Left Termination proof of /tmp/tmpp5bg7X/soundex.pl

Left Termination of the query pattern goal_in_2(g, a) w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇐)

↳2 Prolog

↳3 PrologToPiTRSProof (⇐)

↳4 PiTRS

↳5 DependencyPairsProof (⇔)

↳6 PiDP

↳7 DependencyGraphProof (⇔)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔)

            ↳11 PiDP

                ↳12 PiDPToQDPProof (⇐)

                    ↳13 QDP

                        ↳14 QDPSizeChangeProof (⇔)

                            ↳15 TRUE

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔)

            ↳18 PiDP

                ↳19 PiDPToQDPProof (⇐)

                    ↳20 QDP

                        ↳21 QDPSizeChangeProof (⇔)

                            ↳22 TRUE

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔)

            ↳25 PiDP

                ↳26 PiDPToQDPProof (⇐)

                    ↳27 QDP

                        ↳28 QDPSizeChangeProof (⇔)

                            ↳29 TRUE

(0) Obligation:

Clauses:

goal(Name, Code) :- ','(eq(Name, .(First, Others)), ','(reduce(Others, s(0), First, Reduced), eq(Code, Reduced))).
reduce(X1, s(s(s(s(0)))), X2, []) :- !.
reduce([], X3, X4, []) :- !.
reduce(.(Current, Others), Count, Current, Code) :- ','(vowel_h_w_y(Current), ','(!, reduce(Others, Count, Current, Code))).
reduce(.(Letter, Others), Count, Letter, Code) :- ','(!, reduce(Others, Count, Letter, Code)).
reduce(.(Current, Others), Count, X5, .(Current, Code)) :- reduce(Others, s(Count), Current, Code).
vowel_h_w_y(97).
vowel_h_w_y(101).
vowel_h_w_y(105).
vowel_h_w_y(111).
vowel_h_w_y(117).
vowel_h_w_y(104).
vowel_h_w_y(119).
vowel_h_w_y(121).
eq(X, X).

Queries:

