T466)), merge(T467, .(T466, T468), T465))\n\nT461 is ground\nT465 is ground\nms(T427, .(T461, T465)) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: less(T461, s(T466))\n\nT461 is ground\nms(T427, .(T461, T465)) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: merge(T471, .(T472, T473), T465)\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 5 | merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 6 | merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 7 | merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 8\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 5\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 6 | merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 7 | merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 8\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 7 | merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 8\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 7\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: merge(T471, .(T472, T473), T465), SCOPE: 15, CLAUSE: 8\n\nT465 is ground\nms(T474, .(T461, T465)) !=? ms(.(T475, []), .(T475, []))", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(less(T513, s(T518)), merge(T519, .(T518, T520), T517))\n\nT513 is ground\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: less(T513, s(T518))\n\nT513 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: merge(T523, .(T524, T525), T517)\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 5 | merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 6 | merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 7 | merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 8\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 5\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 6 | merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 7 | merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 8\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 7 | merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 8\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 7\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: merge(T523, .(T524, T525), T517), SCOPE: 16, CLAUSE: 8\n\nT517 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(less(T563, s(T568)), merge(T569, .(T568, T570), T567))\n\nT563 is ground\nT567 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(less(T585, T588), merge(.(T588, T590), T589, T587))\n\nT585 is ground\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: less(T585, T588)\n\nT585 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: merge(.(T593, T594), T595, T587)\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 5 | merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 6 | merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 7 | merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 8\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 6 | merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 7 | merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 8\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 6\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 7 | merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 8\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 7\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: merge(.(T593, T594), T595, T587), SCOPE: 17, CLAUSE: 8\n\nT587 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(less(T632, s(T637)), merge(T638, .(T637, T639), T636))\n\nT632 is ground\nT636 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ','(less(T654, T657), merge(.(T657, T659), T658, T656))\n\nT654 is ground\nT656 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: ','(less(T674, T677), merge(.(T677, T679), T678, T676))\n\nT674 is ground\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(less(T694, T697), merge(.(T697, T699), T698, T696))\n\nT694 is ground\nT696 is ground\nms(T427, .(T694, T696)) !=? ms(.(T428, []), .(T428, []))", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 215 [arrowhead = none ];
215 -> 2;

216 [label="EVAL with clause\nms([], []).\nand substitution\nT1 -> []\nT2 -> []", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 216 [arrowhead = none ];
216 -> 3;

217 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 217 [arrowhead = none ];
217 -> 4;

218 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 218 [arrowhead = none ];
218 -> 5;

219 [label="EVAL with clause\nms(.(X326, []), .(X326, [])).\nand substitution\nX326 -> T234\nT1 -> .(T234, [])\nT2 -> .(T234, [])", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 219 [arrowhead = none ];
219 -> 107;

220 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 220 [arrowhead = none ];
220 -> 108;

221 [label="BACKTRACK\nfor clause: ms(.(X, []), .(X, []))because of non-unification", fontsize=14, style = filled, fillcolor = white];
5 -> 221 [arrowhead = none ];
221 -> 6;

222 [label="EVAL with clause\nms(.(X7, .(X8, X9)), X10) :- ','(split(.(X7, .(X8, X9)), X11, X12), ','(ms(X11, X13), ','(ms(X12, X14), merge(X13, X14, X10)))).\nand substitution\nX7 -> T10\nX8 -> T11\nX9 -> T12\nT1 -> .(T10, .(T11, T12))\nX10 -> []\nT7 -> T10\nT8 -> T11\nT9 -> T12", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 222 [arrowhead = none ];
222 -> 7;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 223 [arrowhead = none ];
223 -> 8;

224 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 224 [arrowhead = none ];
224 -> 9;

225 [label="BACKTRACK\nfor clause: split([], [], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
9 -> 225 [arrowhead = none ];
225 -> 10;

226 [label="ONLY EVAL with clause\nsplit(.(X37, X38), .(X37, X39), X40) :- split(X38, X40, X39).\nand substitution\nT10 -> T29\nX37 -> T29\nT11 -> T27\nT12 -> T28\nX38 -> .(T27, T28)\nX39 -> X41\nX11 -> .(T29, X41)\nX12 -> X42\nX40 -> X42\nT25 -> T27\nT26 -> T28\nT24 -> T29", fontsize=14, style = filled, fillcolor = white];
10 -> 226 [arrowhead = none ];
226 -> 11;

227 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
11 -> 227 [arrowhead = none ];
227 -> 12;

228 [label="SPLIT 2\nreplacements:\nX42 -> T32\nX41 -> T33\nT29 -> T34", fontsize=14, style = filled, fillcolor = violet];
11 -> 228 [arrowhead = none ];
228 -> 13;

229 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
12 -> 229 [arrowhead = none ];
229 -> 14;

230 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
13 -> 230 [arrowhead = none ];
230 -> 25;

231 [label="SPLIT 2\nreplacements:\nX13 -> T54\nT32 -> T55", fontsize=14, style = filled, fillcolor = violet];
13 -> 231 [arrowhead = none ];
231 -> 26;

232 [label="BACKTRACK\nfor clause: split([], [], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
14 -> 232 [arrowhead = none ];
232 -> 15;

233 [label="ONLY EVAL with clause\nsplit(.(X67, X68), .(X67, X69), X70) :- split(X68, X70, X69).\nand substitution\nT27 -> T42\nX67 -> T42\nT28 -> T44\nX68 -> T44\nX69 -> X71\nX42 -> .(T42, X71)\nX41 -> X72\nX70 -> X72\nT43 -> T44", fontsize=14, style = filled, fillcolor = white];
15 -> 233 [arrowhead = none ];
233 -> 16;

234 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 234 [arrowhead = none ];
234 -> 17;

235 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
17 -> 235 [arrowhead = none ];
235 -> 18;

236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
17 -> 236 [arrowhead = none ];
236 -> 19;

237 [label="EVAL with clause\nsplit([], [], []).\nand substitution\nT44 -> []\nX72 -> []\nX71 -> []", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 237 [arrowhead = none ];
237 -> 20;

238 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 238 [arrowhead = none ];
238 -> 21;

239 [label="EVAL with clause\nsplit(.(X85, X86), .(X85, X87), X88) :- split(X86, X88, X87).\nand substitution\nX85 -> T49\nX86 -> T51\nT44 -> .(T49, T51)\nX87 -> X89\nX72 -> .(T49, X89)\nX71 -> X90\nX88 -> X90\nT50 -> T51", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 239 [arrowhead = none ];
239 -> 23;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 240 [arrowhead = none ];
240 -> 24;

241 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 241 [arrowhead = none ];
241 -> 22;

242 [label="INSTANCE with matching:\nT44 -> T51\nX72 -> X90\nX71 -> X89", fontsize=14, style = filled, fillcolor = lightgrey];
23 -> 242 [arrowhead = none , style=dashed];
242 -> 16[style=dashed];

243 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 243 [arrowhead = none ];
243 -> 27;

244 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
26 -> 244 [arrowhead = none ];
244 -> 92;

245 [label="SPLIT 2\nreplacements:\nX14 -> T211\nT54 -> T212", fontsize=14, style = filled, fillcolor = violet];
26 -> 245 [arrowhead = none ];
245 -> 93;

246 [label="BACKTRACK\nfor clause: ms([], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
27 -> 246 [arrowhead = none ];
246 -> 28;

247 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
28 -> 247 [arrowhead = none ];
247 -> 29;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
28 -> 248 [arrowhead = none ];
248 -> 30;

249 [label="EVAL with clause\nms(.(X103, []), .(X103, [])).\nand substitution\nT34 -> T62\nX103 -> T62\nT33 -> []\nX13 -> .(T62, [])", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 249 [arrowhead = none ];
249 -> 31;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 250 [arrowhead = none ];
250 -> 32;

251 [label="EVAL with clause\nms(.(X119, .(X120, X121)), X122) :- ','(split(.(X119, .(X120, X121)), X123, X124), ','(ms(X123, X125), ','(ms(X124, X126), merge(X125, X126, X122)))).\nand substitution\nT34 -> T72\nX119 -> T72\nX120 -> T73\nX121 -> T74\nT33 -> .(T73, T74)\nX13 -> X127\nX122 -> X127\nT69 -> T72\nT70 -> T73\nT71 -> T74", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 251 [arrowhead = none ];
251 -> 34;

252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 252 [arrowhead = none ];
252 -> 35;

253 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 253 [arrowhead = none ];
253 -> 33;

254 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
34 -> 254 [arrowhead = none ];
254 -> 36;

255 [label="SPLIT 2\nreplacements:\nX123 -> T78\nX124 -> T79", fontsize=14, style = filled, fillcolor = violet];
34 -> 255 [arrowhead = none ];
255 -> 37;

256 [label="INSTANCE with matching:\nT27 -> T72\nT28 -> .(T73, T74)\nX42 -> X123\nX41 -> X124", fontsize=14, style = filled, fillcolor = lightgrey];
36 -> 256 [arrowhead = none , style=dashed];
256 -> 12[style=dashed];

257 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
37 -> 257 [arrowhead = none ];
257 -> 38;

258 [label="SPLIT 2\nreplacements:\nX125 -> T83\nT79 -> T84", fontsize=14, style = filled, fillcolor = violet];
37 -> 258 [arrowhead = none ];
258 -> 39;

259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
38 -> 259 [arrowhead = none ];
259 -> 40;

260 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
39 -> 260 [arrowhead = none ];
260 -> 53;

261 [label="SPLIT 2\nreplacements:\nX126 -> T105\nT83 -> T106", fontsize=14, style = filled, fillcolor = violet];
39 -> 261 [arrowhead = none ];
261 -> 54;

262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 262 [arrowhead = none ];
262 -> 41;

263 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 263 [arrowhead = none ];
263 -> 42;

264 [label="EVAL with clause\nms([], []).\nand substitution\nT78 -> []\nX125 -> []", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 264 [arrowhead = none ];
264 -> 43;

265 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 265 [arrowhead = none ];
265 -> 44;

266 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
42 -> 266 [arrowhead = none ];
266 -> 46;

267 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
42 -> 267 [arrowhead = none ];
267 -> 47;

268 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
43 -> 268 [arrowhead = none ];
268 -> 45;

269 [label="EVAL with clause\nms(.(X148, []), .(X148, [])).\nand substitution\nX148 -> T89\nT78 -> .(T89, [])\nX125 -> .(T89, [])", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 269 [arrowhead = none ];
269 -> 48;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 270 [arrowhead = none ];
270 -> 49;

271 [label="EVAL with clause\nms(.(X164, .(X165, X166)), X167) :- ','(split(.(X164, .(X165, X166)), X168, X169), ','(ms(X168, X170), ','(ms(X169, X171), merge(X170, X171, X167)))).\nand substitution\nX164 -> T99\nX165 -> T100\nX166 -> T101\nT78 -> .(T99, .(T100, T101))\nX125 -> X172\nX167 -> X172\nT96 -> T99\nT97 -> T100\nT98 -> T101", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 271 [arrowhead = none ];
271 -> 51;

272 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 272 [arrowhead = none ];
272 -> 52;

273 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 273 [arrowhead = none ];
273 -> 50;

274 [label="INSTANCE with matching:\nT72 -> T99\nT73 -> T100\nT74 -> T101\nX123 -> X168\nX124 -> X169\nX125 -> X170\nX126 -> X171\nX127 -> X172", fontsize=14, style = filled, fillcolor = lightgrey];
51 -> 274 [arrowhead = none , style=dashed];
274 -> 34[style=dashed];

275 [label="INSTANCE with matching:\nT78 -> T84\nX125 -> X126", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 275 [arrowhead = none , style=dashed];
275 -> 38[style=dashed];

276 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 276 [arrowhead = none ];
276 -> 55;

277 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 277 [arrowhead = none ];
277 -> 56;

278 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 278 [arrowhead = none ];
278 -> 57;

279 [label="EVAL with clause\nmerge([], X189, X189).\nand substitution\nT106 -> []\nT105 -> T113\nX189 -> T113\nX127 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 279 [arrowhead = none ];
279 -> 58;

280 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 280 [arrowhead = none ];
280 -> 59;

281 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
57 -> 281 [arrowhead = none ];
281 -> 61;

282 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
57 -> 282 [arrowhead = none ];
282 -> 62;

283 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 283 [arrowhead = none ];
283 -> 60;

284 [label="EVAL with clause\nmerge(X195, [], X195).\nand substitution\nT106 -> T118\nX195 -> T118\nT105 -> []\nX127 -> T118", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 284 [arrowhead = none ];
284 -> 63;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 285 [arrowhead = none ];
285 -> 64;

286 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 286 [arrowhead = none ];
286 -> 66;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 287 [arrowhead = none ];
287 -> 67;

288 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
63 -> 288 [arrowhead = none ];
288 -> 65;

289 [label="EVAL with clause\nmerge(.(X221, X222), .(X223, X224), .(X221, X225)) :- ','(less(X221, s(X223)), merge(X222, .(X223, X224), X225)).\nand substitution\nX221 -> T139\nX222 -> T141\nT106 -> .(T139, T141)\nX223 -> T140\nX224 -> T142\nT105 -> .(T140, T142)\nX225 -> X226\nX127 -> .(T139, X226)\nT135 -> T139\nT137 -> T140\nT136 -> T141\nT138 -> T142", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 289 [arrowhead = none ];
289 -> 68;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 290 [arrowhead = none ];
290 -> 69;

291 [label="EVAL with clause\nmerge(.(X282, X283), .(X284, X285), .(X284, X286)) :- ','(less(X284, X282), merge(.(X282, X283), X285, X286)).\nand substitution\nX282 -> T197\nX283 -> T199\nT106 -> .(T197, T199)\nX284 -> T196\nX285 -> T198\nT105 -> .(T196, T198)\nX286 -> X287\nX127 -> .(T196, X287)\nT194 -> T196\nT192 -> T197\nT195 -> T198\nT193 -> T199", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 291 [arrowhead = none ];
291 -> 88;

292 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 292 [arrowhead = none ];
292 -> 89;

293 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
68 -> 293 [arrowhead = none ];
293 -> 70;

294 [label="SPLIT 2\nnew knowledge:\nT139 is ground\nreplacements:\nT141 -> T145\nT140 -> T146\nT142 -> T147", fontsize=14, style = filled, fillcolor = violet];
68 -> 294 [arrowhead = none ];
294 -> 71;

295 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
70 -> 295 [arrowhead = none ];
295 -> 72;

296 [label="INSTANCE with matching:\nT106 -> T145\nT105 -> .(T146, T147)\nX127 -> X226", fontsize=14, style = filled, fillcolor = lightgrey];
71 -> 296 [arrowhead = none , style=dashed];
296 -> 54[style=dashed];

297 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
72 -> 297 [arrowhead = none ];
297 -> 73;

298 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
72 -> 298 [arrowhead = none ];
298 -> 74;

299 [label="EVAL with clause\nless(0, s(X240)).\nand substitution\nT139 -> 0\nT140 -> T154\nX240 -> T154", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 299 [arrowhead = none ];
299 -> 75;