goal(g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: goal(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: goal(T1, T2), SCOPE: 1, CLAUSE: 0\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(eq(T3, .(X10, X11)), ','(reduce(X11, s(0), X10, X12), eq(T5, X12)))\n\nT3 is ground\nX10 is free; \nX11 is free; \nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(eq(T3, .(X10, X11)), ','(reduce(X11, s(0), X10, X12), eq(T5, X12))), SCOPE: 2, CLAUSE: 14\n\nT3 is ground\nX10 is free; \nX11 is free; \nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(reduce(T8, s(0), T7, X12), eq(T5, X12))\n\nT7 is ground\nT8 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: \n\nX10 is free\nX11 is free; \nX14 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: reduce(T8, s(0), T7, X12)\n\nT7 is ground\nT8 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: eq(T5, T9)\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 1 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 2 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 3 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 4 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT7 is ground\nT8 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 2 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 3 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 4 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT7 is ground\nT8 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: !_3 | reduce([], s(0), T10, X12), SCOPE: 3, CLAUSE: 3 | reduce([], s(0), T10, X12), SCOPE: 3, CLAUSE: 4 | reduce([], s(0), T10, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT10 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 3 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 4 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT7 is ground\nT8 is ground\nX12 is free; \nX19 is free; \nX20 is free; \nreduce(T8, s(0), T7, X12) !=? reduce([], X19, X20, [])", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))) | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX19 is free; \nX20 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 4 | reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT7 is ground\nT8 is ground\nX12 is free; \nX19 is free; \nX20 is free; \nX25 is free; \nX26 is free; \nX27 is free; \nX28 is free; \nreduce(T8, s(0), T7, X12) !=? reduce([], X19, X20, [])\nreduce(T8, s(0), T7, X12) !=? reduce(.(X25, X26), X27, X25, X28)", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 6 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 7 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(!_3, reduce(T12, s(0), 97, X29)) | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 7 | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(97), ','(!_3, reduce(T12, s(0), 97, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(97, T12), s(0), 97, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(97, T12), s(0), 97, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 7 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: reduce(T12, s(0), 97, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(!_3, reduce(T12, s(0), 101, X29)) | ','(vowel_h_w_y(101), ','(!_3, reduce(T12, s(0), 101, X29))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(101), ','(!_3, reduce(T12, s(0), 101, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(101), ','(!_3, reduce(T12, s(0), 101, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(101), ','(!_3, reduce(T12, s(0), 101, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(101), ','(!_3, reduce(T12, s(0), 101, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(101), ','(!_3, reduce(T12, s(0), 101, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(101, T12), s(0), 101, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(101, T12), s(0), 101, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: reduce(T12, s(0), 101, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(!_3, reduce(T12, s(0), 105, X29)) | ','(vowel_h_w_y(105), ','(!_3, reduce(T12, s(0), 105, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(105), ','(!_3, reduce(T12, s(0), 105, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(105), ','(!_3, reduce(T12, s(0), 105, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(105), ','(!_3, reduce(T12, s(0), 105, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(105), ','(!_3, reduce(T12, s(0), 105, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(105, T12), s(0), 105, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(105, T12), s(0), 105, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)\nvowel_h_w_y(T11) !=? vowel_h_w_y(105)", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: reduce(T12, s(0), 105, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(!_3, reduce(T12, s(0), 111, X29)) | ','(vowel_h_w_y(111), ','(!_3, reduce(T12, s(0), 111, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(111), ','(!_3, reduce(T12, s(0), 111, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(111), ','(!_3, reduce(T12, s(0), 111, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(111), ','(!_3, reduce(T12, s(0), 111, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(111, T12), s(0), 111, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(111, T12), s(0), 111, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)\nvowel_h_w_y(T11) !=? vowel_h_w_y(105)\nvowel_h_w_y(T11) !=? vowel_h_w_y(111)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: reduce(T12, s(0), 111, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(!_3, reduce(T12, s(0), 117, X29)) | ','(vowel_h_w_y(117), ','(!_3, reduce(T12, s(0), 117, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(117), ','(!_3, reduce(T12, s(0), 117, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(117), ','(!_3, reduce(T12, s(0), 117, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(117, T12), s(0), 117, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(117, T12), s(0), 117, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)\nvowel_h_w_y(T11) !=? vowel_h_w_y(105)\nvowel_h_w_y(T11) !=? vowel_h_w_y(111)\nvowel_h_w_y(T11) !=? vowel_h_w_y(117)", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: reduce(T12, s(0), 117, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(!_3, reduce(T12, s(0), 104, X29)) | ','(vowel_h_w_y(104), ','(!_3, reduce(T12, s(0), 104, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(104), ','(!_3, reduce(T12, s(0), 104, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(104, T12), s(0), 104, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(104, T12), s(0), 104, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)\nvowel_h_w_y(T11) !=? vowel_h_w_y(105)\nvowel_h_w_y(T11) !=? vowel_h_w_y(111)\nvowel_h_w_y(T11) !=? vowel_h_w_y(117)\nvowel_h_w_y(T11) !=? vowel_h_w_y(104)", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: reduce(T12, s(0), 104, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(!_3, reduce(T12, s(0), 119, X29)) | ','(vowel_h_w_y(119), ','(!_3, reduce(T12, s(0), 119, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(119, T12), s(0), 119, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(119, T12), s(0), 119, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(vowel_h_w_y(T11), ','(!_3, reduce(T12, s(0), T11, X29))), SCOPE: 4, CLAUSE: 13 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nX29 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)\nvowel_h_w_y(T11) !=? vowel_h_w_y(105)\nvowel_h_w_y(T11) !=? vowel_h_w_y(111)\nvowel_h_w_y(T11) !=? vowel_h_w_y(117)\nvowel_h_w_y(T11) !=? vowel_h_w_y(104)\nvowel_h_w_y(T11) !=? vowel_h_w_y(119)", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: reduce(T12, s(0), 119, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(!_3, reduce(T12, s(0), 121, X29)) | reduce(.(121, T12), s(0), 121, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(121, T12), s(0), 121, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT12 is ground\nX12 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 4 | reduce(.(T11, T12), s(0), T11, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT11 is ground\nT12 is ground\nX12 is free; \nvowel_h_w_y(T11) !=? vowel_h_w_y(97)\nvowel_h_w_y(T11) !=? vowel_h_w_y(101)\nvowel_h_w_y(T11) !=? vowel_h_w_y(105)\nvowel_h_w_y(T11) !=? vowel_h_w_y(111)\nvowel_h_w_y(T11) !=? vowel_h_w_y(117)\nvowel_h_w_y(T11) !=? vowel_h_w_y(104)\nvowel_h_w_y(T11) !=? vowel_h_w_y(119)\nvowel_h_w_y(T11) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: reduce(T12, s(0), 121, X29)\n\nT12 is ground\nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(!_3, reduce(T14, s(0), T13, X38)) | reduce(.(T13, T14), s(0), T13, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT13 is ground\nT14 is ground\nX12 is free; \nX38 is free; \nvowel_h_w_y(T13) !=? vowel_h_w_y(97)\nvowel_h_w_y(T13) !=? vowel_h_w_y(101)\nvowel_h_w_y(T13) !=? vowel_h_w_y(105)\nvowel_h_w_y(T13) !=? vowel_h_w_y(111)\nvowel_h_w_y(T13) !=? vowel_h_w_y(117)\nvowel_h_w_y(T13) !=? vowel_h_w_y(104)\nvowel_h_w_y(T13) !=? vowel_h_w_y(119)\nvowel_h_w_y(T13) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: reduce(T14, s(0), T13, X38)\n\nT13 is ground\nT14 is ground\nX38 is free; \nvowel_h_w_y(T13) !=? vowel_h_w_y(97)\nvowel_h_w_y(T13) !=? vowel_h_w_y(101)\nvowel_h_w_y(T13) !=? vowel_h_w_y(105)\nvowel_h_w_y(T13) !=? vowel_h_w_y(111)\nvowel_h_w_y(T13) !=? vowel_h_w_y(117)\nvowel_h_w_y(T13) !=? vowel_h_w_y(104)\nvowel_h_w_y(T13) !=? vowel_h_w_y(119)\nvowel_h_w_y(T13) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(!_3, reduce(T16, s(0), T15, X47)) | reduce(.(T15, T16), s(0), T15, X12), SCOPE: 3, CLAUSE: 5 | ?_3\n\nT15 is ground\nT16 is ground\nX12 is free; \nX19 is free; \nX20 is free; \nX25 is free; \nX26 is free; \nX27 is free; \nX28 is free; \nX47 is free; \nreduce(.(T15, T16), s(0), T15, X12) !=? reduce(.(X25, X26), X27, X25, X28)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: reduce(T8, s(0), T7, X12), SCOPE: 3, CLAUSE: 5\n\nT7 is ground\nT8 is ground\nX12 is free; \nX19 is free; \nX20 is free; \nX25 is free; \nX26 is free; \nX27 is free; \nX28 is free; \nX43 is free; \nX44 is free; \nX45 is free; \nX46 is free; \nreduce(T8, s(0), T7, X12) !=? reduce([], X19, X20, [])\nreduce(T8, s(0), T7, X12) !=? reduce(.(X25, X26), X27, X25, X28)\nreduce(T8, s(0), T7, X12) !=? reduce(.(X43, X44), X45, X43, X46)", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: reduce(T16, s(0), T15, X47)\n\nT15 is ground\nT16 is ground\nX12 is free; \nX25 is free; \nX26 is free; \nX27 is free; \nX28 is free; \nX47 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: reduce(T18, s(s(0)), T17, X58)\n\nT17 is ground\nT18 is ground\nX12 is free; \nX19 is free; \nX20 is free; \nX25 is free; \nX26 is free; \nX27 is free; \nX28 is free; \nX43 is free; \nX44 is free; \nX45 is free; \nX46 is free; \nX58 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\nX12 is free\nX19 is free; \nX20 is free; \nX25 is free; \nX26 is free; \nX27 is free; \nX28 is free; \nX53 is free; \nX54 is free; \nX55 is free; \nX56 is free; \nX57 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 1 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 2 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 3 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 4 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT17 is ground\nT18 is ground\nX58 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 2 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 3 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 4 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT17 is ground\nT18 is ground\nX58 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: !_5 | reduce([], s(s(0)), T20, X58), SCOPE: 5, CLAUSE: 3 | reduce([], s(s(0)), T20, X58), SCOPE: 5, CLAUSE: 4 | reduce([], s(s(0)), T20, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT20 is ground\nX58 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 3 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 4 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT17 is ground\nT18 is ground\nX58 is free; \nX63 is free; \nX64 is free; \nreduce(T18, s(s(0)), T17, X58) !=? reduce([], X63, X64, [])", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))) | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX63 is free; \nX64 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 4 | reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT17 is ground\nT18 is ground\nX58 is free; \nX63 is free; \nX64 is free; \nX69 is free; \nX70 is free; \nX71 is free; \nX72 is free; \nreduce(T18, s(s(0)), T17, X58) !=? reduce([], X63, X64, [])\nreduce(T18, s(s(0)), T17, X58) !=? reduce(.(X69, X70), X71, X69, X72)", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 6 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 7 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(!_5, reduce(T22, s(s(0)), 97, X73)) | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 7 | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(97), ','(!_5, reduce(T22, s(s(0)), 97, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(97, T22), s(s(0)), 97, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(97, T22), s(s(0)), 97, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 7 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: reduce(T22, s(s(0)), 97, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 1 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 2 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 3 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 4 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 5 | ?_7\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 2 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 3 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 4 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 5 | ?_7\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 2 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 3 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 4 | reduce(T22, s(s(0)), 97, X73), SCOPE: 7, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(!_5, reduce(T22, s(s(0)), 101, X73)) | ','(vowel_h_w_y(101), ','(!_5, reduce(T22, s(s(0)), 101, X73))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(101), ','(!_5, reduce(T22, s(s(0)), 101, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(101), ','(!_5, reduce(T22, s(s(0)), 101, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(101), ','(!_5, reduce(T22, s(s(0)), 101, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(101), ','(!_5, reduce(T22, s(s(0)), 101, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(101), ','(!_5, reduce(T22, s(s(0)), 101, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(101, T22), s(s(0)), 101, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(101, T22), s(s(0)), 101, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: reduce(T22, s(s(0)), 101, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 1 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 2 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 3 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 4 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 5 | ?_8\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 2 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 3 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 4 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 5 | ?_8\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 2 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 3 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 4 | reduce(T22, s(s(0)), 101, X73), SCOPE: 8, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(!_5, reduce(T22, s(s(0)), 105, X73)) | ','(vowel_h_w_y(105), ','(!_5, reduce(T22, s(s(0)), 105, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(105), ','(!_5, reduce(T22, s(s(0)), 105, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(105), ','(!_5, reduce(T22, s(s(0)), 105, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(105), ','(!_5, reduce(T22, s(s(0)), 105, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(105), ','(!_5, reduce(T22, s(s(0)), 105, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(105, T22), s(s(0)), 105, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(105, T22), s(s(0)), 105, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)\nvowel_h_w_y(T21) !=? vowel_h_w_y(105)", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: reduce(T22, s(s(0)), 105, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 1 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 2 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 3 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 4 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 5 | ?_9\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 2 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 3 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 4 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 5 | ?_9\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 2 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 3 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 4 | reduce(T22, s(s(0)), 105, X73), SCOPE: 9, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(!_5, reduce(T22, s(s(0)), 111, X73)) | ','(vowel_h_w_y(111), ','(!_5, reduce(T22, s(s(0)), 111, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(111), ','(!_5, reduce(T22, s(s(0)), 111, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(111), ','(!_5, reduce(T22, s(s(0)), 111, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(111), ','(!_5, reduce(T22, s(s(0)), 111, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(111, T22), s(s(0)), 111, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(111, T22), s(s(0)), 111, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)\nvowel_h_w_y(T21) !=? vowel_h_w_y(105)\nvowel_h_w_y(T21) !=? vowel_h_w_y(111)", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: reduce(T22, s(s(0)), 111, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 1 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 2 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 3 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 4 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 5 | ?_10\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 2 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 3 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 4 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 5 | ?_10\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 2 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 3 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 4 | reduce(T22, s(s(0)), 111, X73), SCOPE: 10, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(!_5, reduce(T22, s(s(0)), 117, X73)) | ','(vowel_h_w_y(117), ','(!_5, reduce(T22, s(s(0)), 117, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(117), ','(!_5, reduce(T22, s(s(0)), 117, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(117), ','(!_5, reduce(T22, s(s(0)), 117, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(117, T22), s(s(0)), 117, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(117, T22), s(s(0)), 117, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)\nvowel_h_w_y(T21) !=? vowel_h_w_y(105)\nvowel_h_w_y(T21) !=? vowel_h_w_y(111)\nvowel_h_w_y(T21) !=? vowel_h_w_y(117)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: reduce(T22, s(s(0)), 117, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 1 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 2 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 3 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 4 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 5 | ?_11\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 2 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 3 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 4 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 5 | ?_11\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 2 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 3 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 4 | reduce(T22, s(s(0)), 117, X73), SCOPE: 11, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(!_5, reduce(T22, s(s(0)), 104, X73)) | ','(vowel_h_w_y(104), ','(!_5, reduce(T22, s(s(0)), 104, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(104), ','(!_5, reduce(T22, s(s(0)), 104, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(104, T22), s(s(0)), 104, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(104, T22), s(s(0)), 104, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)\nvowel_h_w_y(T21) !=? vowel_h_w_y(105)\nvowel_h_w_y(T21) !=? vowel_h_w_y(111)\nvowel_h_w_y(T21) !=? vowel_h_w_y(117)\nvowel_h_w_y(T21) !=? vowel_h_w_y(104)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: reduce(T22, s(s(0)), 104, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 1 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 2 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 3 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 4 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 5 | ?_12\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 2 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 3 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 4 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 5 | ?_12\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 2 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 3 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 4 | reduce(T22, s(s(0)), 104, X73), SCOPE: 12, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(!_5, reduce(T22, s(s(0)), 119, X73)) | ','(vowel_h_w_y(119), ','(!_5, reduce(T22, s(s(0)), 119, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(119, T22), s(s(0)), 119, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(119, T22), s(s(0)), 119, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(vowel_h_w_y(T21), ','(!_5, reduce(T22, s(s(0)), T21, X73))), SCOPE: 6, CLAUSE: 13 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nX73 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)\nvowel_h_w_y(T21) !=? vowel_h_w_y(105)\nvowel_h_w_y(T21) !=? vowel_h_w_y(111)\nvowel_h_w_y(T21) !=? vowel_h_w_y(117)\nvowel_h_w_y(T21) !=? vowel_h_w_y(104)\nvowel_h_w_y(T21) !=? vowel_h_w_y(119)", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: reduce(T22, s(s(0)), 119, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 1 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 2 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 3 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 4 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 5 | ?_13\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 2 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 3 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 4 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 5 | ?_13\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 2 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 3 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 4 | reduce(T22, s(s(0)), 119, X73), SCOPE: 13, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ','(!_5, reduce(T22, s(s(0)), 121, X73)) | reduce(.(121, T22), s(s(0)), 121, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(121, T22), s(s(0)), 121, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT22 is ground\nX58 is free; \nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 4 | reduce(.(T21, T22), s(s(0)), T21, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT21 is ground\nT22 is ground\nX58 is free; \nvowel_h_w_y(T21) !=? vowel_h_w_y(97)\nvowel_h_w_y(T21) !=? vowel_h_w_y(101)\nvowel_h_w_y(T21) !=? vowel_h_w_y(105)\nvowel_h_w_y(T21) !=? vowel_h_w_y(111)\nvowel_h_w_y(T21) !=? vowel_h_w_y(117)\nvowel_h_w_y(T21) !=? vowel_h_w_y(104)\nvowel_h_w_y(T21) !=? vowel_h_w_y(119)\nvowel_h_w_y(T21) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: reduce(T22, s(s(0)), 121, X73)\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 1 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 2 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 3 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 4 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 5 | ?_14\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 2 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 3 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 4 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 5 | ?_14\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 2 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 3 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 4 | reduce(T22, s(s(0)), 121, X73), SCOPE: 14, CLAUSE: 5\n\nT22 is ground\nX73 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(!_5, reduce(T24, s(s(0)), T23, X130)) | reduce(.(T23, T24), s(s(0)), T23, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT23 is ground\nT24 is ground\nX58 is free; \nX130 is free; \nvowel_h_w_y(T23) !=? vowel_h_w_y(97)\nvowel_h_w_y(T23) !=? vowel_h_w_y(101)\nvowel_h_w_y(T23) !=? vowel_h_w_y(105)\nvowel_h_w_y(T23) !=? vowel_h_w_y(111)\nvowel_h_w_y(T23) !=? vowel_h_w_y(117)\nvowel_h_w_y(T23) !=? vowel_h_w_y(104)\nvowel_h_w_y(T23) !=? vowel_h_w_y(119)\nvowel_h_w_y(T23) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: reduce(T24, s(s(0)), T23, X130)\n\nT23 is ground\nT24 is ground\nX130 is free; \nvowel_h_w_y(T23) !=? vowel_h_w_y(97)\nvowel_h_w_y(T23) !=? vowel_h_w_y(101)\nvowel_h_w_y(T23) !=? vowel_h_w_y(105)\nvowel_h_w_y(T23) !=? vowel_h_w_y(111)\nvowel_h_w_y(T23) !=? vowel_h_w_y(117)\nvowel_h_w_y(T23) !=? vowel_h_w_y(104)\nvowel_h_w_y(T23) !=? vowel_h_w_y(119)\nvowel_h_w_y(T23) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 1 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 2 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 3 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 4 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 5 | ?_15\n\nT23 is ground\nT24 is ground\nX130 is free; \nvowel_h_w_y(T23) !=? vowel_h_w_y(97)\nvowel_h_w_y(T23) !=? vowel_h_w_y(101)\nvowel_h_w_y(T23) !=? vowel_h_w_y(105)\nvowel_h_w_y(T23) !=? vowel_h_w_y(111)\nvowel_h_w_y(T23) !=? vowel_h_w_y(117)\nvowel_h_w_y(T23) !=? vowel_h_w_y(104)\nvowel_h_w_y(T23) !=? vowel_h_w_y(119)\nvowel_h_w_y(T23) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 2 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 3 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 4 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 5 | ?_15\n\nT23 is ground\nT24 is ground\nX130 is free; \nvowel_h_w_y(T23) !=? vowel_h_w_y(97)\nvowel_h_w_y(T23) !=? vowel_h_w_y(101)\nvowel_h_w_y(T23) !=? vowel_h_w_y(105)\nvowel_h_w_y(T23) !=? vowel_h_w_y(111)\nvowel_h_w_y(T23) !=? vowel_h_w_y(117)\nvowel_h_w_y(T23) !=? vowel_h_w_y(104)\nvowel_h_w_y(T23) !=? vowel_h_w_y(119)\nvowel_h_w_y(T23) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 2 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 3 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 4 | reduce(T24, s(s(0)), T23, X130), SCOPE: 15, CLAUSE: 5\n\nT23 is ground\nT24 is ground\nX130 is free; \nvowel_h_w_y(T23) !=? vowel_h_w_y(97)\nvowel_h_w_y(T23) !=? vowel_h_w_y(101)\nvowel_h_w_y(T23) !=? vowel_h_w_y(105)\nvowel_h_w_y(T23) !=? vowel_h_w_y(111)\nvowel_h_w_y(T23) !=? vowel_h_w_y(117)\nvowel_h_w_y(T23) !=? vowel_h_w_y(104)\nvowel_h_w_y(T23) !=? vowel_h_w_y(119)\nvowel_h_w_y(T23) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(!_5, reduce(T26, s(s(0)), T25, X145)) | reduce(.(T25, T26), s(s(0)), T25, X58), SCOPE: 5, CLAUSE: 5 | ?_5\n\nT25 is ground\nT26 is ground\nX58 is free; \nX63 is free; \nX64 is free; \nX69 is free; \nX70 is free; \nX71 is free; \nX72 is free; \nX145 is free; \nreduce(.(T25, T26), s(s(0)), T25, X58) !=? reduce(.(X69, X70), X71, X69, X72)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: reduce(T18, s(s(0)), T17, X58), SCOPE: 5, CLAUSE: 5\n\nT17 is ground\nT18 is ground\nX58 is free; \nX63 is free; \nX64 is free; \nX69 is free; \nX70 is free; \nX71 is free; \nX72 is free; \nX141 is free; \nX142 is free; \nX143 is free; \nX144 is free; \nreduce(T18, s(s(0)), T17, X58) !=? reduce([], X63, X64, [])\nreduce(T18, s(s(0)), T17, X58) !=? reduce(.(X69, X70), X71, X69, X72)\nreduce(T18, s(s(0)), T17, X58) !=? reduce(.(X141, X142), X143, X141, X144)", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: reduce(T26, s(s(0)), T25, X145)\n\nT25 is ground\nT26 is ground\nX58 is free; \nX69 is free; \nX70 is free; \nX71 is free; \nX72 is free; \nX145 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 1 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 2 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 3 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 4 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 5 | ?_16\n\nT25 is ground\nT26 is ground\nX145 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 2 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 3 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 4 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 5 | ?_16\n\nT25 is ground\nT26 is ground\nX145 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 2 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 3 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 4 | reduce(T26, s(s(0)), T25, X145), SCOPE: 16, CLAUSE: 5\n\nT25 is ground\nT26 is ground\nX145 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: reduce(T28, s(s(s(0))), T27, X162)\n\nT27 is ground\nT28 is ground\nX58 is free; \nX63 is free; \nX64 is free; \nX69 is free; \nX70 is free; \nX71 is free; \nX72 is free; \nX141 is free; \nX142 is free; \nX143 is free; \nX144 is free; \nX162 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: \n\nX58 is free\nX63 is free; \nX64 is free; \nX69 is free; \nX70 is free; \nX71 is free; \nX72 is free; \nX157 is free; \nX158 is free; \nX159 is free; \nX160 is free; \nX161 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 1 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 2 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 3 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 4 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT27 is ground\nT28 is ground\nX162 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 2 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 3 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 4 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT27 is ground\nT28 is ground\nX162 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: !_17 | reduce([], s(s(s(0))), T30, X162), SCOPE: 17, CLAUSE: 3 | reduce([], s(s(s(0))), T30, X162), SCOPE: 17, CLAUSE: 4 | reduce([], s(s(s(0))), T30, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT30 is ground\nX162 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 3 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 4 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT27 is ground\nT28 is ground\nX162 is free; \nX167 is free; \nX168 is free; \nreduce(T28, s(s(s(0))), T27, X162) !=? reduce([], X167, X168, [])", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))) | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX167 is free; \nX168 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 4 | reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT27 is ground\nT28 is ground\nX162 is free; \nX167 is free; \nX168 is free; \nX173 is free; \nX174 is free; \nX175 is free; \nX176 is free; \nreduce(T28, s(s(s(0))), T27, X162) !=? reduce([], X167, X168, [])\nreduce(T28, s(s(s(0))), T27, X162) !=? reduce(.(X173, X174), X175, X173, X176)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 6 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 7 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 8 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(!_17, reduce(T32, s(s(s(0))), 97, X177)) | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 7 | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 8 | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(97), ','(!_17, reduce(T32, s(s(s(0))), 97, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(97, T32), s(s(s(0))), 97, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(97, T32), s(s(s(0))), 97, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 7 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 8 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: reduce(T32, s(s(s(0))), 97, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 1 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 2 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 3 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 4 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 5 | ?_19\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 2 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 3 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 4 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 5 | ?_19\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 2 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 3 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 4 | reduce(T32, s(s(s(0))), 97, X177), SCOPE: 19, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(!_17, reduce(T32, s(s(s(0))), 101, X177)) | ','(vowel_h_w_y(101), ','(!_17, reduce(T32, s(s(s(0))), 101, X177))), SCOPE: 18, CLAUSE: 8 | ','(vowel_h_w_y(101), ','(!_17, reduce(T32, s(s(s(0))), 101, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(101), ','(!_17, reduce(T32, s(s(s(0))), 101, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(101), ','(!_17, reduce(T32, s(s(s(0))), 101, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(101), ','(!_17, reduce(T32, s(s(s(0))), 101, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(101), ','(!