300 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 300 [arrowhead = none ];
300 -> 76;

301 [label="EVAL with clause\nless(s(X246), s(X247)) :- less(X246, X247).\nand substitution\nX246 -> T161\nT139 -> s(T161)\nT140 -> T162\nX247 -> T162\nT159 -> T161\nT160 -> T162", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 301 [arrowhead = none ];
301 -> 78;

302 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 302 [arrowhead = none ];
302 -> 79;

303 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
75 -> 303 [arrowhead = none ];
303 -> 77;

304 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
78 -> 304 [arrowhead = none ];
304 -> 80;

305 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
80 -> 305 [arrowhead = none ];
305 -> 81;

306 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
80 -> 306 [arrowhead = none ];
306 -> 82;

307 [label="EVAL with clause\nless(0, s(X256)).\nand substitution\nT161 -> 0\nX256 -> T169\nT162 -> s(T169)", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 307 [arrowhead = none ];
307 -> 83;

308 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 308 [arrowhead = none ];
308 -> 84;

309 [label="EVAL with clause\nless(s(X262), s(X263)) :- less(X262, X263).\nand substitution\nX262 -> T176\nT161 -> s(T176)\nX263 -> T177\nT162 -> s(T177)\nT174 -> T176\nT175 -> T177", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 309 [arrowhead = none ];
309 -> 86;

310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 310 [arrowhead = none ];
310 -> 87;

311 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 311 [arrowhead = none ];
311 -> 85;

312 [label="INSTANCE with matching:\nT161 -> T176\nT162 -> T177", fontsize=14, style = filled, fillcolor = lightgrey];
86 -> 312 [arrowhead = none , style=dashed];
312 -> 78[style=dashed];

313 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
88 -> 313 [arrowhead = none ];
313 -> 90;

314 [label="SPLIT 2\nnew knowledge:\nT196 is ground\nreplacements:\nT197 -> T202\nT199 -> T203\nT198 -> T204", fontsize=14, style = filled, fillcolor = violet];
88 -> 314 [arrowhead = none ];
314 -> 91;

315 [label="INSTANCE with matching:\nT161 -> T196\nT162 -> T197", fontsize=14, style = filled, fillcolor = lightgrey];
90 -> 315 [arrowhead = none , style=dashed];
315 -> 78[style=dashed];

316 [label="INSTANCE with matching:\nT106 -> .(T202, T203)\nT105 -> T204\nX127 -> X287", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 316 [arrowhead = none , style=dashed];
316 -> 54[style=dashed];

317 [label="INSTANCE with matching:\nT78 -> T55\nX125 -> X14", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 317 [arrowhead = none , style=dashed];
317 -> 38[style=dashed];

318 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
93 -> 318 [arrowhead = none ];
318 -> 94;

319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 319 [arrowhead = none ];
319 -> 95;

320 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 320 [arrowhead = none ];
320 -> 96;

321 [label="EVAL with clause\nmerge([], X307, X307).\nand substitution\nT212 -> []\nT211 -> []\nX307 -> []\nT219 -> []", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 321 [arrowhead = none ];
321 -> 97;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 322 [arrowhead = none ];
322 -> 98;

323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 323 [arrowhead = none ];
323 -> 100;

324 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 324 [arrowhead = none ];
324 -> 101;

325 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 325 [arrowhead = none ];
325 -> 99;

326 [label="EVAL with clause\nmerge(X313, [], X313).\nand substitution\nT212 -> []\nX313 -> []\nT211 -> []\nT224 -> []", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 326 [arrowhead = none ];
326 -> 102;

327 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 327 [arrowhead = none ];
327 -> 103;

328 [label="BACKTRACK\nfor clause: merge(.(X, Xs), .(Y, Ys), .(X, Zs)) :- ','(less(X, s(Y)), merge(Xs, .(Y, Ys), Zs))because of non-unification", fontsize=14, style = filled, fillcolor = white];
101 -> 328 [arrowhead = none ];
328 -> 105;

329 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 329 [arrowhead = none ];
329 -> 104;

330 [label="BACKTRACK\nfor clause: merge(.(X, Xs), .(Y, Ys), .(Y, Zs)) :- ','(less(Y, X), merge(.(X, Xs), Ys, Zs))because of non-unification", fontsize=14, style = filled, fillcolor = white];
105 -> 330 [arrowhead = none ];
330 -> 106;

331 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 331 [arrowhead = none ];
331 -> 109;

332 [label="EVAL with clause\nms(.(X488, .(X489, X490)), X491) :- ','(split(.(X488, .(X489, X490)), X492, X493), ','(ms(X492, X494), ','(ms(X493, X495), merge(X494, X495, X491)))).\nand substitution\nX488 -> T388\nX489 -> T389\nX490 -> T390\nT1 -> .(T388, .(T389, T390))\nT2 -> T387\nX491 -> T387\nT384 -> T388\nT385 -> T389\nT386 -> T390", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 332 [arrowhead = none ];
332 -> 142;

333 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 333 [arrowhead = none ];
333 -> 143;

334 [label="EVAL with clause\nms(.(X332, .(X333, X334)), X335) :- ','(split(.(X332, .(X333, X334)), X336, X337), ','(ms(X336, X338), ','(ms(X337, X339), merge(X338, X339, X335)))).\nand substitution\nX332 -> T243\nX333 -> T244\nX334 -> T245\nT1 -> .(T243, .(T244, T245))\nT234 -> T242\nX335 -> .(T242, [])\nT239 -> T243\nT240 -> T244\nT241 -> T245", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 334 [arrowhead = none ];
334 -> 110;

335 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 335 [arrowhead = none ];
335 -> 111;

336 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
110 -> 336 [arrowhead = none ];
336 -> 112;

337 [label="BACKTRACK\nfor clause: split([], [], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
112 -> 337 [arrowhead = none ];
337 -> 113;

338 [label="ONLY EVAL with clause\nsplit(.(X362, X363), .(X362, X364), X365) :- split(X363, X365, X364).\nand substitution\nT243 -> T262\nX362 -> T262\nT244 -> T260\nT245 -> T261\nX363 -> .(T260, T261)\nX364 -> X366\nX336 -> .(T262, X366)\nX337 -> X367\nX365 -> X367\nT258 -> T260\nT259 -> T261\nT257 -> T262", fontsize=14, style = filled, fillcolor = white];
113 -> 338 [arrowhead = none ];
338 -> 114;

339 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
114 -> 339 [arrowhead = none ];
339 -> 115;

340 [label="SPLIT 2\nreplacements:\nX367 -> T265\nX366 -> T266\nT262 -> T267", fontsize=14, style = filled, fillcolor = violet];
114 -> 340 [arrowhead = none ];
340 -> 116;

341 [label="INSTANCE with matching:\nT27 -> T260\nT28 -> T261\nX42 -> X367\nX41 -> X366", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 341 [arrowhead = none , style=dashed];
341 -> 12[style=dashed];

342 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
116 -> 342 [arrowhead = none ];
342 -> 117;

343 [label="SPLIT 2\nreplacements:\nX338 -> T272\nT265 -> T273", fontsize=14, style = filled, fillcolor = violet];
116 -> 343 [arrowhead = none ];
343 -> 118;

344 [label="INSTANCE with matching:\nT34 -> T267\nT33 -> T266\nX13 -> X338", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 344 [arrowhead = none , style=dashed];
344 -> 25[style=dashed];

345 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
118 -> 345 [arrowhead = none ];
345 -> 119;

346 [label="SPLIT 2\nreplacements:\nX339 -> T276\nT272 -> T277", fontsize=14, style = filled, fillcolor = violet];
118 -> 346 [arrowhead = none ];
346 -> 120;

347 [label="INSTANCE with matching:\nT55 -> T273\nX14 -> X339", fontsize=14, style = filled, fillcolor = lightgrey];
119 -> 347 [arrowhead = none , style=dashed];
347 -> 92[style=dashed];

348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
120 -> 348 [arrowhead = none ];
348 -> 121;

349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 349 [arrowhead = none ];
349 -> 122;

350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 350 [arrowhead = none ];
350 -> 123;

351 [label="EVAL with clause\nmerge([], X390, X390).\nand substitution\nT277 -> []\nT276 -> .(T291, [])\nX390 -> .(T291, [])\nT242 -> T291\nT290 -> .(T291, [])", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 351 [arrowhead = none ];
351 -> 124;

352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 352 [arrowhead = none ];
352 -> 125;

353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
123 -> 353 [arrowhead = none ];
353 -> 127;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
123 -> 354 [arrowhead = none ];
354 -> 128;

355 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 355 [arrowhead = none ];
355 -> 126;

356 [label="EVAL with clause\nmerge(X396, [], X396).\nand substitution\nT277 -> .(T301, [])\nX396 -> .(T301, [])\nT276 -> []\nT242 -> T301\nT300 -> .(T301, [])", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 356 [arrowhead = none ];
356 -> 129;

357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 357 [arrowhead = none ];
357 -> 130;

358 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
128 -> 358 [arrowhead = none ];
358 -> 132;

359 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
128 -> 359 [arrowhead = none ];
359 -> 133;

360 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 360 [arrowhead = none ];
360 -> 131;

361 [label="EVAL with clause\nmerge(.(X418, X419), .(X420, X421), .(X418, X422)) :- ','(less(X418, s(X420)), merge(X419, .(X420, X421), X422)).\nand substitution\nX418 -> T318\nX419 -> T323\nT277 -> .(T318, T323)\nX420 -> T322\nX421 -> T324\nT276 -> .(T322, T324)\nT242 -> T318\nX422 -> []\nT320 -> T322\nT319 -> T323\nT321 -> T324", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 361 [arrowhead = none ];
361 -> 134;

362 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 362 [arrowhead = none ];
362 -> 135;

363 [label="EVAL with clause\nmerge(.(X456, X457), .(X458, X459), .(X458, X460)) :- ','(less(X458, X456), merge(.(X456, X457), X459, X460)).\nand substitution\nX456 -> T358\nX457 -> T360\nT277 -> .(T358, T360)\nX458 -> T356\nX459 -> T359\nT276 -> .(T356, T359)\nT242 -> T356\nX460 -> []\nT354 -> T358\nT357 -> T359\nT355 -> T360", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 363 [arrowhead = none ];
363 -> 138;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 364 [arrowhead = none ];
364 -> 139;

365 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
134 -> 365 [arrowhead = none ];
365 -> 136;

366 [label="SPLIT 2\nreplacements:\nT323 -> T327\nT322 -> T328\nT324 -> T329", fontsize=14, style = filled, fillcolor = violet];
134 -> 366 [arrowhead = none ];
366 -> 137;

367 [label="INSTANCE with matching:\nT139 -> T318\nT140 -> T322", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 367 [arrowhead = none , style=dashed];
367 -> 70[style=dashed];

368 [label="INSTANCE with matching:\nT212 -> T327\nT211 -> .(T328, T329)", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 368 [arrowhead = none , style=dashed];
368 -> 93[style=dashed];

369 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
138 -> 369 [arrowhead = none ];
369 -> 140;

370 [label="SPLIT 2\nreplacements:\nT358 -> T363\nT360 -> T364\nT359 -> T365", fontsize=14, style = filled, fillcolor = violet];
138 -> 370 [arrowhead = none ];
370 -> 141;

371 [label="INSTANCE with matching:\nT196 -> T356\nT197 -> T358", fontsize=14, style = filled, fillcolor = lightgrey];
140 -> 371 [arrowhead = none , style=dashed];
371 -> 90[style=dashed];

372 [label="INSTANCE with matching:\nT212 -> .(T363, T364)\nT211 -> T365", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 372 [arrowhead = none , style=dashed];
372 -> 93[style=dashed];

373 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
142 -> 373 [arrowhead = none ];
373 -> 144;

374 [label="BACKTRACK\nfor clause: split([], [], [])because of non-unification", fontsize=14, style = filled, fillcolor = white];
144 -> 374 [arrowhead = none ];
374 -> 145;

375 [label="ONLY EVAL with clause\nsplit(.(X518, X519), .(X518, X520), X521) :- split(X519, X521, X520).\nand substitution\nT388 -> T407\nX518 -> T407\nT389 -> T405\nT390 -> T406\nX519 -> .(T405, T406)\nX520 -> X522\nX492 -> .(T407, X522)\nX493 -> X523\nX521 -> X523\nT403 -> T405\nT404 -> T406\nT402 -> T407", fontsize=14, style = filled, fillcolor = white];
145 -> 375 [arrowhead = none ];
375 -> 146;

376 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
146 -> 376 [arrowhead = none ];
376 -> 147;

377 [label="SPLIT 2\nreplacements:\nX523 -> T410\nX522 -> T411\nT407 -> T412\nT1 -> T413\nX326 -> T414", fontsize=14, style = filled, fillcolor = violet];
146 -> 377 [arrowhead = none ];
377 -> 148;

378 [label="INSTANCE with matching:\nT27 -> T405\nT28 -> T406\nX42 -> X523\nX41 -> X522", fontsize=14, style = filled, fillcolor = lightgrey];
147 -> 378 [arrowhead = none , style=dashed];
378 -> 12[style=dashed];

379 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
148 -> 379 [arrowhead = none ];
379 -> 149;

380 [label="SPLIT 2\nreplacements:\nX494 -> T419\nT410 -> T420\nT413 -> T421\nT414 -> T422", fontsize=14, style = filled, fillcolor = violet];
148 -> 380 [arrowhead = none ];
380 -> 150;

381 [label="INSTANCE with matching:\nT34 -> T412\nT33 -> T411\nX13 -> X494", fontsize=14, style = filled, fillcolor = lightgrey];
149 -> 381 [arrowhead = none , style=dashed];
381 -> 25[style=dashed];

382 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
150 -> 382 [arrowhead = none ];
382 -> 151;

383 [label="SPLIT 2\nreplacements:\nX495 -> T425\nT419 -> T426\nT421 -> T427\nT422 -> T428", fontsize=14, style = filled, fillcolor = violet];
150 -> 383 [arrowhead = none ];
383 -> 152;

384 [label="INSTANCE with matching:\nT55 -> T420\nX14 -> X495", fontsize=14, style = filled, fillcolor = lightgrey];
151 -> 384 [arrowhead = none , style=dashed];
384 -> 92[style=dashed];

385 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
152 -> 385 [arrowhead = none ];
385 -> 153;

386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 386 [arrowhead = none ];
386 -> 154;

387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 387 [arrowhead = none ];
387 -> 155;

388 [label="EVAL with clause\nmerge([], X546, X546).\nand substitution\nT426 -> []\nT425 -> T435\nX546 -> T435\nT387 -> T435", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 388 [arrowhead = none ];
388 -> 156;

389 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 389 [arrowhead = none ];
389 -> 157;

390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 390 [arrowhead = none ];
390 -> 159;

391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 391 [arrowhead = none ];
391 -> 160;

392 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 392 [arrowhead = none ];
392 -> 158;

393 [label="EVAL with clause\nmerge(X552, [], X552).\nand substitution\nT426 -> T440\nX552 -> T440\nT425 -> []\nT387 -> T440", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 393 [arrowhead = none ];
393 -> 161;

394 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 394 [arrowhead = none ];
394 -> 162;

395 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
160 -> 395 [arrowhead = none ];
395 -> 164;

396 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
160 -> 396 [arrowhead = none ];
396 -> 165;

397 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
161 -> 397 [arrowhead = none ];
397 -> 163;

398 [label="EVAL with clause\nmerge(.(X574, X575), .(X576, X577), .(X574, X578)) :- ','(less(X574, s(X576)), merge(X575, .(X576, X577), X578)).\nand substitution\nX574 -> T461\nX575 -> T467\nT426 -> .(T461, T467)\nX576 -> T466\nX577 -> T468\nT425 -> .(T466, T468)\nX578 -> T465\nT387 -> .(T461, T465)\nT463 -> T466\nT462 -> T467\nT464 -> T468", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 398 [arrowhead = none ];
398 -> 166;

399 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 399 [arrowhead = none ];
399 -> 167;

400 [label="EVAL with clause\nmerge(.(X793, X794), .(X795, X796), .(X795, X797)) :- ','(less(X795, X793), merge(.(X793, X794), X796, X797)).\nand substitution\nX793 -> T697\nX794 -> T699\nT426 -> .(T697, T699)\nX795 -> T694\nX796 -> T698\nT425 -> .(T694, T698)\nX797 -> T696\nT387 -> .(T694, T696)\nT692 -> T697\nT695 -> T698\nT693 -> T699", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 400 [arrowhead = none ];
400 -> 213;

401 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 401 [arrowhead = none ];
401 -> 214;

402 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
166 -> 402 [arrowhead = none ];
402 -> 168;

403 [label="SPLIT 2\nreplacements:\nT467 -> T471\nT466 -> T472\nT468 -> T473\nT427 -> T474\nT428 -> T475", fontsize=14, style = filled, fillcolor = violet];
166 -> 403 [arrowhead = none ];
403 -> 169;

404 [label="INSTANCE with matching:\nT318 -> T461\nT322 -> T466", fontsize=14, style = filled, fillcolor = lightgrey];
168 -> 404 [arrowhead = none , style=dashed];
404 -> 136[style=dashed];

405 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
169 -> 405 [arrowhead = none ];
405 -> 170;

406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 406 [arrowhead = none ];
406 -> 171;

407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 407 [arrowhead = none ];
407 -> 172;

408 [label="EVAL with clause\nmerge([], X594, X594).\nand substitution\nT471 -> []\nT472 -> T490\nT473 -> T491\nX594 -> .(T490, T491)\nT465 -> .(T490, T491)", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 408 [arrowhead = none ];
408 -> 173;

409 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 409 [arrowhead = none ];
409 -> 174;

410 [label="BACKTRACK\nfor clause: merge(Xs, [], Xs)because of non-unification", fontsize=14, style = filled, fillcolor = white];
172 -> 410 [arrowhead = none ];
410 -> 176;

411 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 411 [arrowhead = none ];
411 -> 175;

412 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 412 [arrowhead = none ];
412 -> 177;

413 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 413 [arrowhead = none ];
413 -> 178;

414 [label="EVAL with clause\nmerge(.(X617, X618), .(X619, X620), .(X617, X621)) :- ','(less(X617, s(X619)), merge(X618, .(X619, X620), X621)).\nand substitution\nX617 -> T513\nX618 -> T519\nT471 -> .(T513, T519)\nT472 -> T518\nX619 -> T518\nT473 -> T520\nX620 -> T520\nX621 -> T517\nT465 -> .(T513, T517)\nT515 -> T518\nT514 -> T519\nT516 -> T520", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 414 [arrowhead = none ];
414 -> 179;

415 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 415 [arrowhead = none ];
415 -> 180;

416 [label="EVAL with clause\nmerge(.(X771, X772), .(X773, X774), .(X773, X775)) :- ','(less(X773, X771), merge(.(X771, X772), X774, X775)).\nand substitution\nX771 -> T677\nX772 -> T679\nT471 -> .(T677, T679)\nT472 -> T674\nX773 -> T674\nT473 -> T678\nX774 -> T678\nX775 -> T676\nT465 -> .(T674, T676)\nT672 -> T677\nT675 -> T678\nT673 -> T679", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 416 [arrowhead = none ];
416 -> 211;

417 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 417 [arrowhead = none ];
417 -> 212;

418 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
179 -> 418 [arrowhead = none ];
418 -> 181;

419 [label="SPLIT 2\nreplacements:\nT519 -> T523\nT518 -> T524\nT520 -> T525", fontsize=14, style = filled, fillcolor = violet];
179 -> 419 [arrowhead = none ];
419 -> 182;

420 [label="INSTANCE with matching:\nT318 -> T513\nT322 -> T518", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 420 [arrowhead = none , style=dashed];
420 -> 136[style=dashed];

421 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
182 -> 421 [arrowhead = none ];
421 -> 183;

422 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
183 -> 422 [arrowhead = none ];
422 -> 184;

423 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
183 -> 423 [arrowhead = none ];
423 -> 185;

424 [label="EVAL with clause\nmerge([], X637, X637).\nand substitution\nT523 -> []\nT524 -> T540\nT525 -> T541\nX637 -> .(T540, T541)\nT517 -> .(T540, T541)", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 424 [arrowhead = none ];
424 -> 186;

425 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 425 [arrowhead = none ];
425 -> 187;

426 [label="BACKTRACK\nfor clause: merge(Xs, [], Xs)because of non-unification", fontsize=14, style = filled, fillcolor = white];
185 -> 426 [arrowhead = none ];
426 -> 189;

427 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
186 -> 427 [arrowhead = none ];
427 -> 188;

428 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 428 [arrowhead = none ];
428 -> 190;

429 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 429 [arrowhead = none ];
429 -> 191;

430 [label="EVAL with clause\nmerge(.(X660, X661), .(X662, X663), .(X660, X664)) :- ','(less(X660, s(X662)), merge(X661, .(X662, X663), X664)).\nand substitution\nX660 -> T563\nX661 -> T569\nT523 -> .(T563, T569)\nT524 -> T568\nX662 -> T568\nT525 -> T570\nX663 -> T570\nX664 -> T567\nT517 -> .(T563, T567)\nT565 -> T568\nT564 -> T569\nT566 -> T570", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 430 [arrowhead = none ];
430 -> 192;

431 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 431 [arrowhead = none ];
431 -> 193;

432 [label="EVAL with clause\nmerge(.(X682, X683), .(X684, X685), .(X684, X686)) :- ','(less(X684, X682), merge(.(X682, X683), X685, X686)).\nand substitution\nX682 -> T588\nX683 -> T590\nT523 -> .(T588, T590)\nT524 -> T585\nX684 -> T585\nT525 -> T589\nX685 -> T589\nX686 -> T587\nT517 -> .(T585, T587)\nT583 -> T588\nT586 -> T589\nT584 -> T590", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 432 [arrowhead = none ];
432 -> 194;

433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 433 [arrowhead = none ];
433 -> 195;

434 [label="INSTANCE with matching:\nT513 -> T563\nT518 -> T568\nT519 -> T569\nT520 -> T570\nT517 -> T567", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 434 [arrowhead = none , style=dashed];
434 -> 179[style=dashed];

435 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
194 -> 435 [arrowhead = none ];
435 -> 196;

436 [label="SPLIT 2\nreplacements:\nT588 -> T593\nT590 -> T594\nT589 -> T595", fontsize=14, style = filled, fillcolor = violet];
194 -> 436 [arrowhead = none ];
436 -> 197;

437 [label="INSTANCE with matching:\nT356 -> T585\nT358 -> T588", fontsize=14, style = filled, fillcolor = lightgrey];
196 -> 437 [arrowhead = none , style=dashed];
437 -> 140[style=dashed];

438 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
197 -> 438 [arrowhead = none ];
438 -> 198;

439 [label="BACKTRACK\nfor clause: merge([], Xs, Xs)because of non-unification", fontsize=14, style = filled, fillcolor = white];
198 -> 439 [arrowhead = none ];
439 -> 199;

440 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
199 -> 440 [arrowhead = none ];
440 -> 200;

441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
199 -> 441 [arrowhead = none ];
441 -> 201;

442 [label="EVAL with clause\nmerge(X705, [], X705).\nand substitution\nT593 -> T610\nT594 -> T611\nX705 -> .(T610, T611)\nT595 -> []\nT587 -> .(T610, T611)", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 442 [arrowhead = none ];
442 -> 202;

443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 443 [arrowhead = none ];
443 -> 203;

444 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
201 -> 444 [arrowhead = none ];
444 -> 205;

445 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
201 -> 445 [arrowhead = none ];
445 -> 206;

446 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
202 -> 446 [arrowhead = none ];
446 -> 204;

447 [label="EVAL with clause\nmerge(.(X727, X728), .(X729, X730), .(X727, X731)) :- ','(less(X727, s(X729)), merge(X728, .(X729, X730), X731)).\nand substitution\nT593 -> T632\nX727 -> T632\nT594 -> T638\nX728 -> T638\nX729 -> T637\nX730 -> T639\nT595 -> .(T637, T639)\nX731 -> T636\nT587 -> .(T632, T636)\nT634 -> T637\nT633 -> T638\nT635 -> T639", fontsize=14, style = filled, fillcolor = lightblue];
205 -> 447 [arrowhead = none ];
447 -> 207;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
205 -> 448 [arrowhead = none ];
448 -> 208;

449 [label="EVAL with clause\nmerge(.(X749, X750), .(X751, X752), .(X751, X753)) :- ','(less(X751, X749), merge(.(X749, X750), X752, X753)).\nand substitution\nT593 -> T657\nX749 -> T657\nT594 -> T659\nX750 -> T659\nX751 -> T654\nX752 -> T658\nT595 -> .(T654, T658)\nX753 -> T656\nT587 -> .(T654, T656)\nT652 -> T657\nT655 -> T658\nT653 -> T659", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 449 [arrowhead = none ];
449 -> 209;

450 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 450 [arrowhead = none ];
450 -> 210;

451 [label="INSTANCE with matching:\nT513 -> T632\nT518 -> T637\nT519 -> T638\nT520 -> T639\nT517 -> T636", fontsize=14, style = filled, fillcolor = lightgrey];
207 -> 451 [arrowhead = none , style=dashed];
451 -> 179[style=dashed];

452 [label="INSTANCE with matching:\nT585 -> T654\nT588 -> T657\nT590 -> T659\nT589 -> T658\nT587 -> T656", fontsize=14, style = filled, fillcolor = lightgrey];
209 -> 452 [arrowhead = none , style=dashed];
452 -> 194[style=dashed];

453 [label="INSTANCE with matching:\nT585 -> T674\nT588 -> T677\nT590 -> T679\nT589 -> T678\nT587 -> T676", fontsize=14, style = filled, fillcolor = lightgrey];
211 -> 453 [arrowhead = none , style=dashed];
453 -> 194[style=dashed];

454 [label="INSTANCE with matching:\nT674 -> T694\nT677 -> T697\nT679 -> T699\nT678 -> T698\nT676 -> T696", fontsize=14, style = filled, fillcolor = lightgrey];
213 -> 454 [arrowhead = none , style=dashed];
454 -> 211[style=dashed];

}

(2) Obligation:

Triples:

split16(.(T49, T51), .(T49, X89), X90) :- split16(T51, X90, X89).
split12(T42, T44, .(T42, X71), X72) :- split16(T44, X72, X71).
p34(T72, T73, T74, X123, X124, X125, X126, X127) :- split12(T72, .(T73, T74), X123, X124).
p34(T72, T73, T74, T78, T79, X125, X126, X127) :- ','(splitc12(T72, .(T73, T74), T78, T79), ms38(T78, X125)).
p34(T72, T73, T74, T78, T84, T83, X126, X127) :- ','(splitc12(T72, .(T73, T74), T78, T84), ','(msc38(T78, T83), ms38(T84, X126))).
p34(T72, T73, T74, T78, T84, T106, T105, X127) :- ','(splitc12(T72, .(T73, T74), T78, T84), ','(msc38(T78, T106), ','(msc38(T84, T105), merge54(T106, T105, X127)))).
ms38(.(T99, .(T100, T101)), X172) :- p34(T99, T100, T101, X168, X169, X170, X171, X172).
merge54(.(T139, T141), .(T140, T142), .(T139, X226)) :- less70(T139, T140).
merge54(.(T139, T145), .(T146, T147), .(T139, X226)) :- ','(lessc70(T139, T146), merge54(T145, .(T146, T147), X226)).
merge54(.(T197, T199), .(T196, T198), .(T196, X287)) :- less78(T196, T197).
merge54(.(T202, T203), .(T196, T204), .(T196, X287)) :- ','(lessc78(T196, T202), merge54(.(T202, T203), T204, X287)).
less78(s(T176), s(T177)) :- less78(T176, T177).
ms25(T72, .(T73, T74), X127) :- p34(T72, T73, T74, X123, X124, X125, X126, X127).
less70(s(T161), T162) :- less78(T161, T162).
p179(T513, T518, T519, T520, T517) :- less70(T513, T518).
p179(T513, T568, .(T563, T569), T570, .(T563, T567)) :- ','(lessc70(T513, T568), p179(T563, T568, T569, T570, T567)).
p179(T513, T585, .(T588, T590), T589, .(T585, T587)) :- ','(lessc70(T513, T585), p194(T585, T588, T590, T589, T587)).
p194(T585, T588, T590, T589, T587) :- less78(T585, T588).
p194(T585, T632, T638, .(T637, T639), .(T632, T636)) :- ','(lessc78(T585, T632), p179(T632, T637, T638, T639, T636)).
p194(T585, T657, T659, .(T654, T658), .(T654, T656)) :- ','(lessc78(T585, T657), p194(T654, T657, T659, T658, T656)).
ms1(.(T29, .(T27, T28)), []) :- split12(T27, T28, X42, X41).
ms1(.(T34, .(T27, T28)), []) :- ','(splitc12(T27, T28, T32, T33), ms25(T34, T33, X13)).
ms1(.(T34, .(T27, T28)), []) :- ','(splitc12(T27, T28, T55, T33), ','(msc25(T34, T33, T54), ms38(T55, X14))).
ms1(.(T34, .(T27, T28)), []) :- ','(splitc12(T27, T28, T55, T33), ','(msc25(T34, T33, T212), ','(msc38(T55, T211), merge93(T212, T211)))).
ms1(.(T262, .(T260, T261)), .(T242, [])) :- split12(T260, T261, X367, X366).
ms1(.(T267, .(T260, T261)), .(T242, [])) :- ','(splitc12(T260, T261, T265, T266), ms25(T267, T266, X338)).
ms1(.(T267, .(T260, T261)), .(T242, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, T272), ms38(T273, X339))).
ms1(.(T267, .(T260, T261)), .(T318, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, .(T318, T323)), ','(msc38(T273, .(T322, T324)), less70(T318, T322)))).
ms1(.(T267, .(T260, T261)), .(T318, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, .(T318, T327)), ','(msc38(T273, .(T328, T329)), ','(lessc70(T318, T328), merge93(T327, .(T328, T329)))))).
ms1(.(T267, .(T260, T261)), .(T356, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, .(T358, T360)), ','(msc38(T273, .(T356, T359)), less78(T356, T358)))).
ms1(.(T267, .(T260, T261)), .(T356, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, .(T363, T364)), ','(msc38(T273, .(T356, T365)), ','(lessc78(T356, T363), merge93(.(T363, T364), T365))))).
ms1(.(T407, .(T405, T406)), T387) :- split12(T405, T406, X523, X522).
ms1(.(T412, .(T405, T406)), T387) :- ','(splitc12(T405, T406, T410, T411), ms25(T412, T411, X494)).
ms1(.(T412, .(T405, T406)), T387) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, T419), ms38(T420, X495))).
ms1(.(T412, .(T405, T406)), .(T461, T465)) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T461, T467)), ','(msc38(T420, .(T466, T468)), less70(T461, T466)))).
ms1(.(T412, .(T405, T406)), .(T461, .(T513, T517))) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T461, .(T513, T519))), ','(msc38(T420, .(T518, T520)), ','(lessc70(T461, T518), p179(T513, T518, T519, T520, T517))))).
ms1(.(T412, .(T405, T406)), .(T461, .(T674, T676))) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T461, .(T677, T679))), ','(msc38(T420, .(T674, T678)), ','(lessc70(T461, T674), p194(T674, T677, T679, T678, T676))))).
ms1(.(T412, .(T405, T406)), .(T694, T696)) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T697, T699)), ','(msc38(T420, .(T694, T698)), p194(T694, T697, T699, T698, T696)))).