_17, reduce(T32, s(s(s(0))), 101, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(101, T32), s(s(s(0))), 101, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(101, T32), s(s(s(0))), 101, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 8 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: reduce(T32, s(s(s(0))), 101, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 1 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 2 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 3 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 4 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 5 | ?_20\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 2 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 3 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 4 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 5 | ?_20\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 2 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 3 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 4 | reduce(T32, s(s(s(0))), 101, X177), SCOPE: 20, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(!_17, reduce(T32, s(s(s(0))), 105, X177)) | ','(vowel_h_w_y(105), ','(!_17, reduce(T32, s(s(s(0))), 105, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(105), ','(!_17, reduce(T32, s(s(s(0))), 105, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(105), ','(!_17, reduce(T32, s(s(s(0))), 105, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(105), ','(!_17, reduce(T32, s(s(s(0))), 105, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(105), ','(!_17, reduce(T32, s(s(s(0))), 105, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(105, T32), s(s(s(0))), 105, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(105, T32), s(s(s(0))), 105, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 9 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)\nvowel_h_w_y(T31) !=? vowel_h_w_y(105)", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: reduce(T32, s(s(s(0))), 105, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 1 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 2 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 3 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 4 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 5 | ?_21\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 2 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 3 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 4 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 5 | ?_21\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 2 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 3 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 4 | reduce(T32, s(s(s(0))), 105, X177), SCOPE: 21, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(!_17, reduce(T32, s(s(s(0))), 111, X177)) | ','(vowel_h_w_y(111), ','(!_17, reduce(T32, s(s(s(0))), 111, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(111), ','(!_17, reduce(T32, s(s(s(0))), 111, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(111), ','(!_17, reduce(T32, s(s(s(0))), 111, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(111), ','(!_17, reduce(T32, s(s(s(0))), 111, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(111, T32), s(s(s(0))), 111, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(111, T32), s(s(s(0))), 111, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 10 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)\nvowel_h_w_y(T31) !=? vowel_h_w_y(105)\nvowel_h_w_y(T31) !=? vowel_h_w_y(111)", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: reduce(T32, s(s(s(0))), 111, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 1 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 2 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 3 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 4 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 5 | ?_22\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 2 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 3 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 4 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 5 | ?_22\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 2 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 3 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 4 | reduce(T32, s(s(s(0))), 111, X177), SCOPE: 22, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: ','(!_17, reduce(T32, s(s(s(0))), 117, X177)) | ','(vowel_h_w_y(117), ','(!_17, reduce(T32, s(s(s(0))), 117, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(117), ','(!_17, reduce(T32, s(s(s(0))), 117, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(117), ','(!_17, reduce(T32, s(s(s(0))), 117, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(117, T32), s(s(s(0))), 117, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(117, T32), s(s(s(0))), 117, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 11 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)\nvowel_h_w_y(T31) !=? vowel_h_w_y(105)\nvowel_h_w_y(T31) !=? vowel_h_w_y(111)\nvowel_h_w_y(T31) !=? vowel_h_w_y(117)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: reduce(T32, s(s(s(0))), 117, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 1 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 2 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 3 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 4 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 5 | ?_23\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 2 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 3 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 4 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 5 | ?_23\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 2 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 3 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 4 | reduce(T32, s(s(s(0))), 117, X177), SCOPE: 23, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(!_17, reduce(T32, s(s(s(0))), 104, X177)) | ','(vowel_h_w_y(104), ','(!_17, reduce(T32, s(s(s(0))), 104, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(104), ','(!_17, reduce(T32, s(s(s(0))), 104, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(104, T32), s(s(s(0))), 104, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(104, T32), s(s(s(0))), 104, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 12 | ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)\nvowel_h_w_y(T31) !=? vowel_h_w_y(105)\nvowel_h_w_y(T31) !=? vowel_h_w_y(111)\nvowel_h_w_y(T31) !=? vowel_h_w_y(117)\nvowel_h_w_y(T31) !=? vowel_h_w_y(104)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: reduce(T32, s(s(s(0))), 104, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 1 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 2 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 3 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 4 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 5 | ?_24\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 2 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 3 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 4 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 5 | ?_24\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 2 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 3 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 4 | reduce(T32, s(s(s(0))), 104, X177), SCOPE: 24, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: ','(!_17, reduce(T32, s(s(s(0))), 119, X177)) | ','(vowel_h_w_y(119), ','(!_17, reduce(T32, s(s(s(0))), 119, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(119, T32), s(s(s(0))), 119, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(119, T32), s(s(s(0))), 119, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(vowel_h_w_y(T31), ','(!_17, reduce(T32, s(s(s(0))), T31, X177))), SCOPE: 18, CLAUSE: 13 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nX177 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)\nvowel_h_w_y(T31) !=? vowel_h_w_y(105)\nvowel_h_w_y(T31) !=? vowel_h_w_y(111)\nvowel_h_w_y(T31) !=? vowel_h_w_y(117)\nvowel_h_w_y(T31) !=? vowel_h_w_y(104)\nvowel_h_w_y(T31) !=? vowel_h_w_y(119)", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: reduce(T32, s(s(s(0))), 119, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 1 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 2 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 3 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 4 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 5 | ?_25\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 2 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 3 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 4 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 5 | ?_25\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 2 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 3 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 4 | reduce(T32, s(s(s(0))), 119, X177), SCOPE: 25, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(!_17, reduce(T32, s(s(s(0))), 121, X177)) | reduce(.(121, T32), s(s(s(0))), 121, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(121, T32), s(s(s(0))), 121, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT32 is ground\nX162 is free; \nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 4 | reduce(.(T31, T32), s(s(s(0))), T31, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT31 is ground\nT32 is ground\nX162 is free; \nvowel_h_w_y(T31) !=? vowel_h_w_y(97)\nvowel_h_w_y(T31) !=? vowel_h_w_y(101)\nvowel_h_w_y(T31) !=? vowel_h_w_y(105)\nvowel_h_w_y(T31) !=? vowel_h_w_y(111)\nvowel_h_w_y(T31) !=? vowel_h_w_y(117)\nvowel_h_w_y(T31) !=? vowel_h_w_y(104)\nvowel_h_w_y(T31) !=? vowel_h_w_y(119)\nvowel_h_w_y(T31) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: reduce(T32, s(s(s(0))), 121, X177)\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 1 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 2 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 3 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 4 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 5 | ?_26\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 2 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 3 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 4 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 5 | ?_26\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 2 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 3 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 4 | reduce(T32, s(s(s(0))), 121, X177), SCOPE: 26, CLAUSE: 5\n\nT32 is ground\nX177 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(!_17, reduce(T34, s(s(s(0))), T33, X234)) | reduce(.(T33, T34), s(s(s(0))), T33, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT33 is ground\nT34 is ground\nX162 is free; \nX234 is free; \nvowel_h_w_y(T33) !=? vowel_h_w_y(97)\nvowel_h_w_y(T33) !=? vowel_h_w_y(101)\nvowel_h_w_y(T33) !=? vowel_h_w_y(105)\nvowel_h_w_y(T33) !=? vowel_h_w_y(111)\nvowel_h_w_y(T33) !=? vowel_h_w_y(117)\nvowel_h_w_y(T33) !=? vowel_h_w_y(104)\nvowel_h_w_y(T33) !=? vowel_h_w_y(119)\nvowel_h_w_y(T33) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: reduce(T34, s(s(s(0))), T33, X234)\n\nT33 is ground\nT34 is ground\nX234 is free; \nvowel_h_w_y(T33) !=? vowel_h_w_y(97)\nvowel_h_w_y(T33) !=? vowel_h_w_y(101)\nvowel_h_w_y(T33) !=? vowel_h_w_y(105)\nvowel_h_w_y(T33) !=? vowel_h_w_y(111)\nvowel_h_w_y(T33) !=? vowel_h_w_y(117)\nvowel_h_w_y(T33) !=? vowel_h_w_y(104)\nvowel_h_w_y(T33) !=? vowel_h_w_y(119)\nvowel_h_w_y(T33) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 1 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 2 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 3 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 4 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 5 | ?_27\n\nT33 is ground\nT34 is ground\nX234 is free; \nvowel_h_w_y(T33) !=? vowel_h_w_y(97)\nvowel_h_w_y(T33) !=? vowel_h_w_y(101)\nvowel_h_w_y(T33) !=? vowel_h_w_y(105)\nvowel_h_w_y(T33) !=? vowel_h_w_y(111)\nvowel_h_w_y(T33) !=? vowel_h_w_y(117)\nvowel_h_w_y(T33) !=? vowel_h_w_y(104)\nvowel_h_w_y(T33) !=? vowel_h_w_y(119)\nvowel_h_w_y(T33) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 2 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 3 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 4 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 5 | ?_27\n\nT33 is ground\nT34 is ground\nX234 is free; \nvowel_h_w_y(T33) !=? vowel_h_w_y(97)\nvowel_h_w_y(T33) !=? vowel_h_w_y(101)\nvowel_h_w_y(T33) !=? vowel_h_w_y(105)\nvowel_h_w_y(T33) !=? vowel_h_w_y(111)\nvowel_h_w_y(T33) !=? vowel_h_w_y(117)\nvowel_h_w_y(T33) !=? vowel_h_w_y(104)\nvowel_h_w_y(T33) !=? vowel_h_w_y(119)\nvowel_h_w_y(T33) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 2 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 3 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 4 | reduce(T34, s(s(s(0))), T33, X234), SCOPE: 27, CLAUSE: 5\n\nT33 is ground\nT34 is ground\nX234 is free; \nvowel_h_w_y(T33) !=? vowel_h_w_y(97)\nvowel_h_w_y(T33) !=? vowel_h_w_y(101)\nvowel_h_w_y(T33) !=? vowel_h_w_y(105)\nvowel_h_w_y(T33) !=? vowel_h_w_y(111)\nvowel_h_w_y(T33) !=? vowel_h_w_y(117)\nvowel_h_w_y(T33) !=? vowel_h_w_y(104)\nvowel_h_w_y(T33) !=? vowel_h_w_y(119)\nvowel_h_w_y(T33) !=? vowel_h_w_y(121)", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: ','(!_17, reduce(T36, s(s(s(0))), T35, X249)) | reduce(.(T35, T36), s(s(s(0))), T35, X162), SCOPE: 17, CLAUSE: 5 | ?_17\n\nT35 is ground\nT36 is ground\nX162 is free; \nX167 is free; \nX168 is free; \nX173 is free; \nX174 is free; \nX175 is free; \nX176 is free; \nX249 is free; \nreduce(.(T35, T36), s(s(s(0))), T35, X162) !=? reduce(.(X173, X174), X175, X173, X176)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: reduce(T28, s(s(s(0))), T27, X162), SCOPE: 17, CLAUSE: 5\n\nT27 is ground\nT28 is ground\nX162 is free; \nX167 is free; \nX168 is free; \nX173 is free; \nX174 is free; \nX175 is free; \nX176 is free; \nX245 is free; \nX246 is free; \nX247 is free; \nX248 is free; \nreduce(T28, s(s(s(0))), T27, X162) !=? reduce([], X167, X168, [])\nreduce(T28, s(s(s(0))), T27, X162) !=? reduce(.(X173, X174), X175, X173, X176)\nreduce(T28, s(s(s(0))), T27, X162) !=? reduce(.(X245, X246), X247, X245, X248)", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: reduce(T36, s(s(s(0))), T35, X249)\n\nT35 is ground\nT36 is ground\nX162 is free; \nX173 is free; \nX174 is free; \nX175 is free; \nX176 is free; \nX249 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 1 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 2 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 3 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 4 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 5 | ?_28\n\nT35 is ground\nT36 is ground\nX249 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 2 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 3 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 4 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 5 | ?_28\n\nT35 is ground\nT36 is ground\nX249 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 2 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 3 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 4 | reduce(T36, s(s(s(0))), T35, X249), SCOPE: 28, CLAUSE: 5\n\nT35 is ground\nT36 is ground\nX249 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: reduce(T38, s(s(s(s(0)))), T37, X266)\n\nT37 is ground\nT38 is ground\nX162 is free; \nX167 is free; \nX168 is free; \nX173 is free; \nX174 is free; \nX175 is free; \nX176 is free; \nX245 is free; \nX246 is free; \nX247 is free; \nX248 is free; \nX266 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\nX162 is free\nX167 is free; \nX168 is free; \nX173 is free; \nX174 is free; \nX175 is free; \nX176 is free; \nX261 is free; \nX262 is free; \nX263 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: reduce(T38, s(s(s(s(0)))), T37, X266), SCOPE: 29, CLAUSE: 1 | reduce(T38, s(s(s(s(0)))), T37, X266), SCOPE: 29, CLAUSE: 2 | reduce(T38, s(s(s(s(0)))), T37, X266), SCOPE: 29, CLAUSE: 3 | reduce(T38, s(s(s(s(0)))), T37, X266), SCOPE: 29, CLAUSE: 4 | reduce(T38, s(s(s(s(0)))), T37, X266), SCOPE: 29, CLAUSE: 5 | ?_29\n\nT37 is ground\nT38 is ground\nX266 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: !_29 | reduce(T40, s(s(s(s(0)))), T41, X266), SCOPE: 29, CLAUSE: 2 | reduce(T40, s(s(s(s(0)))), T41, X266), SCOPE: 29, CLAUSE: 3 | reduce(T40, s(s(s(s(0)))), T41, X266), SCOPE: 29, CLAUSE: 4 | reduce(T40, s(s(s(s(0)))), T41, X266), SCOPE: 29, CLAUSE: 5 | ?_29\n\nT40 is ground\nT41 is ground\nX266 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: eq(T5, T9), SCOPE: 30, CLAUSE: 14\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\nX272 is free", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 217 [arrowhead = none ];
217 -> 2;