Clauses:

splitc16([], [], []).
splitc16(.(T49, T51), .(T49, X89), X90) :- splitc16(T51, X90, X89).
splitc12(T42, T44, .(T42, X71), X72) :- splitc16(T44, X72, X71).
qc34(T72, T73, T74, T78, T84, T106, T105, X127) :- ','(splitc12(T72, .(T73, T74), T78, T84), ','(msc38(T78, T106), ','(msc38(T84, T105), mergec54(T106, T105, X127)))).
msc38([], []).
msc38(.(T89, []), .(T89, [])).
msc38(.(T99, .(T100, T101)), X172) :- qc34(T99, T100, T101, X168, X169, X170, X171, X172).
mergec54([], T113, T113).
mergec54(T118, [], T118).
mergec54(.(T139, T145), .(T146, T147), .(T139, X226)) :- ','(lessc70(T139, T146), mergec54(T145, .(T146, T147), X226)).
mergec54(.(T202, T203), .(T196, T204), .(T196, X287)) :- ','(lessc78(T196, T202), mergec54(.(T202, T203), T204, X287)).
lessc78(0, s(T169)).
lessc78(s(T176), s(T177)) :- lessc78(T176, T177).
msc25(T62, [], .(T62, [])).
msc25(T72, .(T73, T74), X127) :- qc34(T72, T73, T74, X123, X124, X125, X126, X127).
lessc70(0, T154).
lessc70(s(T161), T162) :- lessc78(T161, T162).
mergec93([], []).
mergec93([], []).
qc179(T513, T540, [], T541, .(T540, T541)) :- lessc70(T513, T540).
qc179(T513, T568, .(T563, T569), T570, .(T563, T567)) :- ','(lessc70(T513, T568), qc179(T563, T568, T569, T570, T567)).
qc179(T513, T585, .(T588, T590), T589, .(T585, T587)) :- ','(lessc70(T513, T585), qc194(T585, T588, T590, T589, T587)).
qc194(T585, T610, T611, [], .(T610, T611)) :- lessc78(T585, T610).
qc194(T585, T632, T638, .(T637, T639), .(T632, T636)) :- ','(lessc78(T585, T632), qc179(T632, T637, T638, T639, T636)).
qc194(T585, T657, T659, .(T654, T658), .(T654, T656)) :- ','(lessc78(T585, T657), qc194(T654, T657, T659, T658, T656)).

Afs:

ms1(x1, x2) = ms1(x2)

(3) UndefinedPredicateInTriplesTransformerProof (SOUND transformation)

Deleted triples and predicates having undefined goals [UNKNOWN].

(4) Obligation:

Triples:

split16(.(T49, T51), .(T49, X89), X90) :- split16(T51, X90, X89).
split12(T42, T44, .(T42, X71), X72) :- split16(T44, X72, X71).
p34(T72, T73, T74, X123, X124, X125, X126, X127) :- split12(T72, .(T73, T74), X123, X124).
p34(T72, T73, T74, T78, T79, X125, X126, X127) :- ','(splitc12(T72, .(T73, T74), T78, T79), ms38(T78, X125)).
p34(T72, T73, T74, T78, T84, T83, X126, X127) :- ','(splitc12(T72, .(T73, T74), T78, T84), ','(msc38(T78, T83), ms38(T84, X126))).
p34(T72, T73, T74, T78, T84, T106, T105, X127) :- ','(splitc12(T72, .(T73, T74), T78, T84), ','(msc38(T78, T106), ','(msc38(T84, T105), merge54(T106, T105, X127)))).
ms38(.(T99, .(T100, T101)), X172) :- p34(T99, T100, T101, X168, X169, X170, X171, X172).
merge54(.(T139, T141), .(T140, T142), .(T139, X226)) :- less70(T139, T140).
merge54(.(T139, T145), .(T146, T147), .(T139, X226)) :- ','(lessc70(T139, T146), merge54(T145, .(T146, T147), X226)).
merge54(.(T197, T199), .(T196, T198), .(T196, X287)) :- less78(T196, T197).
merge54(.(T202, T203), .(T196, T204), .(T196, X287)) :- ','(lessc78(T196, T202), merge54(.(T202, T203), T204, X287)).
less78(s(T176), s(T177)) :- less78(T176, T177).
ms25(T72, .(T73, T74), X127) :- p34(T72, T73, T74, X123, X124, X125, X126, X127).
less70(s(T161), T162) :- less78(T161, T162).
p179(T513, T518, T519, T520, T517) :- less70(T513, T518).
p179(T513, T568, .(T563, T569), T570, .(T563, T567)) :- ','(lessc70(T513, T568), p179(T563, T568, T569, T570, T567)).
p179(T513, T585, .(T588, T590), T589, .(T585, T587)) :- ','(lessc70(T513, T585), p194(T585, T588, T590, T589, T587)).
p194(T585, T588, T590, T589, T587) :- less78(T585, T588).
p194(T585, T632, T638, .(T637, T639), .(T632, T636)) :- ','(lessc78(T585, T632), p179(T632, T637, T638, T639, T636)).
p194(T585, T657, T659, .(T654, T658), .(T654, T656)) :- ','(lessc78(T585, T657), p194(T654, T657, T659, T658, T656)).
ms1(.(T29, .(T27, T28)), []) :- split12(T27, T28, X42, X41).
ms1(.(T34, .(T27, T28)), []) :- ','(splitc12(T27, T28, T32, T33), ms25(T34, T33, X13)).
ms1(.(T34, .(T27, T28)), []) :- ','(splitc12(T27, T28, T55, T33), ','(msc25(T34, T33, T54), ms38(T55, X14))).
ms1(.(T262, .(T260, T261)), .(T242, [])) :- split12(T260, T261, X367, X366).
ms1(.(T267, .(T260, T261)), .(T242, [])) :- ','(splitc12(T260, T261, T265, T266), ms25(T267, T266, X338)).
ms1(.(T267, .(T260, T261)), .(T242, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, T272), ms38(T273, X339))).
ms1(.(T267, .(T260, T261)), .(T318, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, .(T318, T323)), ','(msc38(T273, .(T322, T324)), less70(T318, T322)))).
ms1(.(T267, .(T260, T261)), .(T356, [])) :- ','(splitc12(T260, T261, T273, T266), ','(msc25(T267, T266, .(T358, T360)), ','(msc38(T273, .(T356, T359)), less78(T356, T358)))).
ms1(.(T407, .(T405, T406)), T387) :- split12(T405, T406, X523, X522).
ms1(.(T412, .(T405, T406)), T387) :- ','(splitc12(T405, T406, T410, T411), ms25(T412, T411, X494)).
ms1(.(T412, .(T405, T406)), T387) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, T419), ms38(T420, X495))).
ms1(.(T412, .(T405, T406)), .(T461, T465)) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T461, T467)), ','(msc38(T420, .(T466, T468)), less70(T461, T466)))).
ms1(.(T412, .(T405, T406)), .(T461, .(T513, T517))) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T461, .(T513, T519))), ','(msc38(T420, .(T518, T520)), ','(lessc70(T461, T518), p179(T513, T518, T519, T520, T517))))).
ms1(.(T412, .(T405, T406)), .(T461, .(T674, T676))) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T461, .(T677, T679))), ','(msc38(T420, .(T674, T678)), ','(lessc70(T461, T674), p194(T674, T677, T679, T678, T676))))).
ms1(.(T412, .(T405, T406)), .(T694, T696)) :- ','(splitc12(T405, T406, T420, T411), ','(msc25(T412, T411, .(T697, T699)), ','(msc38(T420, .(T694, T698)), p194(T694, T697, T699, T698, T696)))).

Clauses:

splitc16([], [], []).
splitc16(.(T49, T51), .(T49, X89), X90) :- splitc16(T51, X90, X89).
splitc12(T42, T44, .(T42, X71), X72) :- splitc16(T44, X72, X71).
qc34(T72, T73, T74, T78, T84, T106, T105, X127) :- ','(splitc12(T72, .(T73, T74), T78, T84), ','(msc38(T78, T106), ','(msc38(T84, T105), mergec54(T106, T105, X127)))).
msc38([], []).
msc38(.(T89, []), .(T89, [])).
msc38(.(T99, .(T100, T101)), X172) :- qc34(T99, T100, T101, X168, X169, X170, X171, X172).
mergec54([], T113, T113).
mergec54(T118, [], T118).
mergec54(.(T139, T145), .(T146, T147), .(T139, X226)) :- ','(lessc70(T139, T146), mergec54(T145, .(T146, T147), X226)).
mergec54(.(T202, T203), .(T196, T204), .(T196, X287)) :- ','(lessc78(T196, T202), mergec54(.(T202, T203), T204, X287)).
lessc78(0, s(T169)).
lessc78(s(T176), s(T177)) :- lessc78(T176, T177).
msc25(T62, [], .(T62, [])).
msc25(T72, .(T73, T74), X127) :- qc34(T72, T73, T74, X123, X124, X125, X126, X127).
lessc70(0, T154).
lessc70(s(T161), T162) :- lessc78(T161, T162).
mergec93([], []).
mergec93([], []).
qc179(T513, T540, [], T541, .(T540, T541)) :- lessc70(T513, T540).
qc179(T513, T568, .(T563, T569), T570, .(T563, T567)) :- ','(lessc70(T513, T568), qc179(T563, T568, T569, T570, T567)).
qc179(T513, T585, .(T588, T590), T589, .(T585, T587)) :- ','(lessc70(T513, T585), qc194(T585, T588, T590, T589, T587)).
qc194(T585, T610, T611, [], .(T610, T611)) :- lessc78(T585, T610).
qc194(T585, T632, T638, .(T637, T639), .(T632, T636)) :- ','(lessc78(T585, T632), qc179(T632, T637, T638, T639, T636)).
qc194(T585, T657, T659, .(T654, T658), .(T654, T656)) :- ','(lessc78(T585, T657), qc194(T654, T657, T659, T658, T656)).

Afs:

ms1(x1, x2) = ms1(x2)

(5) TriplesToPiDPProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
ms1_in: (f,b)
split12_in: (f,f,f,f)
split16_in: (f,f,f)
splitc12_in: (f,f,f,f)
splitc16_in: (f,f,f)
ms25_in: (f,f,f)
p34_in: (f,f,f,f,f,f,f,f)
ms38_in: (f,f)
msc38_in: (f,f)
qc34_in: (f,f,f,f,f,f,f,f)
mergec54_in: (f,f,f)
lessc70_in: (f,f) (b,f) (b,b)
lessc78_in: (f,f) (b,f) (b,b)
merge54_in: (f,f,f)
less70_in: (f,f) (b,f)
less78_in: (f,f) (b,f)
msc25_in: (f,f,f)
p179_in: (b,f,f,f,b)
p194_in: (b,f,f,f,b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