218 [label="EVAL with clause\ngoal(X8, X9) :- ','(eq(X8, .(X10, X11)), ','(reduce(X11, s(0), X10, X12), eq(X9, X12))).\nand substitution\nT1 -> T3\nX8 -> T3\nT2 -> T5\nX9 -> T5\nT4 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 218 [arrowhead = none ];
218 -> 3;

219 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 219 [arrowhead = none ];
219 -> 4;

220 [label="EVAL with clause\neq(X14, X14).\nand substitution\nT3 -> .(T7, T8)\nX14 -> .(T7, T8)\nX10 -> T7\nX11 -> T8\nT6 -> .(T7, T8)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 220 [arrowhead = none ];
220 -> 5;

221 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 221 [arrowhead = none ];
221 -> 6;

222 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
5 -> 222 [arrowhead = none ];
222 -> 7;

223 [label="SPLIT 2\nnew knowledge:\nT9 is ground\nreplacements:\nX12 -> T9", fontsize=14, style = filled, fillcolor = violet];
5 -> 223 [arrowhead = none ];
223 -> 8;

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

225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 225 [arrowhead = none ];
225 -> 213;

226 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
9 -> 226 [arrowhead = none ];
226 -> 10;

227 [label="EVAL with clause\nreduce([], X19, X20, []) :- !.\nand substitution\nT8 -> []\nX19 -> s(0)\nT7 -> T10\nX20 -> T10\nX12 -> []", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 227 [arrowhead = none ];
227 -> 11;

228 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 228 [arrowhead = none ];
228 -> 12;

229 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 229 [arrowhead = none ];
229 -> 13;

230 [label="EVAL with clause\nreduce(.(X25, X26), X27, X25, X28) :- ','(vowel_h_w_y(X25), ','(!, reduce(X26, X27, X25, X28))).\nand substitution\nX25 -> T11\nX26 -> T12\nT8 -> .(T11, T12)\nX27 -> s(0)\nT7 -> T11\nX12 -> X29\nX28 -> X29", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 230 [arrowhead = none ];
230 -> 15;

231 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 231 [arrowhead = none ];
231 -> 16;

232 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 232 [arrowhead = none ];
232 -> 14;

233 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 233 [arrowhead = none ];
233 -> 17;

234 [label="EVAL with clause\nreduce(.(X43, X44), X45, X43, X46) :- ','(!, reduce(X44, X45, X43, X46)).\nand substitution\nX43 -> T15\nX44 -> T16\nT8 -> .(T15, T16)\nX45 -> s(0)\nT7 -> T15\nX12 -> X47\nX46 -> X47", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 234 [arrowhead = none ];
234 -> 44;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 235 [arrowhead = none ];
235 -> 45;

236 [label="EVAL with clause\nvowel_h_w_y(97).\nand substitution\nT11 -> 97", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 236 [arrowhead = none ];
236 -> 18;

237 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 237 [arrowhead = none ];
237 -> 19;

238 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 238 [arrowhead = none ];
238 -> 20;

239 [label="EVAL with clause\nvowel_h_w_y(101).\nand substitution\nT11 -> 101", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 239 [arrowhead = none ];
239 -> 21;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 240 [arrowhead = none ];
240 -> 22;

241 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 97\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
20 -> 241 [arrowhead = none , style=dashed];
241 -> 7[style=dashed];

242 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 242 [arrowhead = none ];
242 -> 23;

243 [label="EVAL with clause\nvowel_h_w_y(105).\nand substitution\nT11 -> 105", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 243 [arrowhead = none ];
243 -> 24;

244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 244 [arrowhead = none ];
244 -> 25;

245 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 101\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
23 -> 245 [arrowhead = none , style=dashed];
245 -> 7[style=dashed];

246 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 246 [arrowhead = none ];
246 -> 26;

247 [label="EVAL with clause\nvowel_h_w_y(111).\nand substitution\nT11 -> 111", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 247 [arrowhead = none ];
247 -> 27;

248 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 248 [arrowhead = none ];
248 -> 28;

249 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 105\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
26 -> 249 [arrowhead = none , style=dashed];
249 -> 7[style=dashed];

250 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 250 [arrowhead = none ];
250 -> 29;

251 [label="EVAL with clause\nvowel_h_w_y(117).\nand substitution\nT11 -> 117", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 251 [arrowhead = none ];
251 -> 30;

252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 252 [arrowhead = none ];
252 -> 31;

253 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 111\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
29 -> 253 [arrowhead = none , style=dashed];
253 -> 7[style=dashed];

254 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 254 [arrowhead = none ];
254 -> 32;

255 [label="EVAL with clause\nvowel_h_w_y(104).\nand substitution\nT11 -> 104", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 255 [arrowhead = none ];
255 -> 33;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 256 [arrowhead = none ];
256 -> 34;

257 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 117\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 257 [arrowhead = none , style=dashed];
257 -> 7[style=dashed];

258 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 258 [arrowhead = none ];
258 -> 35;

259 [label="EVAL with clause\nvowel_h_w_y(119).\nand substitution\nT11 -> 119", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 259 [arrowhead = none ];
259 -> 36;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 260 [arrowhead = none ];
260 -> 37;

261 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 104\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
35 -> 261 [arrowhead = none , style=dashed];
261 -> 7[style=dashed];

262 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 262 [arrowhead = none ];
262 -> 38;

263 [label="EVAL with clause\nvowel_h_w_y(121).\nand substitution\nT11 -> 121", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 263 [arrowhead = none ];
263 -> 39;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 264 [arrowhead = none ];
264 -> 40;

265 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 119\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
38 -> 265 [arrowhead = none , style=dashed];
265 -> 7[style=dashed];

266 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 266 [arrowhead = none ];
266 -> 41;

267 [label="EVAL with clause\nreduce(.(X34, X35), X36, X34, X37) :- ','(!, reduce(X35, X36, X34, X37)).\nand substitution\nT11 -> T13\nX34 -> T13\nT12 -> T14\nX35 -> T14\nX36 -> s(0)\nX12 -> X38\nX37 -> X38", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 267 [arrowhead = none ];
267 -> 42;

268 [label="INSTANCE with matching:\nT8 -> T12\nT7 -> 121\nX12 -> X29", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 268 [arrowhead = none , style=dashed];
268 -> 7[style=dashed];

269 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 269 [arrowhead = none ];
269 -> 43;

270 [label="INSTANCE with matching:\nT8 -> T14\nT7 -> T13\nX12 -> X38", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 270 [arrowhead = none , style=dashed];
270 -> 7[style=dashed];

271 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
44 -> 271 [arrowhead = none ];
271 -> 46;

272 [label="EVAL with clause\nreduce(.(X53, X54), X55, X56, .(X53, X57)) :- reduce(X54, s(X55), X53, X57).\nand substitution\nX53 -> T17\nX54 -> T18\nT8 -> .(T17, T18)\nX55 -> s(0)\nT7 -> T19\nX56 -> T19\nX57 -> X58\nX12 -> .(T17, X58)", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 272 [arrowhead = none ];
272 -> 47;

273 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 273 [arrowhead = none ];
273 -> 48;

274 [label="INSTANCE with matching:\nT8 -> T16\nT7 -> T15\nX12 -> X47", fontsize=14, style = filled, fillcolor = lightgrey];
46 -> 274 [arrowhead = none , style=dashed];
274 -> 7[style=dashed];

275 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 275 [arrowhead = none ];
275 -> 49;

276 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
49 -> 276 [arrowhead = none ];
276 -> 50;

277 [label="EVAL with clause\nreduce([], X63, X64, []) :- !.\nand substitution\nT18 -> []\nX63 -> s(s(0))\nT17 -> T20\nX64 -> T20\nX58 -> []", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 277 [arrowhead = none ];
277 -> 51;

278 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 278 [arrowhead = none ];
278 -> 52;