MS1_IN_AG(.(T29, .(T27, T28)), []) → U33_AG(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
MS1_IN_AG(.(T29, .(T27, T28)), []) → SPLIT12_IN_AAAA(T27, T28, X42, X41)
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → U2_AAAA(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → SPLIT16_IN_AAA(T44, X72, X71)
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → U1_AAA(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U34_AG(T34, T27, T28, splitc12_in_aaaa(T27, T28, T32, T33))
U34_AG(T34, T27, T28, splitc12_out_aaaa(T27, T28, T32, T33)) → U35_AG(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
U34_AG(T34, T27, T28, splitc12_out_aaaa(T27, T28, T32, T33)) → MS25_IN_AAA(T34, T33, X13)
MS25_IN_AAA(T72, .(T73, T74), X127) → U21_AAA(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAA(T72, .(T73, T74), X127) → P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → U13_AA(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_out_aa(T78, T83)) → U8_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U12_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → MERGE54_IN_AAA(T106, T105, X127)
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAA(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_AA(T139, T140)
LESS70_IN_AA(s(T161), T162) → U22_AA(T161, T162, less78_in_aa(T161, T162))
LESS70_IN_AA(s(T161), T162) → LESS78_IN_AA(T161, T162)
LESS78_IN_AA(s(T176), s(T177)) → U20_AA(T176, T177, less78_in_aa(T176, T177))
LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)
MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U16_AAA(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U15_AAA(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAA(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_AA(T196, T197)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U19_AAA(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U18_AAA(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U36_AG(T34, T27, T28, splitc12_in_aaaa(T27, T28, T55, T33))
U36_AG(T34, T27, T28, splitc12_out_aaaa(T27, T28, T55, T33)) → U37_AG(T34, T27, T28, T55, msc25_in_aaa(T34, T33, T54))
U37_AG(T34, T27, T28, T55, msc25_out_aaa(T34, T33, T54)) → U38_AG(T34, T27, T28, ms38_in_aa(T55, X14))
U37_AG(T34, T27, T28, T55, msc25_out_aaa(T34, T33, T54)) → MS38_IN_AA(T55, X14)
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → U39_AG(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → SPLIT12_IN_AAAA(T260, T261, X367, X366)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U40_AG(T267, T260, T261, T242, splitc12_in_aaaa(T260, T261, T265, T266))
U40_AG(T267, T260, T261, T242, splitc12_out_aaaa(T260, T261, T265, T266)) → U41_AG(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U40_AG(T267, T260, T261, T242, splitc12_out_aaaa(T260, T261, T265, T266)) → MS25_IN_AAA(T267, T266, X338)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U42_AG(T267, T260, T261, T242, splitc12_in_aaaa(T260, T261, T273, T266))
U42_AG(T267, T260, T261, T242, splitc12_out_aaaa(T260, T261, T273, T266)) → U43_AG(T267, T260, T261, T242, T273, msc25_in_aaa(T267, T266, T272))
U43_AG(T267, T260, T261, T242, T273, msc25_out_aaa(T267, T266, T272)) → U44_AG(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U43_AG(T267, T260, T261, T242, T273, msc25_out_aaa(T267, T266, T272)) → MS38_IN_AA(T273, X339)
MS1_IN_AG(.(T267, .(T260, T261)), .(T318, [])) → U45_AG(T267, T260, T261, T318, splitc12_in_aaaa(T260, T261, T273, T266))
U45_AG(T267, T260, T261, T318, splitc12_out_aaaa(T260, T261, T273, T266)) → U46_AG(T267, T260, T261, T318, T273, msc25_in_aaa(T267, T266, .(T318, T323)))
U46_AG(T267, T260, T261, T318, T273, msc25_out_aaa(T267, T266, .(T318, T323))) → U47_AG(T267, T260, T261, T318, msc38_in_aa(T273, .(T322, T324)))
U47_AG(T267, T260, T261, T318, msc38_out_aa(T273, .(T322, T324))) → U48_AG(T267, T260, T261, T318, less70_in_ga(T318, T322))
U47_AG(T267, T260, T261, T318, msc38_out_aa(T273, .(T322, T324))) → LESS70_IN_GA(T318, T322)
LESS70_IN_GA(s(T161), T162) → U22_GA(T161, T162, less78_in_ga(T161, T162))
LESS70_IN_GA(s(T161), T162) → LESS78_IN_GA(T161, T162)
LESS78_IN_GA(s(T176), s(T177)) → U20_GA(T176, T177, less78_in_ga(T176, T177))
LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)
MS1_IN_AG(.(T267, .(T260, T261)), .(T356, [])) → U49_AG(T267, T260, T261, T356, splitc12_in_aaaa(T260, T261, T273, T266))
U49_AG(T267, T260, T261, T356, splitc12_out_aaaa(T260, T261, T273, T266)) → U50_AG(T267, T260, T261, T356, T273, msc25_in_aaa(T267, T266, .(T358, T360)))
U50_AG(T267, T260, T261, T356, T273, msc25_out_aaa(T267, T266, .(T358, T360))) → U51_AG(T267, T260, T261, T356, T358, msc38_in_aa(T273, .(T356, T359)))
U51_AG(T267, T260, T261, T356, T358, msc38_out_aa(T273, .(T356, T359))) → U52_AG(T267, T260, T261, T356, less78_in_ga(T356, T358))
U51_AG(T267, T260, T261, T356, T358, msc38_out_aa(T273, .(T356, T359))) → LESS78_IN_GA(T356, T358)
MS1_IN_AG(.(T407, .(T405, T406)), T387) → U53_AG(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
MS1_IN_AG(.(T407, .(T405, T406)), T387) → SPLIT12_IN_AAAA(T405, T406, X523, X522)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U54_AG(T412, T405, T406, T387, splitc12_in_aaaa(T405, T406, T410, T411))
U54_AG(T412, T405, T406, T387, splitc12_out_aaaa(T405, T406, T410, T411)) → U55_AG(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U54_AG(T412, T405, T406, T387, splitc12_out_aaaa(T405, T406, T410, T411)) → MS25_IN_AAA(T412, T411, X494)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U56_AG(T412, T405, T406, T387, splitc12_in_aaaa(T405, T406, T420, T411))
U56_AG(T412, T405, T406, T387, splitc12_out_aaaa(T405, T406, T420, T411)) → U57_AG(T412, T405, T406, T387, T420, msc25_in_aaa(T412, T411, T419))
U57_AG(T412, T405, T406, T387, T420, msc25_out_aaa(T412, T411, T419)) → U58_AG(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U57_AG(T412, T405, T406, T387, T420, msc25_out_aaa(T412, T411, T419)) → MS38_IN_AA(T420, X495)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → U59_AG(T412, T405, T406, T461, T465, splitc12_in_aaaa(T405, T406, T420, T411))
U59_AG(T412, T405, T406, T461, T465, splitc12_out_aaaa(T405, T406, T420, T411)) → U60_AG(T412, T405, T406, T461, T465, T420, msc25_in_aaa(T412, T411, .(T461, T467)))
U60_AG(T412, T405, T406, T461, T465, T420, msc25_out_aaa(T412, T411, .(T461, T467))) → U61_AG(T412, T405, T406, T461, T465, msc38_in_aa(T420, .(T466, T468)))
U61_AG(T412, T405, T406, T461, T465, msc38_out_aa(T420, .(T466, T468))) → U62_AG(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U61_AG(T412, T405, T406, T461, T465, msc38_out_aa(T420, .(T466, T468))) → LESS70_IN_GA(T461, T466)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U63_AG(T412, T405, T406, T461, T513, T517, splitc12_in_aaaa(T405, T406, T420, T411))
U63_AG(T412, T405, T406, T461, T513, T517, splitc12_out_aaaa(T405, T406, T420, T411)) → U64_AG(T412, T405, T406, T461, T513, T517, T420, msc25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U64_AG(T412, T405, T406, T461, T513, T517, T420, msc25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U65_AG(T412, T405, T406, T461, T513, T517, T519, msc38_in_aa(T420, .(T518, T520)))
U65_AG(T412, T405, T406, T461, T513, T517, T519, msc38_out_aa(T420, .(T518, T520))) → U66_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, lessc70_in_ga(T461, T518))
U66_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, lessc70_out_ga(T461, T518)) → U67_AG(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
U66_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, lessc70_out_ga(T461, T518)) → P179_IN_GAAAG(T513, T518, T519, T520, T517)
P179_IN_GAAAG(T513, T518, T519, T520, T517) → U23_GAAAG(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
P179_IN_GAAAG(T513, T518, T519, T520, T517) → LESS70_IN_GA(T513, T518)
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_in_ga(T513, T568))
U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_out_ga(T513, T568)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_in_gg(T513, T585))
U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_out_gg(T513, T585)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T588, T590, T589, T587) → U28_GAAAG(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
P194_IN_GAAAG(T585, T588, T590, T589, T587) → LESS78_IN_GA(T585, T588)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_in_gg(T585, T632))
U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_out_gg(T585, T632)) → U30_GAAAG(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_in_ga(T585, T657))
U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_out_ga(T585, T657)) → U32_GAAAG(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U68_AG(T412, T405, T406, T461, T674, T676, splitc12_in_aaaa(T405, T406, T420, T411))
U68_AG(T412, T405, T406, T461, T674, T676, splitc12_out_aaaa(T405, T406, T420, T411)) → U69_AG(T412, T405, T406, T461, T674, T676, T420, msc25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U69_AG(T412, T405, T406, T461, T674, T676, T420, msc25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U70_AG(T412, T405, T406, T461, T674, T676, T677, T679, msc38_in_aa(T420, .(T674, T678)))
U70_AG(T412, T405, T406, T461, T674, T676, T677, T679, msc38_out_aa(T420, .(T674, T678))) → U71_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, lessc70_in_gg(T461, T674))
U71_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, lessc70_out_gg(T461, T674)) → U72_AG(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U71_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, lessc70_out_gg(T461, T674)) → P194_IN_GAAAG(T674, T677, T679, T678, T676)
MS1_IN_AG(.(T412, .(T405, T406)), .(T694, T696)) → U73_AG(T412, T405, T406, T694, T696, splitc12_in_aaaa(T405, T406, T420, T411))
U73_AG(T412, T405, T406, T694, T696, splitc12_out_aaaa(T405, T406, T420, T411)) → U74_AG(T412, T405, T406, T694, T696, T420, msc25_in_aaa(T412, T411, .(T697, T699)))
U74_AG(T412, T405, T406, T694, T696, T420, msc25_out_aaa(T412, T411, .(T697, T699))) → U75_AG(T412, T405, T406, T694, T696, T697, T699, msc38_in_aa(T420, .(T694, T698)))
U75_AG(T412, T405, T406, T694, T696, T697, T699, msc38_out_aa(T420, .(T694, T698))) → U76_AG(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U75_AG(T412, T405, T406, T694, T696, T697, T699, msc38_out_aa(T420, .(T694, T698))) → P194_IN_GAAAG(T694, T697, T699, T698, T696)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
split12_in_aaaa(x1, x2, x3, x4) = split12_in_aaaa
split16_in_aaa(x1, x2, x3) = split16_in_aaa
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
ms25_in_aaa(x1, x2, x3) = ms25_in_aaa
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = p34_in_aaaaaaaa
ms38_in_aa(x1, x2) = ms38_in_aa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
merge54_in_aaa(x1, x2, x3) = merge54_in_aaa
less70_in_aa(x1, x2) = less70_in_aa
less78_in_aa(x1, x2) = less78_in_aa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
less70_in_ga(x1, x2) = less70_in_ga(x1)
s(x1) = s(x1)
less78_in_ga(x1, x2) = less78_in_ga(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
p179_in_gaaag(x1, x2, x3, x4, x5) = p179_in_gaaag(x1, x5)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
p194_in_gaaag(x1, x2, x3, x4, x5) = p194_in_gaaag(x1, x5)
MS1_IN_AG(x1, x2) = MS1_IN_AG(x2)
U33_AG(x1, x2, x3, x4) = U33_AG(x4)
SPLIT12_IN_AAAA(x1, x2, x3, x4) = SPLIT12_IN_AAAA
U2_AAAA(x1, x2, x3, x4, x5) = U2_AAAA(x5)
SPLIT16_IN_AAA(x1, x2, x3) = SPLIT16_IN_AAA
U1_AAA(x1, x2, x3, x4, x5) = U1_AAA(x5)
U34_AG(x1, x2, x3, x4) = U34_AG(x4)
U35_AG(x1, x2, x3, x4) = U35_AG(x4)
MS25_IN_AAA(x1, x2, x3) = MS25_IN_AAA
U21_AAA(x1, x2, x3, x4, x5) = U21_AAA(x5)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = P34_IN_AAAAAAAA
U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U3_AAAAAAAA(x9)
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9)
U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U5_AAAAAAAA(x9)
MS38_IN_AA(x1, x2) = MS38_IN_AA
U13_AA(x1, x2, x3, x4, x5) = U13_AA(x5)
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U7_AAAAAAAA(x9)
U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U8_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U10_AAAAAAAA(x9)
U11_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U11_AAAAAAAA(x9)
U12_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U12_AAAAAAAA(x9)
MERGE54_IN_AAA(x1, x2, x3) = MERGE54_IN_AAA
U14_AAA(x1, x2, x3, x4, x5, x6) = U14_AAA(x6)
LESS70_IN_AA(x1, x2) = LESS70_IN_AA
U22_AA(x1, x2, x3) = U22_AA(x3)
LESS78_IN_AA(x1, x2) = LESS78_IN_AA
U20_AA(x1, x2, x3) = U20_AA(x3)
U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6)
U16_AAA(x1, x2, x3, x4, x5, x6) = U16_AAA(x6)
U17_AAA(x1, x2, x3, x4, x5, x6) = U17_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6) = U18_AAA(x6)
U19_AAA(x1, x2, x3, x4, x5, x6) = U19_AAA(x6)
U36_AG(x1, x2, x3, x4) = U36_AG(x4)
U37_AG(x1, x2, x3, x4, x5) = U37_AG(x5)
U38_AG(x1, x2, x3, x4) = U38_AG(x4)
U39_AG(x1, x2, x3, x4, x5) = U39_AG(x4, x5)
U40_AG(x1, x2, x3, x4, x5) = U40_AG(x4, x5)
U41_AG(x1, x2, x3, x4, x5) = U41_AG(x4, x5)
U42_AG(x1, x2, x3, x4, x5) = U42_AG(x4, x5)
U43_AG(x1, x2, x3, x4, x5, x6) = U43_AG(x4, x6)
U44_AG(x1, x2, x3, x4, x5) = U44_AG(x4, x5)
U45_AG(x1, x2, x3, x4, x5) = U45_AG(x4, x5)
U46_AG(x1, x2, x3, x4, x5, x6) = U46_AG(x4, x6)
U47_AG(x1, x2, x3, x4, x5) = U47_AG(x4, x5)
U48_AG(x1, x2, x3, x4, x5) = U48_AG(x4, x5)
LESS70_IN_GA(x1, x2) = LESS70_IN_GA(x1)
U22_GA(x1, x2, x3) = U22_GA(x1, x3)
LESS78_IN_GA(x1, x2) = LESS78_IN_GA(x1)
U20_GA(x1, x2, x3) = U20_GA(x1, x3)
U49_AG(x1, x2, x3, x4, x5) = U49_AG(x4, x5)
U50_AG(x1, x2, x3, x4, x5, x6) = U50_AG(x4, x6)
U51_AG(x1, x2, x3, x4, x5, x6) = U51_AG(x4, x6)
U52_AG(x1, x2, x3, x4, x5) = U52_AG(x4, x5)
U53_AG(x1, x2, x3, x4, x5) = U53_AG(x4, x5)
U54_AG(x1, x2, x3, x4, x5) = U54_AG(x4, x5)
U55_AG(x1, x2, x3, x4, x5) = U55_AG(x4, x5)
U56_AG(x1, x2, x3, x4, x5) = U56_AG(x4, x5)
U57_AG(x1, x2, x3, x4, x5, x6) = U57_AG(x4, x6)
U58_AG(x1, x2, x3, x4, x5) = U58_AG(x4, x5)
U59_AG(x1, x2, x3, x4, x5, x6) = U59_AG(x4, x5, x6)
U60_AG(x1, x2, x3, x4, x5, x6, x7) = U60_AG(x4, x5, x7)
U61_AG(x1, x2, x3, x4, x5, x6) = U61_AG(x4, x5, x6)
U62_AG(x1, x2, x3, x4, x5, x6) = U62_AG(x4, x5, x6)
U63_AG(x1, x2, x3, x4, x5, x6, x7) = U63_AG(x4, x5, x6, x7)
U64_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U64_AG(x4, x5, x6, x8)
U65_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U65_AG(x4, x5, x6, x8)
U66_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U66_AG(x4, x5, x6, x10)
U67_AG(x1, x2, x3, x4, x5, x6, x7) = U67_AG(x4, x5, x6, x7)
P179_IN_GAAAG(x1, x2, x3, x4, x5) = P179_IN_GAAAG(x1, x5)
U23_GAAAG(x1, x2, x3, x4, x5, x6) = U23_GAAAG(x1, x5, x6)
U24_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U24_GAAAG(x1, x3, x6, x7)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U25_GAAAG(x1, x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U27_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5) = P194_IN_GAAAG(x1, x5)
U28_GAAAG(x1, x2, x3, x4, x5, x6) = U28_GAAAG(x1, x5, x6)
U29_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U29_GAAAG(x1, x2, x6, x7)
U30_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U30_GAAAG(x1, x2, x6, x7)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U31_GAAAG(x1, x4, x6, x7)
U32_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U32_GAAAG(x1, x4, x6, x7)
U68_AG(x1, x2, x3, x4, x5, x6, x7) = U68_AG(x4, x5, x6, x7)
U69_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U69_AG(x4, x5, x6, x8)
U70_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_AG(x4, x5, x6, x9)
U71_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U71_AG(x4, x5, x6, x10)
U72_AG(x1, x2, x3, x4, x5, x6, x7) = U72_AG(x4, x5, x6, x7)
U73_AG(x1, x2, x3, x4, x5, x6) = U73_AG(x4, x5, x6)
U74_AG(x1, x2, x3, x4, x5, x6, x7) = U74_AG(x4, x5, x7)
U75_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U75_AG(x4, x5, x8)
U76_AG(x1, x2, x3, x4, x5, x6) = U76_AG(x4, x5, x6)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(6) Obligation:

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

MS1_IN_AG(.(T29, .(T27, T28)), []) → U33_AG(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
MS1_IN_AG(.(T29, .(T27, T28)), []) → SPLIT12_IN_AAAA(T27, T28, X42, X41)
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → U2_AAAA(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → SPLIT16_IN_AAA(T44, X72, X71)
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → U1_AAA(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U34_AG(T34, T27, T28, splitc12_in_aaaa(T27, T28, T32, T33))
U34_AG(T34, T27, T28, splitc12_out_aaaa(T27, T28, T32, T33)) → U35_AG(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
U34_AG(T34, T27, T28, splitc12_out_aaaa(T27, T28, T32, T33)) → MS25_IN_AAA(T34, T33, X13)
MS25_IN_AAA(T72, .(T73, T74), X127) → U21_AAA(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAA(T72, .(T73, T74), X127) → P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → U13_AA(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_out_aa(T78, T83)) → U8_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U12_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → MERGE54_IN_AAA(T106, T105, X127)
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAA(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_AA(T139, T140)
LESS70_IN_AA(s(T161), T162) → U22_AA(T161, T162, less78_in_aa(T161, T162))
LESS70_IN_AA(s(T161), T162) → LESS78_IN_AA(T161, T162)
LESS78_IN_AA(s(T176), s(T177)) → U20_AA(T176, T177, less78_in_aa(T176, T177))
LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)
MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U16_AAA(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U15_AAA(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAA(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_AA(T196, T197)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U19_AAA(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U18_AAA(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U36_AG(T34, T27, T28, splitc12_in_aaaa(T27, T28, T55, T33))
U36_AG(T34, T27, T28, splitc12_out_aaaa(T27, T28, T55, T33)) → U37_AG(T34, T27, T28, T55, msc25_in_aaa(T34, T33, T54))
U37_AG(T34, T27, T28, T55, msc25_out_aaa(T34, T33, T54)) → U38_AG(T34, T27, T28, ms38_in_aa(T55, X14))
U37_AG(T34, T27, T28, T55, msc25_out_aaa(T34, T33, T54)) → MS38_IN_AA(T55, X14)
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → U39_AG(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → SPLIT12_IN_AAAA(T260, T261, X367, X366)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U40_AG(T267, T260, T261, T242, splitc12_in_aaaa(T260, T261, T265, T266))
U40_AG(T267, T260, T261, T242, splitc12_out_aaaa(T260, T261, T265, T266)) → U41_AG(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U40_AG(T267, T260, T261, T242, splitc12_out_aaaa(T260, T261, T265, T266)) → MS25_IN_AAA(T267, T266, X338)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U42_AG(T267, T260, T261, T242, splitc12_in_aaaa(T260, T261, T273, T266))
U42_AG(T267, T260, T261, T242, splitc12_out_aaaa(T260, T261, T273, T266)) → U43_AG(T267, T260, T261, T242, T273, msc25_in_aaa(T267, T266, T272))
U43_AG(T267, T260, T261, T242, T273, msc25_out_aaa(T267, T266, T272)) → U44_AG(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U43_AG(T267, T260, T261, T242, T273, msc25_out_aaa(T267, T266, T272)) → MS38_IN_AA(T273, X339)
MS1_IN_AG(.(T267, .(T260, T261)), .(T318, [])) → U45_AG(T267, T260, T261, T318, splitc12_in_aaaa(T260, T261, T273, T266))
U45_AG(T267, T260, T261, T318, splitc12_out_aaaa(T260, T261, T273, T266)) → U46_AG(T267, T260, T261, T318, T273, msc25_in_aaa(T267, T266, .(T318, T323)))
U46_AG(T267, T260, T261, T318, T273, msc25_out_aaa(T267, T266, .(T318, T323))) → U47_AG(T267, T260, T261, T318, msc38_in_aa(T273, .(T322, T324)))
U47_AG(T267, T260, T261, T318, msc38_out_aa(T273, .(T322, T324))) → U48_AG(T267, T260, T261, T318, less70_in_ga(T318, T322))
U47_AG(T267, T260, T261, T318, msc38_out_aa(T273, .(T322, T324))) → LESS70_IN_GA(T318, T322)
LESS70_IN_GA(s(T161), T162) → U22_GA(T161, T162, less78_in_ga(T161, T162))
LESS70_IN_GA(s(T161), T162) → LESS78_IN_GA(T161, T162)
LESS78_IN_GA(s(T176), s(T177)) → U20_GA(T176, T177, less78_in_ga(T176, T177))
LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)
MS1_IN_AG(.(T267, .(T260, T261)), .(T356, [])) → U49_AG(T267, T260, T261, T356, splitc12_in_aaaa(T260, T261, T273, T266))
U49_AG(T267, T260, T261, T356, splitc12_out_aaaa(T260, T261, T273, T266)) → U50_AG(T267, T260, T261, T356, T273, msc25_in_aaa(T267, T266, .(T358, T360)))
U50_AG(T267, T260, T261, T356, T273, msc25_out_aaa(T267, T266, .(T358, T360))) → U51_AG(T267, T260, T261, T356, T358, msc38_in_aa(T273, .(T356, T359)))
U51_AG(T267, T260, T261, T356, T358, msc38_out_aa(T273, .(T356, T359))) → U52_AG(T267, T260, T261, T356, less78_in_ga(T356, T358))
U51_AG(T267, T260, T261, T356, T358, msc38_out_aa(T273, .(T356, T359))) → LESS78_IN_GA(T356, T358)
MS1_IN_AG(.(T407, .(T405, T406)), T387) → U53_AG(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
MS1_IN_AG(.(T407, .(T405, T406)), T387) → SPLIT12_IN_AAAA(T405, T406, X523, X522)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U54_AG(T412, T405, T406, T387, splitc12_in_aaaa(T405, T406, T410, T411))
U54_AG(T412, T405, T406, T387, splitc12_out_aaaa(T405, T406, T410, T411)) → U55_AG(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U54_AG(T412, T405, T406, T387, splitc12_out_aaaa(T405, T406, T410, T411)) → MS25_IN_AAA(T412, T411, X494)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U56_AG(T412, T405, T406, T387, splitc12_in_aaaa(T405, T406, T420, T411))
U56_AG(T412, T405, T406, T387, splitc12_out_aaaa(T405, T406, T420, T411)) → U57_AG(T412, T405, T406, T387, T420, msc25_in_aaa(T412, T411, T419))
U57_AG(T412, T405, T406, T387, T420, msc25_out_aaa(T412, T411, T419)) → U58_AG(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U57_AG(T412, T405, T406, T387, T420, msc25_out_aaa(T412, T411, T419)) → MS38_IN_AA(T420, X495)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → U59_AG(T412, T405, T406, T461, T465, splitc12_in_aaaa(T405, T406, T420, T411))
U59_AG(T412, T405, T406, T461, T465, splitc12_out_aaaa(T405, T406, T420, T411)) → U60_AG(T412, T405, T406, T461, T465, T420, msc25_in_aaa(T412, T411, .(T461, T467)))
U60_AG(T412, T405, T406, T461, T465, T420, msc25_out_aaa(T412, T411, .(T461, T467))) → U61_AG(T412, T405, T406, T461, T465, msc38_in_aa(T420, .(T466, T468)))
U61_AG(T412, T405, T406, T461, T465, msc38_out_aa(T420, .(T466, T468))) → U62_AG(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U61_AG(T412, T405, T406, T461, T465, msc38_out_aa(T420, .(T466, T468))) → LESS70_IN_GA(T461, T466)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U63_AG(T412, T405, T406, T461, T513, T517, splitc12_in_aaaa(T405, T406, T420, T411))
U63_AG(T412, T405, T406, T461, T513, T517, splitc12_out_aaaa(T405, T406, T420, T411)) → U64_AG(T412, T405, T406, T461, T513, T517, T420, msc25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U64_AG(T412, T405, T406, T461, T513, T517, T420, msc25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U65_AG(T412, T405, T406, T461, T513, T517, T519, msc38_in_aa(T420, .(T518, T520)))
U65_AG(T412, T405, T406, T461, T513, T517, T519, msc38_out_aa(T420, .(T518, T520))) → U66_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, lessc70_in_ga(T461, T518))
U66_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, lessc70_out_ga(T461, T518)) → U67_AG(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
U66_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, lessc70_out_ga(T461, T518)) → P179_IN_GAAAG(T513, T518, T519, T520, T517)
P179_IN_GAAAG(T513, T518, T519, T520, T517) → U23_GAAAG(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
P179_IN_GAAAG(T513, T518, T519, T520, T517) → LESS70_IN_GA(T513, T518)
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_in_ga(T513, T568))
U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_out_ga(T513, T568)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_in_gg(T513, T585))
U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_out_gg(T513, T585)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T588, T590, T589, T587) → U28_GAAAG(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
P194_IN_GAAAG(T585, T588, T590, T589, T587) → LESS78_IN_GA(T585, T588)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_in_gg(T585, T632))
U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_out_gg(T585, T632)) → U30_GAAAG(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_in_ga(T585, T657))
U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_out_ga(T585, T657)) → U32_GAAAG(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U68_AG(T412, T405, T406, T461, T674, T676, splitc12_in_aaaa(T405, T406, T420, T411))
U68_AG(T412, T405, T406, T461, T674, T676, splitc12_out_aaaa(T405, T406, T420, T411)) → U69_AG(T412, T405, T406, T461, T674, T676, T420, msc25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U69_AG(T412, T405, T406, T461, T674, T676, T420, msc25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U70_AG(T412, T405, T406, T461, T674, T676, T677, T679, msc38_in_aa(T420, .(T674, T678)))
U70_AG(T412, T405, T406, T461, T674, T676, T677, T679, msc38_out_aa(T420, .(T674, T678))) → U71_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, lessc70_in_gg(T461, T674))
U71_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, lessc70_out_gg(T461, T674)) → U72_AG(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U71_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, lessc70_out_gg(T461, T674)) → P194_IN_GAAAG(T674, T677, T679, T678, T676)
MS1_IN_AG(.(T412, .(T405, T406)), .(T694, T696)) → U73_AG(T412, T405, T406, T694, T696, splitc12_in_aaaa(T405, T406, T420, T411))
U73_AG(T412, T405, T406, T694, T696, splitc12_out_aaaa(T405, T406, T420, T411)) → U74_AG(T412, T405, T406, T694, T696, T420, msc25_in_aaa(T412, T411, .(T697, T699)))
U74_AG(T412, T405, T406, T694, T696, T420, msc25_out_aaa(T412, T411, .(T697, T699))) → U75_AG(T412, T405, T406, T694, T696, T697, T699, msc38_in_aa(T420, .(T694, T698)))
U75_AG(T412, T405, T406, T694, T696, T697, T699, msc38_out_aa(T420, .(T694, T698))) → U76_AG(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U75_AG(T412, T405, T406, T694, T696, T697, T699, msc38_out_aa(T420, .(T694, T698))) → P194_IN_GAAAG(T694, T697, T699, T698, T696)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 94 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
LESS78_IN_GA(x1, x2) = LESS78_IN_GA(x1)

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

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
LESS78_IN_GA(x1, x2) = LESS78_IN_GA(x1)

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

(12) PiDPToQDPProof (SOUND transformation)

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

(13) Obligation:

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

LESS78_IN_GA(s(T176)) → LESS78_IN_GA(T176)

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

(14) 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:

LESS78_IN_GA(s(T176)) → LESS78_IN_GA(T176)
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_in_ga(T513, T568))
U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_in_gg(T513, T585))
U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_in_gg(T585, T632))
U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_in_ga(T585, T657))
U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
P179_IN_GAAAG(x1, x2, x3, x4, x5) = P179_IN_GAAAG(x1, x5)
U24_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U24_GAAAG(x1, x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5) = P194_IN_GAAAG(x1, x5)
U29_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U29_GAAAG(x1, x2, x6, x7)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U31_GAAAG(x1, x4, x6, x7)

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

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_in_ga(T513, T568))
U24_GAAAG(T513, T568, T563, T569, T570, T567, lessc70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_in_gg(T513, T585))
U26_GAAAG(T513, T585, T588, T590, T589, T587, lessc70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_in_gg(T585, T632))
U29_GAAAG(T585, T632, T638, T637, T639, T636, lessc78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_in_ga(T585, T657))
U31_GAAAG(T585, T657, T659, T654, T658, T656, lessc78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)

The TRS R consists of the following rules:

lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
P179_IN_GAAAG(x1, x2, x3, x4, x5) = P179_IN_GAAAG(x1, x5)
U24_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U24_GAAAG(x1, x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5) = P194_IN_GAAAG(x1, x5)
U29_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U29_GAAAG(x1, x2, x6, x7)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U31_GAAAG(x1, x4, x6, x7)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

P179_IN_GAAAG(T513, .(T563, T567)) → U24_GAAAG(T513, T563, T567, lessc70_in_ga(T513))
U24_GAAAG(T513, T563, T567, lessc70_out_ga(T513)) → P179_IN_GAAAG(T563, T567)
P179_IN_GAAAG(T513, .(T585, T587)) → U26_GAAAG(T513, T585, T587, lessc70_in_gg(T513, T585))
U26_GAAAG(T513, T585, T587, lessc70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T587)
P194_IN_GAAAG(T585, .(T632, T636)) → U29_GAAAG(T585, T632, T636, lessc78_in_gg(T585, T632))
U29_GAAAG(T585, T632, T636, lessc78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T636)
P194_IN_GAAAG(T585, .(T654, T656)) → U31_GAAAG(T585, T654, T656, lessc78_in_ga(T585))
U31_GAAAG(T585, T654, T656, lessc78_out_ga(T585)) → P194_IN_GAAAG(T654, T656)

The TRS R consists of the following rules:

lessc70_in_ga(0) → lessc70_out_ga(0)
lessc70_in_ga(s(T161)) → U91_ga(T161, lessc78_in_ga(T161))
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
lessc78_in_ga(0) → lessc78_out_ga(0)
lessc78_in_ga(s(T176)) → U89_ga(T176, lessc78_in_ga(T176))
U91_ga(T161, lessc78_out_ga(T161)) → lessc70_out_ga(s(T161))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U89_ga(T176, lessc78_out_ga(T176)) → lessc78_out_ga(s(T176))

The set Q consists of the following terms:

lessc70_in_ga(x0)
lessc70_in_gg(x0, x1)
lessc78_in_gg(x0, x1)
lessc78_in_ga(x0)
U91_ga(x0, x1)
U91_gg(x0, x1, x2)
U89_gg(x0, x1, x2)
U89_ga(x0, x1)

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

(21) 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:

U24_GAAAG(T513, T563, T567, lessc70_out_ga(T513)) → P179_IN_GAAAG(T563, T567)
The graph contains the following edges 2 >= 1, 3 >= 2
U29_GAAAG(T585, T632, T636, lessc78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T636)
The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2
P179_IN_GAAAG(T513, .(T563, T567)) → U24_GAAAG(T513, T563, T567, lessc70_in_ga(T513))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
P179_IN_GAAAG(T513, .(T585, T587)) → U26_GAAAG(T513, T585, T587, lessc70_in_gg(T513, T585))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
U26_GAAAG(T513, T585, T587, lessc70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T587)
The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2
U31_GAAAG(T585, T654, T656, lessc78_out_ga(T585)) → P194_IN_GAAAG(T654, T656)
The graph contains the following edges 2 >= 1, 3 >= 2
P194_IN_GAAAG(T585, .(T632, T636)) → U29_GAAAG(T585, T632, T636, lessc78_in_gg(T585, T632))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
P194_IN_GAAAG(T585, .(T654, T656)) → U31_GAAAG(T585, T654, T656, lessc78_in_ga(T585))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

(22) YES

(23) Obligation:

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

LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
LESS78_IN_AA(x1, x2) = LESS78_IN_AA

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

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
LESS78_IN_AA(x1, x2) = LESS78_IN_AA

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

LESS78_IN_AA → LESS78_IN_AA

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

(28) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = LESS78_IN_AA evaluates to t =LESS78_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from LESS78_IN_AA to LESS78_IN_AA.

(29) NO

(30) Obligation:

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

MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
MERGE54_IN_AAA(x1, x2, x3) = MERGE54_IN_AAA
U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6) = U18_AAA(x6)

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

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
0 = 0
MERGE54_IN_AAA(x1, x2, x3) = MERGE54_IN_AAA
U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6) = U18_AAA(x6)

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

(33) PiDPToQDPProof (SOUND transformation)

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

(34) Obligation:

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

MERGE54_IN_AAA → U15_AAA(lessc70_in_aa)
U15_AAA(lessc70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U18_AAA(lessc78_in_aa)
U18_AAA(lessc78_out_aa(T196)) → MERGE54_IN_AAA

The TRS R consists of the following rules:

lessc70_in_aa → lessc70_out_aa(0)
lessc70_in_aa → U91_aa(lessc78_in_aa)
lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

lessc70_in_aa
lessc78_in_aa
U91_aa(x0)
U89_aa(x0)

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

(35) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule MERGE54_IN_AAA → U15_AAA(lessc70_in_aa) at position [0] we obtained the following new rules [LPAR04]:

MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0))
MERGE54_IN_AAA → U15_AAA(U91_aa(lessc78_in_aa))

(36) Obligation:

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

U15_AAA(lessc70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U18_AAA(lessc78_in_aa)
U18_AAA(lessc78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0))
MERGE54_IN_AAA → U15_AAA(U91_aa(lessc78_in_aa))

The TRS R consists of the following rules:

lessc70_in_aa → lessc70_out_aa(0)
lessc70_in_aa → U91_aa(lessc78_in_aa)
lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

lessc70_in_aa
lessc78_in_aa
U91_aa(x0)
U89_aa(x0)

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

(37) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(38) Obligation:

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

U15_AAA(lessc70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U18_AAA(lessc78_in_aa)
U18_AAA(lessc78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0))
MERGE54_IN_AAA → U15_AAA(U91_aa(lessc78_in_aa))

The TRS R consists of the following rules:

lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

lessc70_in_aa
lessc78_in_aa
U91_aa(x0)
U89_aa(x0)

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

(39) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

lessc70_in_aa

(40) Obligation:

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

U15_AAA(lessc70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U18_AAA(lessc78_in_aa)
U18_AAA(lessc78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0))
MERGE54_IN_AAA → U15_AAA(U91_aa(lessc78_in_aa))

The TRS R consists of the following rules:

lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

lessc78_in_aa
U91_aa(x0)
U89_aa(x0)

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

(41) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule MERGE54_IN_AAA → U18_AAA(lessc78_in_aa) at position [0] we obtained the following new rules [LPAR04]:

MERGE54_IN_AAA → U18_AAA(lessc78_out_aa(0))
MERGE54_IN_AAA → U18_AAA(U89_aa(lessc78_in_aa))

(42) Obligation:

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

U15_AAA(lessc70_out_aa(T139)) → MERGE54_IN_AAA
U18_AAA(lessc78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0))
MERGE54_IN_AAA → U15_AAA(U91_aa(lessc78_in_aa))
MERGE54_IN_AAA → U18_AAA(lessc78_out_aa(0))
MERGE54_IN_AAA → U18_AAA(U89_aa(lessc78_in_aa))

The TRS R consists of the following rules:

lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

lessc78_in_aa
U91_aa(x0)
U89_aa(x0)

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

(43) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by narrowing to the left:

s = MERGE54_IN_AAA evaluates to t =MERGE54_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0))
with rule MERGE54_IN_AAA → U15_AAA(lessc70_out_aa(0)) at position [] and matcher [ ]

U15_AAA(lessc70_out_aa(0)) → MERGE54_IN_AAA
with rule U15_AAA(lessc70_out_aa(T139)) → MERGE54_IN_AAA

Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence

All these steps are and every following step will be a correct step w.r.t to Q.

(44) NO

(45) Obligation:

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

SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
SPLIT16_IN_AAA(x1, x2, x3) = SPLIT16_IN_AAA

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

(46) UsableRulesProof (EQUIVALENT transformation)

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

(47) Obligation:

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

SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
SPLIT16_IN_AAA(x1, x2, x3) = SPLIT16_IN_AAA

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

(48) PiDPToQDPProof (SOUND transformation)

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

(49) Obligation:

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

SPLIT16_IN_AAA → SPLIT16_IN_AAA

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

(50) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = SPLIT16_IN_AAA evaluates to t =SPLIT16_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Matcher: [ ]
Semiunifier: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from SPLIT16_IN_AAA to SPLIT16_IN_AAA.

(51) NO

(52) Obligation:

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

P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
msc25_in_aaa(T62, [], .(T62, [])) → msc25_out_aaa(T62, [], .(T62, []))
msc25_in_aaa(T72, .(T73, T74), X127) → U90_aaa(T72, T73, T74, X127, qc34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
U90_aaa(T72, T73, T74, X127, qc34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → msc25_out_aaa(T72, .(T73, T74), X127)
lessc70_in_ga(0, T154) → lessc70_out_ga(0, T154)
lessc70_in_ga(s(T161), T162) → U91_ga(T161, T162, lessc78_in_ga(T161, T162))
lessc78_in_ga(0, s(T169)) → lessc78_out_ga(0, s(T169))
lessc78_in_ga(s(T176), s(T177)) → U89_ga(T176, T177, lessc78_in_ga(T176, T177))
U89_ga(T176, T177, lessc78_out_ga(T176, T177)) → lessc78_out_ga(s(T176), s(T177))
U91_ga(T161, T162, lessc78_out_ga(T161, T162)) → lessc70_out_ga(s(T161), T162)
lessc70_in_gg(0, T154) → lessc70_out_gg(0, T154)
lessc70_in_gg(s(T161), T162) → U91_gg(T161, T162, lessc78_in_gg(T161, T162))
lessc78_in_gg(0, s(T169)) → lessc78_out_gg(0, s(T169))
lessc78_in_gg(s(T176), s(T177)) → U89_gg(T176, T177, lessc78_in_gg(T176, T177))
U89_gg(T176, T177, lessc78_out_gg(T176, T177)) → lessc78_out_gg(s(T176), s(T177))
U91_gg(T161, T162, lessc78_out_gg(T161, T162)) → lessc70_out_gg(s(T161), T162)

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
msc25_in_aaa(x1, x2, x3) = msc25_in_aaa
msc25_out_aaa(x1, x2, x3) = msc25_out_aaa
U90_aaa(x1, x2, x3, x4, x5) = U90_aaa(x5)
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
lessc70_in_ga(x1, x2) = lessc70_in_ga(x1)
0 = 0
lessc70_out_ga(x1, x2) = lessc70_out_ga(x1)
U91_ga(x1, x2, x3) = U91_ga(x1, x3)
lessc78_in_ga(x1, x2) = lessc78_in_ga(x1)
lessc78_out_ga(x1, x2) = lessc78_out_ga(x1)
U89_ga(x1, x2, x3) = U89_ga(x1, x3)
lessc70_in_gg(x1, x2) = lessc70_in_gg(x1, x2)
lessc70_out_gg(x1, x2) = lessc70_out_gg(x1, x2)
U91_gg(x1, x2, x3) = U91_gg(x1, x2, x3)
lessc78_in_gg(x1, x2) = lessc78_in_gg(x1, x2)
lessc78_out_gg(x1, x2) = lessc78_out_gg(x1, x2)
U89_gg(x1, x2, x3) = U89_gg(x1, x2, x3)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = P34_IN_AAAAAAAA
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9)
MS38_IN_AA(x1, x2) = MS38_IN_AA
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U7_AAAAAAAA(x9)

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

(53) UsableRulesProof (EQUIVALENT transformation)

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

(54) Obligation:

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

P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, msc38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)

The TRS R consists of the following rules:

splitc12_in_aaaa(T42, T44, .(T42, X71), X72) → U79_aaaa(T42, T44, X71, X72, splitc16_in_aaa(T44, X72, X71))
msc38_in_aa([], []) → msc38_out_aa([], [])
msc38_in_aa(.(T89, []), .(T89, [])) → msc38_out_aa(.(T89, []), .(T89, []))
msc38_in_aa(.(T99, .(T100, T101)), X172) → U84_aa(T99, T100, T101, X172, qc34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
U79_aaaa(T42, T44, X71, X72, splitc16_out_aaa(T44, X72, X71)) → splitc12_out_aaaa(T42, T44, .(T42, X71), X72)
U84_aa(T99, T100, T101, X172, qc34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → msc38_out_aa(.(T99, .(T100, T101)), X172)
splitc16_in_aaa([], [], []) → splitc16_out_aaa([], [], [])
splitc16_in_aaa(.(T49, T51), .(T49, X89), X90) → U78_aaa(T49, T51, X89, X90, splitc16_in_aaa(T51, X90, X89))
qc34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_in_aaaa(T72, .(T73, T74), T78, T84))
U78_aaa(T49, T51, X89, X90, splitc16_out_aaa(T51, X90, X89)) → splitc16_out_aaa(.(T49, T51), .(T49, X89), X90)
U80_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, splitc12_out_aaaa(T72, .(T73, T74), T78, T84)) → U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T78, T106))
U81_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T78, T106)) → U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_in_aa(T84, T105))
U82_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, msc38_out_aa(T84, T105)) → U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_in_aaa(T106, T105, X127))
U83_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, mergec54_out_aaa(T106, T105, X127)) → qc34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
mergec54_in_aaa([], T113, T113) → mergec54_out_aaa([], T113, T113)
mergec54_in_aaa(T118, [], T118) → mergec54_out_aaa(T118, [], T118)
mergec54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U85_aaa(T139, T145, T146, T147, X226, lessc70_in_aa(T139, T146))
mergec54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U87_aaa(T202, T203, T196, T204, X287, lessc78_in_aa(T196, T202))
U85_aaa(T139, T145, T146, T147, X226, lessc70_out_aa(T139, T146)) → U86_aaa(T139, T145, T146, T147, X226, mergec54_in_aaa(T145, .(T146, T147), X226))
U87_aaa(T202, T203, T196, T204, X287, lessc78_out_aa(T196, T202)) → U88_aaa(T202, T203, T196, T204, X287, mergec54_in_aaa(.(T202, T203), T204, X287))
lessc70_in_aa(0, T154) → lessc70_out_aa(0, T154)
lessc70_in_aa(s(T161), T162) → U91_aa(T161, T162, lessc78_in_aa(T161, T162))
U86_aaa(T139, T145, T146, T147, X226, mergec54_out_aaa(T145, .(T146, T147), X226)) → mergec54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
lessc78_in_aa(0, s(T169)) → lessc78_out_aa(0, s(T169))
lessc78_in_aa(s(T176), s(T177)) → U89_aa(T176, T177, lessc78_in_aa(T176, T177))
U88_aaa(T202, T203, T196, T204, X287, mergec54_out_aaa(.(T202, T203), T204, X287)) → mergec54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U91_aa(T161, T162, lessc78_out_aa(T161, T162)) → lessc70_out_aa(s(T161), T162)
U89_aa(T176, T177, lessc78_out_aa(T176, T177)) → lessc78_out_aa(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
[] = []
splitc12_in_aaaa(x1, x2, x3, x4) = splitc12_in_aaaa
U79_aaaa(x1, x2, x3, x4, x5) = U79_aaaa(x5)
splitc16_in_aaa(x1, x2, x3) = splitc16_in_aaa
splitc16_out_aaa(x1, x2, x3) = splitc16_out_aaa
U78_aaa(x1, x2, x3, x4, x5) = U78_aaa(x5)
splitc12_out_aaaa(x1, x2, x3, x4) = splitc12_out_aaaa
msc38_in_aa(x1, x2) = msc38_in_aa
msc38_out_aa(x1, x2) = msc38_out_aa
U84_aa(x1, x2, x3, x4, x5) = U84_aa(x5)
qc34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_in_aaaaaaaa
U80_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_aaaaaaaa(x9)
U81_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_aaaaaaaa(x9)
U82_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_aaaaaaaa(x9)
U83_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_aaaaaaaa(x9)
mergec54_in_aaa(x1, x2, x3) = mergec54_in_aaa
mergec54_out_aaa(x1, x2, x3) = mergec54_out_aaa
U85_aaa(x1, x2, x3, x4, x5, x6) = U85_aaa(x6)
lessc70_in_aa(x1, x2) = lessc70_in_aa
lessc70_out_aa(x1, x2) = lessc70_out_aa(x1)
U91_aa(x1, x2, x3) = U91_aa(x3)
lessc78_in_aa(x1, x2) = lessc78_in_aa
lessc78_out_aa(x1, x2) = lessc78_out_aa(x1)
U89_aa(x1, x2, x3) = U89_aa(x3)
U86_aaa(x1, x2, x3, x4, x5, x6) = U86_aaa(x6)
U87_aaa(x1, x2, x3, x4, x5, x6) = U87_aaa(x6)
U88_aaa(x1, x2, x3, x4, x5, x6) = U88_aaa(x6)
qc34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qc34_out_aaaaaaaa
.(x1, x2) = .(x1, x2)
s(x1) = s(x1)
0 = 0
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = P34_IN_AAAAAAAA
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9)
MS38_IN_AA(x1, x2) = MS38_IN_AA
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U7_AAAAAAAA(x9)