279 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 279 [arrowhead = none ];
279 -> 53;

280 [label="EVAL with clause\nreduce(.(X69, X70), X71, X69, X72) :- ','(vowel_h_w_y(X69), ','(!, reduce(X70, X71, X69, X72))).\nand substitution\nX69 -> T21\nX70 -> T22\nT18 -> .(T21, T22)\nX71 -> s(s(0))\nT17 -> T21\nX58 -> X73\nX72 -> X73", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 280 [arrowhead = none ];
280 -> 55;

281 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 281 [arrowhead = none ];
281 -> 56;

282 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 282 [arrowhead = none ];
282 -> 54;

283 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
55 -> 283 [arrowhead = none ];
283 -> 57;

284 [label="EVAL with clause\nreduce(.(X141, X142), X143, X141, X144) :- ','(!, reduce(X142, X143, X141, X144)).\nand substitution\nX141 -> T25\nX142 -> T26\nT18 -> .(T25, T26)\nX143 -> s(s(0))\nT17 -> T25\nX58 -> X145\nX144 -> X145", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 284 [arrowhead = none ];
284 -> 120;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 285 [arrowhead = none ];
285 -> 121;

286 [label="EVAL with clause\nvowel_h_w_y(97).\nand substitution\nT21 -> 97", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 286 [arrowhead = none ];
286 -> 58;

287 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 287 [arrowhead = none ];
287 -> 59;

288 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 288 [arrowhead = none ];
288 -> 60;

289 [label="EVAL with clause\nvowel_h_w_y(101).\nand substitution\nT21 -> 101", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 289 [arrowhead = none ];
289 -> 65;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 290 [arrowhead = none ];
290 -> 66;

291 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
60 -> 291 [arrowhead = none ];
291 -> 61;

292 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
61 -> 292 [arrowhead = none ];
292 -> 62;

293 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 293 [arrowhead = none ];
293 -> 63;

294 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 294 [arrowhead = none ];
294 -> 64;

295 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 97\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 295 [arrowhead = none , style=dashed];
295 -> 50[style=dashed];

296 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 296 [arrowhead = none ];
296 -> 67;

297 [label="EVAL with clause\nvowel_h_w_y(105).\nand substitution\nT21 -> 105", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 297 [arrowhead = none ];
297 -> 72;

298 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 298 [arrowhead = none ];
298 -> 73;

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
67 -> 299 [arrowhead = none ];
299 -> 68;

300 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
68 -> 300 [arrowhead = none ];
300 -> 69;

301 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
69 -> 301 [arrowhead = none ];
301 -> 70;

302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
69 -> 302 [arrowhead = none ];
302 -> 71;

303 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 101\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
70 -> 303 [arrowhead = none , style=dashed];
303 -> 50[style=dashed];

304 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 304 [arrowhead = none ];
304 -> 74;

305 [label="EVAL with clause\nvowel_h_w_y(111).\nand substitution\nT21 -> 111", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 305 [arrowhead = none ];
305 -> 79;

306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 306 [arrowhead = none ];
306 -> 80;

307 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
74 -> 307 [arrowhead = none ];
307 -> 75;

308 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
75 -> 308 [arrowhead = none ];
308 -> 76;

309 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 309 [arrowhead = none ];
309 -> 77;

310 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 310 [arrowhead = none ];
310 -> 78;

311 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 105\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 311 [arrowhead = none , style=dashed];
311 -> 50[style=dashed];

312 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 312 [arrowhead = none ];
312 -> 81;

313 [label="EVAL with clause\nvowel_h_w_y(117).\nand substitution\nT21 -> 117", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 313 [arrowhead = none ];
313 -> 86;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 314 [arrowhead = none ];
314 -> 87;

315 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
81 -> 315 [arrowhead = none ];
315 -> 82;

316 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
82 -> 316 [arrowhead = none ];
316 -> 83;

317 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
83 -> 317 [arrowhead = none ];
317 -> 84;

318 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
83 -> 318 [arrowhead = none ];
318 -> 85;

319 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 111\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
84 -> 319 [arrowhead = none , style=dashed];
319 -> 50[style=dashed];

320 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
86 -> 320 [arrowhead = none ];
320 -> 88;

321 [label="EVAL with clause\nvowel_h_w_y(104).\nand substitution\nT21 -> 104", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 321 [arrowhead = none ];
321 -> 93;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 322 [arrowhead = none ];
322 -> 94;

323 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
88 -> 323 [arrowhead = none ];
323 -> 89;

324 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
89 -> 324 [arrowhead = none ];
324 -> 90;

325 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 325 [arrowhead = none ];
325 -> 91;

326 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 326 [arrowhead = none ];
326 -> 92;

327 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 117\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 327 [arrowhead = none , style=dashed];
327 -> 50[style=dashed];

328 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 328 [arrowhead = none ];
328 -> 95;

329 [label="EVAL with clause\nvowel_h_w_y(119).\nand substitution\nT21 -> 119", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 329 [arrowhead = none ];
329 -> 100;

330 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 330 [arrowhead = none ];
330 -> 101;

331 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
95 -> 331 [arrowhead = none ];
331 -> 96;

332 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
96 -> 332 [arrowhead = none ];
332 -> 97;

333 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
97 -> 333 [arrowhead = none ];
333 -> 98;

334 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
97 -> 334 [arrowhead = none ];
334 -> 99;

335 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 104\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
98 -> 335 [arrowhead = none , style=dashed];
335 -> 50[style=dashed];

336 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 336 [arrowhead = none ];
336 -> 102;

337 [label="EVAL with clause\nvowel_h_w_y(121).\nand substitution\nT21 -> 121", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 337 [arrowhead = none ];
337 -> 107;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 338 [arrowhead = none ];
338 -> 108;

339 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
102 -> 339 [arrowhead = none ];
339 -> 103;

340 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
103 -> 340 [arrowhead = none ];
340 -> 104;

341 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 341 [arrowhead = none ];
341 -> 105;

342 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 342 [arrowhead = none ];
342 -> 106;

343 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 119\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 343 [arrowhead = none , style=dashed];
343 -> 50[style=dashed];

344 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 344 [arrowhead = none ];
344 -> 109;

345 [label="EVAL with clause\nreduce(.(X126, X127), X128, X126, X129) :- ','(!, reduce(X127, X128, X126, X129)).\nand substitution\nT21 -> T23\nX126 -> T23\nT22 -> T24\nX127 -> T24\nX128 -> s(s(0))\nX58 -> X130\nX129 -> X130", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 345 [arrowhead = none ];
345 -> 114;

346 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
109 -> 346 [arrowhead = none ];
346 -> 110;

347 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
110 -> 347 [arrowhead = none ];
347 -> 111;

348 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 348 [arrowhead = none ];
348 -> 112;

349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 349 [arrowhead = none ];
349 -> 113;

350 [label="INSTANCE with matching:\nT18 -> T22\nT17 -> 121\nX58 -> X73", fontsize=14, style = filled, fillcolor = lightgrey];
112 -> 350 [arrowhead = none , style=dashed];
350 -> 50[style=dashed];

351 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
114 -> 351 [arrowhead = none ];
351 -> 115;

352 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
115 -> 352 [arrowhead = none ];
352 -> 116;

353 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
116 -> 353 [arrowhead = none ];
353 -> 117;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
117 -> 354 [arrowhead = none ];
354 -> 118;

355 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
117 -> 355 [arrowhead = none ];
355 -> 119;

356 [label="INSTANCE with matching:\nT18 -> T24\nT17 -> T23\nX58 -> X130", fontsize=14, style = filled, fillcolor = lightgrey];
118 -> 356 [arrowhead = none , style=dashed];
356 -> 50[style=dashed];

357 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 357 [arrowhead = none ];
357 -> 122;

358 [label="EVAL with clause\nreduce(.(X157, X158), X159, X160, .(X157, X161)) :- reduce(X158, s(X159), X157, X161).\nand substitution\nX157 -> T27\nX158 -> T28\nT18 -> .(T27, T28)\nX159 -> s(s(0))\nT17 -> T29\nX160 -> T29\nX161 -> X162\nX58 -> .(T27, X162)", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 358 [arrowhead = none ];
358 -> 127;

359 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 359 [arrowhead = none ];
359 -> 128;

360 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
122 -> 360 [arrowhead = none ];
360 -> 123;

361 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
123 -> 361 [arrowhead = none ];
361 -> 124;

362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 362 [arrowhead = none ];
362 -> 125;

363 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 363 [arrowhead = none ];
363 -> 126;

364 [label="INSTANCE with matching:\nT18 -> T26\nT17 -> T25\nX58 -> X145", fontsize=14, style = filled, fillcolor = lightgrey];
125 -> 364 [arrowhead = none , style=dashed];
364 -> 50[style=dashed];

365 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 365 [arrowhead = none ];
365 -> 129;

366 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
129 -> 366 [arrowhead = none ];
366 -> 130;

367 [label="EVAL with clause\nreduce([], X167, X168, []) :- !.\nand substitution\nT28 -> []\nX167 -> s(s(s(0)))\nT27 -> T30\nX168 -> T30\nX162 -> []", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 367 [arrowhead = none ];
367 -> 131;

368 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 368 [arrowhead = none ];
368 -> 132;

369 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 369 [arrowhead = none ];
369 -> 133;

370 [label="EVAL with clause\nreduce(.(X173, X174), X175, X173, X176) :- ','(vowel_h_w_y(X173), ','(!, reduce(X174, X175, X173, X176))).\nand substitution\nX173 -> T31\nX174 -> T32\nT28 -> .(T31, T32)\nX175 -> s(s(s(0)))\nT27 -> T31\nX162 -> X177\nX176 -> X177", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 370 [arrowhead = none ];
370 -> 135;

371 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 371 [arrowhead = none ];
371 -> 136;

372 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 372 [arrowhead = none ];
372 -> 134;

373 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
135 -> 373 [arrowhead = none ];
373 -> 137;