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

(55) PiDPToQDPProof (SOUND transformation)

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

(56) Obligation:

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

P34_IN_AAAAAAAA → U4_AAAAAAAA(splitc12_in_aaaa)
U4_AAAAAAAA(splitc12_out_aaaa) → MS38_IN_AA
MS38_IN_AA → P34_IN_AAAAAAAA
P34_IN_AAAAAAAA → U6_AAAAAAAA(splitc12_in_aaaa)
U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(msc38_in_aa)
U7_AAAAAAAA(msc38_out_aa) → MS38_IN_AA

The TRS R consists of the following rules:

splitc12_in_aaaa → U79_aaaa(splitc16_in_aaa)
msc38_in_aa → msc38_out_aa
msc38_in_aa → U84_aa(qc34_in_aaaaaaaa)
U79_aaaa(splitc16_out_aaa) → splitc12_out_aaaa
U84_aa(qc34_out_aaaaaaaa) → msc38_out_aa
splitc16_in_aaa → splitc16_out_aaa
splitc16_in_aaa → U78_aaa(splitc16_in_aaa)
qc34_in_aaaaaaaa → U80_aaaaaaaa(splitc12_in_aaaa)
U78_aaa(splitc16_out_aaa) → splitc16_out_aaa
U80_aaaaaaaa(splitc12_out_aaaa) → U81_aaaaaaaa(msc38_in_aa)
U81_aaaaaaaa(msc38_out_aa) → U82_aaaaaaaa(msc38_in_aa)
U82_aaaaaaaa(msc38_out_aa) → U83_aaaaaaaa(mergec54_in_aaa)
U83_aaaaaaaa(mergec54_out_aaa) → qc34_out_aaaaaaaa
mergec54_in_aaa → mergec54_out_aaa
mergec54_in_aaa → U85_aaa(lessc70_in_aa)
mergec54_in_aaa → U87_aaa(lessc78_in_aa)
U85_aaa(lessc70_out_aa(T139)) → U86_aaa(mergec54_in_aaa)
U87_aaa(lessc78_out_aa(T196)) → U88_aaa(mergec54_in_aaa)
lessc70_in_aa → lessc70_out_aa(0)
lessc70_in_aa → U91_aa(lessc78_in_aa)
U86_aaa(mergec54_out_aaa) → mergec54_out_aaa
lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U88_aaa(mergec54_out_aaa) → mergec54_out_aaa
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

splitc12_in_aaaa
msc38_in_aa
U79_aaaa(x0)
U84_aa(x0)
splitc16_in_aaa
qc34_in_aaaaaaaa
U78_aaa(x0)
U80_aaaaaaaa(x0)
U81_aaaaaaaa(x0)
U82_aaaaaaaa(x0)
U83_aaaaaaaa(x0)
mergec54_in_aaa
U85_aaa(x0)
U87_aaa(x0)
lessc70_in_aa
U86_aaa(x0)
lessc78_in_aa
U88_aaa(x0)
U91_aa(x0)
U89_aa(x0)

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

(57) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAA → U4_AAAAAAAA(splitc12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAA → U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))

(58) Obligation:

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

U4_AAAAAAAA(splitc12_out_aaaa) → MS38_IN_AA
MS38_IN_AA → P34_IN_AAAAAAAA
P34_IN_AAAAAAAA → U6_AAAAAAAA(splitc12_in_aaaa)
U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(msc38_in_aa)
U7_AAAAAAAA(msc38_out_aa) → MS38_IN_AA
P34_IN_AAAAAAAA → U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))

The TRS R consists of the following rules:

splitc12_in_aaaa → U79_aaaa(splitc16_in_aaa)
msc38_in_aa → msc38_out_aa
msc38_in_aa → U84_aa(qc34_in_aaaaaaaa)
U79_aaaa(splitc16_out_aaa) → splitc12_out_aaaa
U84_aa(qc34_out_aaaaaaaa) → msc38_out_aa
splitc16_in_aaa → splitc16_out_aaa
splitc16_in_aaa → U78_aaa(splitc16_in_aaa)
qc34_in_aaaaaaaa → U80_aaaaaaaa(splitc12_in_aaaa)
U78_aaa(splitc16_out_aaa) → splitc16_out_aaa
U80_aaaaaaaa(splitc12_out_aaaa) → U81_aaaaaaaa(msc38_in_aa)
U81_aaaaaaaa(msc38_out_aa) → U82_aaaaaaaa(msc38_in_aa)
U82_aaaaaaaa(msc38_out_aa) → U83_aaaaaaaa(mergec54_in_aaa)
U83_aaaaaaaa(mergec54_out_aaa) → qc34_out_aaaaaaaa
mergec54_in_aaa → mergec54_out_aaa
mergec54_in_aaa → U85_aaa(lessc70_in_aa)
mergec54_in_aaa → U87_aaa(lessc78_in_aa)
U85_aaa(lessc70_out_aa(T139)) → U86_aaa(mergec54_in_aaa)
U87_aaa(lessc78_out_aa(T196)) → U88_aaa(mergec54_in_aaa)
lessc70_in_aa → lessc70_out_aa(0)
lessc70_in_aa → U91_aa(lessc78_in_aa)
U86_aaa(mergec54_out_aaa) → mergec54_out_aaa
lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U88_aaa(mergec54_out_aaa) → mergec54_out_aaa
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

splitc12_in_aaaa
msc38_in_aa
U79_aaaa(x0)
U84_aa(x0)
splitc16_in_aaa
qc34_in_aaaaaaaa
U78_aaa(x0)
U80_aaaaaaaa(x0)
U81_aaaaaaaa(x0)
U82_aaaaaaaa(x0)
U83_aaaaaaaa(x0)
mergec54_in_aaa
U85_aaa(x0)
U87_aaa(x0)
lessc70_in_aa
U86_aaa(x0)
lessc78_in_aa
U88_aaa(x0)
U91_aa(x0)
U89_aa(x0)

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

(59) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAA → U6_AAAAAAAA(splitc12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAA → U6_AAAAAAAA(U79_aaaa(splitc16_in_aaa))

(60) Obligation:

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

U4_AAAAAAAA(splitc12_out_aaaa) → MS38_IN_AA
MS38_IN_AA → P34_IN_AAAAAAAA
U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(msc38_in_aa)
U7_AAAAAAAA(msc38_out_aa) → MS38_IN_AA
P34_IN_AAAAAAAA → U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))
P34_IN_AAAAAAAA → U6_AAAAAAAA(U79_aaaa(splitc16_in_aaa))

The TRS R consists of the following rules:

splitc12_in_aaaa → U79_aaaa(splitc16_in_aaa)
msc38_in_aa → msc38_out_aa
msc38_in_aa → U84_aa(qc34_in_aaaaaaaa)
U79_aaaa(splitc16_out_aaa) → splitc12_out_aaaa
U84_aa(qc34_out_aaaaaaaa) → msc38_out_aa
splitc16_in_aaa → splitc16_out_aaa
splitc16_in_aaa → U78_aaa(splitc16_in_aaa)
qc34_in_aaaaaaaa → U80_aaaaaaaa(splitc12_in_aaaa)
U78_aaa(splitc16_out_aaa) → splitc16_out_aaa
U80_aaaaaaaa(splitc12_out_aaaa) → U81_aaaaaaaa(msc38_in_aa)
U81_aaaaaaaa(msc38_out_aa) → U82_aaaaaaaa(msc38_in_aa)
U82_aaaaaaaa(msc38_out_aa) → U83_aaaaaaaa(mergec54_in_aaa)
U83_aaaaaaaa(mergec54_out_aaa) → qc34_out_aaaaaaaa
mergec54_in_aaa → mergec54_out_aaa
mergec54_in_aaa → U85_aaa(lessc70_in_aa)
mergec54_in_aaa → U87_aaa(lessc78_in_aa)
U85_aaa(lessc70_out_aa(T139)) → U86_aaa(mergec54_in_aaa)
U87_aaa(lessc78_out_aa(T196)) → U88_aaa(mergec54_in_aaa)
lessc70_in_aa → lessc70_out_aa(0)
lessc70_in_aa → U91_aa(lessc78_in_aa)
U86_aaa(mergec54_out_aaa) → mergec54_out_aaa
lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U88_aaa(mergec54_out_aaa) → mergec54_out_aaa
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

splitc12_in_aaaa
msc38_in_aa
U79_aaaa(x0)
U84_aa(x0)
splitc16_in_aaa
qc34_in_aaaaaaaa
U78_aaa(x0)
U80_aaaaaaaa(x0)
U81_aaaaaaaa(x0)
U82_aaaaaaaa(x0)
U83_aaaaaaaa(x0)
mergec54_in_aaa
U85_aaa(x0)
U87_aaa(x0)
lessc70_in_aa
U86_aaa(x0)
lessc78_in_aa
U88_aaa(x0)
U91_aa(x0)
U89_aa(x0)

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

(61) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(msc38_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(msc38_out_aa)
U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(U84_aa(qc34_in_aaaaaaaa))

(62) Obligation:

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

U4_AAAAAAAA(splitc12_out_aaaa) → MS38_IN_AA
MS38_IN_AA → P34_IN_AAAAAAAA
U7_AAAAAAAA(msc38_out_aa) → MS38_IN_AA
P34_IN_AAAAAAAA → U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))
P34_IN_AAAAAAAA → U6_AAAAAAAA(U79_aaaa(splitc16_in_aaa))
U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(msc38_out_aa)
U6_AAAAAAAA(splitc12_out_aaaa) → U7_AAAAAAAA(U84_aa(qc34_in_aaaaaaaa))

The TRS R consists of the following rules:

splitc12_in_aaaa → U79_aaaa(splitc16_in_aaa)
msc38_in_aa → msc38_out_aa
msc38_in_aa → U84_aa(qc34_in_aaaaaaaa)
U79_aaaa(splitc16_out_aaa) → splitc12_out_aaaa
U84_aa(qc34_out_aaaaaaaa) → msc38_out_aa
splitc16_in_aaa → splitc16_out_aaa
splitc16_in_aaa → U78_aaa(splitc16_in_aaa)
qc34_in_aaaaaaaa → U80_aaaaaaaa(splitc12_in_aaaa)
U78_aaa(splitc16_out_aaa) → splitc16_out_aaa
U80_aaaaaaaa(splitc12_out_aaaa) → U81_aaaaaaaa(msc38_in_aa)
U81_aaaaaaaa(msc38_out_aa) → U82_aaaaaaaa(msc38_in_aa)
U82_aaaaaaaa(msc38_out_aa) → U83_aaaaaaaa(mergec54_in_aaa)
U83_aaaaaaaa(mergec54_out_aaa) → qc34_out_aaaaaaaa
mergec54_in_aaa → mergec54_out_aaa
mergec54_in_aaa → U85_aaa(lessc70_in_aa)
mergec54_in_aaa → U87_aaa(lessc78_in_aa)
U85_aaa(lessc70_out_aa(T139)) → U86_aaa(mergec54_in_aaa)
U87_aaa(lessc78_out_aa(T196)) → U88_aaa(mergec54_in_aaa)
lessc70_in_aa → lessc70_out_aa(0)
lessc70_in_aa → U91_aa(lessc78_in_aa)
U86_aaa(mergec54_out_aaa) → mergec54_out_aaa
lessc78_in_aa → lessc78_out_aa(0)
lessc78_in_aa → U89_aa(lessc78_in_aa)
U88_aaa(mergec54_out_aaa) → mergec54_out_aaa
U91_aa(lessc78_out_aa(T161)) → lessc70_out_aa(s(T161))
U89_aa(lessc78_out_aa(T176)) → lessc78_out_aa(s(T176))

The set Q consists of the following terms:

splitc12_in_aaaa
msc38_in_aa
U79_aaaa(x0)
U84_aa(x0)
splitc16_in_aaa
qc34_in_aaaaaaaa
U78_aaa(x0)
U80_aaaaaaaa(x0)
U81_aaaaaaaa(x0)
U82_aaaaaaaa(x0)
U83_aaaaaaaa(x0)
mergec54_in_aaa
U85_aaa(x0)
U87_aaa(x0)
lessc70_in_aa
U86_aaa(x0)
lessc78_in_aa
U88_aaa(x0)
U91_aa(x0)
U89_aa(x0)

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

(63) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by narrowing to the left:

s = U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa)) evaluates to t =U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa)) → U4_AAAAAAAA(U79_aaaa(splitc16_out_aaa))
with rule splitc16_in_aaa → splitc16_out_aaa at position [0,0] and matcher [ ]

U4_AAAAAAAA(U79_aaaa(splitc16_out_aaa)) → U4_AAAAAAAA(splitc12_out_aaaa)
with rule U79_aaaa(splitc16_out_aaa) → splitc12_out_aaaa at position [0] and matcher [ ]

U4_AAAAAAAA(splitc12_out_aaaa) → MS38_IN_AA
with rule U4_AAAAAAAA(splitc12_out_aaaa) → MS38_IN_AA at position [] and matcher [ ]

MS38_IN_AA → P34_IN_AAAAAAAA
with rule MS38_IN_AA → P34_IN_AAAAAAAA at position [] and matcher [ ]

P34_IN_AAAAAAAA → U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))
with rule P34_IN_AAAAAAAA → U4_AAAAAAAA(U79_aaaa(splitc16_in_aaa))

Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence

All these steps are and every following step will be a correct step w.r.t to Q.

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) UndefinedPredicateInTriplesTransformerProof (SOUND transformation)

(4) Obligation:

(5) TriplesToPiDPProof (SOUND transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (SOUND transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) NonTerminationProof (EQUIVALENT transformation)

(29) NO

(30) Obligation:

(31) UsableRulesProof (EQUIVALENT transformation)

(32) Obligation:

(33) PiDPToQDPProof (SOUND transformation)

(34) Obligation:

(35) Narrowing (SOUND transformation)

(36) Obligation:

(37) UsableRulesProof (EQUIVALENT transformation)

(38) Obligation:

(39) QReductionProof (EQUIVALENT transformation)

(40) Obligation:

(41) Narrowing (SOUND transformation)

(42) Obligation:

(43) NonTerminationProof (EQUIVALENT transformation)

(44) NO

(45) Obligation:

(46) UsableRulesProof (EQUIVALENT transformation)

(47) Obligation:

(48) PiDPToQDPProof (SOUND transformation)

(49) Obligation:

(50) NonTerminationProof (EQUIVALENT transformation)

(51) NO

(52) Obligation:

(53) UsableRulesProof (EQUIVALENT transformation)

(54) Obligation:

(55) PiDPToQDPProof (SOUND transformation)

(56) Obligation:

(57) Narrowing (SOUND transformation)

(58) Obligation:

(59) Narrowing (SOUND transformation)

(60) Obligation:

(61) Narrowing (SOUND transformation)

(62) Obligation:

(63) NonTerminationProof (EQUIVALENT transformation)

(64) NO