374 [label="EVAL with clause\nreduce(.(X245, X246), X247, X245, X248) :- ','(!, reduce(X246, X247, X245, X248)).\nand substitution\nX245 -> T35\nX246 -> T36\nT28 -> .(T35, T36)\nX247 -> s(s(s(0)))\nT27 -> T35\nX162 -> X249\nX248 -> X249", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 374 [arrowhead = none ];
374 -> 200;

375 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 375 [arrowhead = none ];
375 -> 201;

376 [label="EVAL with clause\nvowel_h_w_y(97).\nand substitution\nT31 -> 97", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 376 [arrowhead = none ];
376 -> 138;

377 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 377 [arrowhead = none ];
377 -> 139;

378 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 378 [arrowhead = none ];
378 -> 140;

379 [label="EVAL with clause\nvowel_h_w_y(101).\nand substitution\nT31 -> 101", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 379 [arrowhead = none ];
379 -> 145;

380 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 380 [arrowhead = none ];
380 -> 146;

381 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
140 -> 381 [arrowhead = none ];
381 -> 141;

382 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
141 -> 382 [arrowhead = none ];
382 -> 142;

383 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 383 [arrowhead = none ];
383 -> 143;

384 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 384 [arrowhead = none ];
384 -> 144;

385 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 97\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
143 -> 385 [arrowhead = none , style=dashed];
385 -> 130[style=dashed];

386 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
145 -> 386 [arrowhead = none ];
386 -> 147;

387 [label="EVAL with clause\nvowel_h_w_y(105).\nand substitution\nT31 -> 105", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 387 [arrowhead = none ];
387 -> 152;

388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 388 [arrowhead = none ];
388 -> 153;

389 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 389 [arrowhead = none ];
389 -> 148;

390 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
148 -> 390 [arrowhead = none ];
390 -> 149;

391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 391 [arrowhead = none ];
391 -> 150;

392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 392 [arrowhead = none ];
392 -> 151;

393 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 101\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
150 -> 393 [arrowhead = none , style=dashed];
393 -> 130[style=dashed];

394 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
152 -> 394 [arrowhead = none ];
394 -> 154;

395 [label="EVAL with clause\nvowel_h_w_y(111).\nand substitution\nT31 -> 111", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 395 [arrowhead = none ];
395 -> 159;

396 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 396 [arrowhead = none ];
396 -> 160;

397 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
154 -> 397 [arrowhead = none ];
397 -> 155;

398 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
155 -> 398 [arrowhead = none ];
398 -> 156;

399 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
156 -> 399 [arrowhead = none ];
399 -> 157;

400 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
156 -> 400 [arrowhead = none ];
400 -> 158;

401 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 105\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
157 -> 401 [arrowhead = none , style=dashed];
401 -> 130[style=dashed];

402 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
159 -> 402 [arrowhead = none ];
402 -> 161;

403 [label="EVAL with clause\nvowel_h_w_y(117).\nand substitution\nT31 -> 117", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 403 [arrowhead = none ];
403 -> 166;

404 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 404 [arrowhead = none ];
404 -> 167;

405 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 405 [arrowhead = none ];
405 -> 162;

406 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
162 -> 406 [arrowhead = none ];
406 -> 163;

407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
163 -> 407 [arrowhead = none ];
407 -> 164;

408 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
163 -> 408 [arrowhead = none ];
408 -> 165;

409 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 111\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
164 -> 409 [arrowhead = none , style=dashed];
409 -> 130[style=dashed];

410 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 410 [arrowhead = none ];
410 -> 168;

411 [label="EVAL with clause\nvowel_h_w_y(104).\nand substitution\nT31 -> 104", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 411 [arrowhead = none ];
411 -> 173;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 412 [arrowhead = none ];
412 -> 174;

413 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
168 -> 413 [arrowhead = none ];
413 -> 169;

414 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
169 -> 414 [arrowhead = none ];
414 -> 170;

415 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 415 [arrowhead = none ];
415 -> 171;

416 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 416 [arrowhead = none ];
416 -> 172;

417 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 117\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
171 -> 417 [arrowhead = none , style=dashed];
417 -> 130[style=dashed];

418 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 418 [arrowhead = none ];
418 -> 175;

419 [label="EVAL with clause\nvowel_h_w_y(119).\nand substitution\nT31 -> 119", fontsize=14, style = filled, fillcolor = lightblue];
174 -> 419 [arrowhead = none ];
419 -> 180;

420 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
174 -> 420 [arrowhead = none ];
420 -> 181;

421 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
175 -> 421 [arrowhead = none ];
421 -> 176;

422 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
176 -> 422 [arrowhead = none ];
422 -> 177;

423 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
177 -> 423 [arrowhead = none ];
423 -> 178;

424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
177 -> 424 [arrowhead = none ];
424 -> 179;

425 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 104\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
178 -> 425 [arrowhead = none , style=dashed];
425 -> 130[style=dashed];

426 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
180 -> 426 [arrowhead = none ];
426 -> 182;

427 [label="EVAL with clause\nvowel_h_w_y(121).\nand substitution\nT31 -> 121", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 427 [arrowhead = none ];
427 -> 187;

428 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 428 [arrowhead = none ];
428 -> 188;

429 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
182 -> 429 [arrowhead = none ];
429 -> 183;

430 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
183 -> 430 [arrowhead = none ];
430 -> 184;

431 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 431 [arrowhead = none ];
431 -> 185;

432 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 432 [arrowhead = none ];
432 -> 186;

433 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 119\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 433 [arrowhead = none , style=dashed];
433 -> 130[style=dashed];

434 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 434 [arrowhead = none ];
434 -> 189;

435 [label="EVAL with clause\nreduce(.(X230, X231), X232, X230, X233) :- ','(!, reduce(X231, X232, X230, X233)).\nand substitution\nT31 -> T33\nX230 -> T33\nT32 -> T34\nX231 -> T34\nX232 -> s(s(s(0)))\nX162 -> X234\nX233 -> X234", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 435 [arrowhead = none ];
435 -> 194;

436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
189 -> 436 [arrowhead = none ];
436 -> 190;

437 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
190 -> 437 [arrowhead = none ];
437 -> 191;

438 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 438 [arrowhead = none ];
438 -> 192;

439 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 439 [arrowhead = none ];
439 -> 193;

440 [label="INSTANCE with matching:\nT28 -> T32\nT27 -> 121\nX162 -> X177", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 440 [arrowhead = none , style=dashed];
440 -> 130[style=dashed];

441 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 441 [arrowhead = none ];
441 -> 195;

442 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
195 -> 442 [arrowhead = none ];
442 -> 196;

443 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
196 -> 443 [arrowhead = none ];
443 -> 197;

444 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 444 [arrowhead = none ];
444 -> 198;

445 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 445 [arrowhead = none ];
445 -> 199;

446 [label="INSTANCE with matching:\nT28 -> T34\nT27 -> T33\nX162 -> X234", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 446 [arrowhead = none , style=dashed];
446 -> 130[style=dashed];

447 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 447 [arrowhead = none ];
447 -> 202;

448 [label="EVAL with clause\nreduce(.(X261, X262), X263, X264, .(X261, X265)) :- reduce(X262, s(X263), X261, X265).\nand substitution\nX261 -> T37\nX262 -> T38\nT28 -> .(T37, T38)\nX263 -> s(s(s(0)))\nT27 -> T39\nX264 -> T39\nX265 -> X266\nX162 -> .(T37, X266)", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 448 [arrowhead = none ];
448 -> 207;

449 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 449 [arrowhead = none ];
449 -> 208;

450 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
202 -> 450 [arrowhead = none ];
450 -> 203;

451 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
203 -> 451 [arrowhead = none ];
451 -> 204;

452 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 452 [arrowhead = none ];
452 -> 205;

453 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 453 [arrowhead = none ];
453 -> 206;

454 [label="INSTANCE with matching:\nT28 -> T36\nT27 -> T35\nX162 -> X249", fontsize=14, style = filled, fillcolor = lightgrey];
205 -> 454 [arrowhead = none , style=dashed];
454 -> 130[style=dashed];

455 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 455 [arrowhead = none ];
455 -> 209;

456 [label="EVAL with clause\nreduce(X269, s(s(s(s(0)))), X270, []) :- !.\nand substitution\nT38 -> T40\nX269 -> T40\nT37 -> T41\nX270 -> T41\nX266 -> []", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 456 [arrowhead = none ];
456 -> 210;

457 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 457 [arrowhead = none ];
457 -> 211;

458 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
211 -> 458 [arrowhead = none ];
458 -> 212;

459 [label="EVAL with clause\neq(X272, X272).\nand substitution\nT5 -> T42\nX272 -> T42\nT9 -> T42", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 459 [arrowhead = none ];
459 -> 214;

460 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 460 [arrowhead = none ];
460 -> 215;

461 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
214 -> 461 [arrowhead = none ];
461 -> 216;

}

(2) Obligation:

Clauses:

reduce7([], T10, []).
reduce7(.(97, T12), 97, X29) :- reduce7(T12, 97, X29).
reduce7(.(101, T12), 101, X29) :- reduce7(T12, 101, X29).
reduce7(.(105, T12), 105, X29) :- reduce7(T12, 105, X29).
reduce7(.(111, T12), 111, X29) :- reduce7(T12, 111, X29).
reduce7(.(117, T12), 117, X29) :- reduce7(T12, 117, X29).
reduce7(.(104, T12), 104, X29) :- reduce7(T12, 104, X29).
reduce7(.(119, T12), 119, X29) :- reduce7(T12, 119, X29).
reduce7(.(121, T12), 121, X29) :- reduce7(T12, 121, X29).
reduce7(.(T13, T14), T13, X38) :- reduce7(T14, T13, X38).
reduce7(.(T15, T16), T15, X47) :- reduce7(T16, T15, X47).
reduce7(.(T20, []), T19, .(T20, [])).
reduce7(.(97, .(97, T22)), T19, .(97, X73)) :- reduce50(T22, 97, X73).
reduce7(.(101, .(101, T22)), T19, .(101, X73)) :- reduce50(T22, 101, X73).
reduce7(.(105, .(105, T22)), T19, .(105, X73)) :- reduce50(T22, 105, X73).
reduce7(.(111, .(111, T22)), T19, .(111, X73)) :- reduce50(T22, 111, X73).
reduce7(.(117, .(117, T22)), T19, .(117, X73)) :- reduce50(T22, 117, X73).
reduce7(.(104, .(104, T22)), T19, .(104, X73)) :- reduce50(T22, 104, X73).
reduce7(.(119, .(119, T22)), T19, .(119, X73)) :- reduce50(T22, 119, X73).
reduce7(.(121, .(121, T22)), T19, .(121, X73)) :- reduce50(T22, 121, X73).
reduce7(.(T23, .(T23, T24)), T19, .(T23, X130)) :- reduce50(T24, T23, X130).
reduce7(.(T25, .(T25, T26)), T19, .(T25, X145)) :- reduce50(T26, T25, X145).
reduce7(.(T29, .(T30, [])), T19, .(T29, .(T30, []))).
reduce7(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) :- reduce130(T32, 97, X177).
reduce7(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) :- reduce130(T32, 101, X177).
reduce7(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) :- reduce130(T32, 105, X177).
reduce7(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) :- reduce130(T32, 111, X177).
reduce7(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) :- reduce130(T32, 117, X177).
reduce7(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) :- reduce130(T32, 104, X177).
reduce7(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) :- reduce130(T32, 119, X177).
reduce7(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) :- reduce130(T32, 121, X177).
reduce7(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) :- reduce130(T34, T33, X234).
reduce7(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) :- reduce130(T36, T35, X249).
reduce7(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))).
reduce50([], T20, []).
reduce50(.(97, T22), 97, X73) :- reduce50(T22, 97, X73).
reduce50(.(101, T22), 101, X73) :- reduce50(T22, 101, X73).
reduce50(.(105, T22), 105, X73) :- reduce50(T22, 105, X73).
reduce50(.(111, T22), 111, X73) :- reduce50(T22, 111, X73).
reduce50(.(117, T22), 117, X73) :- reduce50(T22, 117, X73).
reduce50(.(104, T22), 104, X73) :- reduce50(T22, 104, X73).
reduce50(.(119, T22), 119, X73) :- reduce50(T22, 119, X73).
reduce50(.(121, T22), 121, X73) :- reduce50(T22, 121, X73).
reduce50(.(T23, T24), T23, X130) :- reduce50(T24, T23, X130).
reduce50(.(T25, T26), T25, X145) :- reduce50(T26, T25, X145).
reduce50(.(T30, []), T29, .(T30, [])).
reduce50(.(97, .(97, T32)), T29, .(97, X177)) :- reduce130(T32, 97, X177).
reduce50(.(101, .(101, T32)), T29, .(101, X177)) :- reduce130(T32, 101, X177).
reduce50(.(105, .(105, T32)), T29, .(105, X177)) :- reduce130(T32, 105, X177).
reduce50(.(111, .(111, T32)), T29, .(111, X177)) :- reduce130(T32, 111, X177).
reduce50(.(117, .(117, T32)), T29, .(117, X177)) :- reduce130(T32, 117, X177).
reduce50(.(104, .(104, T32)), T29, .(104, X177)) :- reduce130(T32, 104, X177).
reduce50(.(119, .(119, T32)), T29, .(119, X177)) :- reduce130(T32, 119, X177).
reduce50(.(121, .(121, T32)), T29, .(121, X177)) :- reduce130(T32, 121, X177).
reduce50(.(T33, .(T33, T34)), T29, .(T33, X234)) :- reduce130(T34, T33, X234).
reduce50(.(T35, .(T35, T36)), T29, .(T35, X249)) :- reduce130(T36, T35, X249).
reduce50(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))).
reduce130([], T30, []).
reduce130(.(97, T32), 97, X177) :- reduce130(T32, 97, X177).
reduce130(.(101, T32), 101, X177) :- reduce130(T32, 101, X177).
reduce130(.(105, T32), 105, X177) :- reduce130(T32, 105, X177).
reduce130(.(111, T32), 111, X177) :- reduce130(T32, 111, X177).
reduce130(.(117, T32), 117, X177) :- reduce130(T32, 117, X177).
reduce130(.(104, T32), 104, X177) :- reduce130(T32, 104, X177).
reduce130(.(119, T32), 119, X177) :- reduce130(T32, 119, X177).
reduce130(.(121, T32), 121, X177) :- reduce130(T32, 121, X177).
reduce130(.(T33, T34), T33, X234) :- reduce130(T34, T33, X234).
reduce130(.(T35, T36), T35, X249) :- reduce130(T36, T35, X249).
reduce130(.(T41, T40), T39, .(T41, [])).
goal1(.(T7, T8), T5) :- reduce7(T8, T7, X12).
goal1(.(T7, T8), T42) :- reduce7(T8, T7, T42).

Queries:

goal1(g,a).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
goal1_in: (b,f)
reduce7_in: (b,b,f)
reduce50_in: (b,b,f)
reduce130_in: (b,b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

(5) DependencyPairsProof (EQUIVALENT transformation)

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

GOAL1_IN_GA(.(T7, T8), T5) → U61_GA(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
GOAL1_IN_GA(.(T7, T8), T5) → REDUCE7_IN_GGA(T8, T7, X12)
REDUCE7_IN_GGA(.(97, T12), 97, X29) → U1_GGA(T12, X29, reduce7_in_gga(T12, 97, X29))
REDUCE7_IN_GGA(.(97, T12), 97, X29) → REDUCE7_IN_GGA(T12, 97, X29)
REDUCE7_IN_GGA(.(101, T12), 101, X29) → U2_GGA(T12, X29, reduce7_in_gga(T12, 101, X29))
REDUCE7_IN_GGA(.(101, T12), 101, X29) → REDUCE7_IN_GGA(T12, 101, X29)
REDUCE7_IN_GGA(.(105, T12), 105, X29) → U3_GGA(T12, X29, reduce7_in_gga(T12, 105, X29))
REDUCE7_IN_GGA(.(105, T12), 105, X29) → REDUCE7_IN_GGA(T12, 105, X29)
REDUCE7_IN_GGA(.(111, T12), 111, X29) → U4_GGA(T12, X29, reduce7_in_gga(T12, 111, X29))
REDUCE7_IN_GGA(.(111, T12), 111, X29) → REDUCE7_IN_GGA(T12, 111, X29)
REDUCE7_IN_GGA(.(117, T12), 117, X29) → U5_GGA(T12, X29, reduce7_in_gga(T12, 117, X29))
REDUCE7_IN_GGA(.(117, T12), 117, X29) → REDUCE7_IN_GGA(T12, 117, X29)
REDUCE7_IN_GGA(.(104, T12), 104, X29) → U6_GGA(T12, X29, reduce7_in_gga(T12, 104, X29))
REDUCE7_IN_GGA(.(104, T12), 104, X29) → REDUCE7_IN_GGA(T12, 104, X29)
REDUCE7_IN_GGA(.(119, T12), 119, X29) → U7_GGA(T12, X29, reduce7_in_gga(T12, 119, X29))
REDUCE7_IN_GGA(.(119, T12), 119, X29) → REDUCE7_IN_GGA(T12, 119, X29)
REDUCE7_IN_GGA(.(121, T12), 121, X29) → U8_GGA(T12, X29, reduce7_in_gga(T12, 121, X29))
REDUCE7_IN_GGA(.(121, T12), 121, X29) → REDUCE7_IN_GGA(T12, 121, X29)
REDUCE7_IN_GGA(.(T13, T14), T13, X38) → U9_GGA(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
REDUCE7_IN_GGA(.(T13, T14), T13, X38) → REDUCE7_IN_GGA(T14, T13, X38)
REDUCE7_IN_GGA(.(T15, T16), T15, X47) → U10_GGA(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
REDUCE7_IN_GGA(.(97, .(97, T22)), T19, .(97, X73)) → U11_GGA(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
REDUCE7_IN_GGA(.(97, .(97, T22)), T19, .(97, X73)) → REDUCE50_IN_GGA(T22, 97, X73)
REDUCE50_IN_GGA(.(97, T22), 97, X73) → U31_GGA(T22, X73, reduce50_in_gga(T22, 97, X73))
REDUCE50_IN_GGA(.(97, T22), 97, X73) → REDUCE50_IN_GGA(T22, 97, X73)
REDUCE50_IN_GGA(.(101, T22), 101, X73) → U32_GGA(T22, X73, reduce50_in_gga(T22, 101, X73))
REDUCE50_IN_GGA(.(101, T22), 101, X73) → REDUCE50_IN_GGA(T22, 101, X73)
REDUCE50_IN_GGA(.(105, T22), 105, X73) → U33_GGA(T22, X73, reduce50_in_gga(T22, 105, X73))
REDUCE50_IN_GGA(.(105, T22), 105, X73) → REDUCE50_IN_GGA(T22, 105, X73)
REDUCE50_IN_GGA(.(111, T22), 111, X73) → U34_GGA(T22, X73, reduce50_in_gga(T22, 111, X73))
REDUCE50_IN_GGA(.(111, T22), 111, X73) → REDUCE50_IN_GGA(T22, 111, X73)
REDUCE50_IN_GGA(.(117, T22), 117, X73) → U35_GGA(T22, X73, reduce50_in_gga(T22, 117, X73))
REDUCE50_IN_GGA(.(117, T22), 117, X73) → REDUCE50_IN_GGA(T22, 117, X73)
REDUCE50_IN_GGA(.(104, T22), 104, X73) → U36_GGA(T22, X73, reduce50_in_gga(T22, 104, X73))
REDUCE50_IN_GGA(.(104, T22), 104, X73) → REDUCE50_IN_GGA(T22, 104, X73)
REDUCE50_IN_GGA(.(119, T22), 119, X73) → U37_GGA(T22, X73, reduce50_in_gga(T22, 119, X73))
REDUCE50_IN_GGA(.(119, T22), 119, X73) → REDUCE50_IN_GGA(T22, 119, X73)
REDUCE50_IN_GGA(.(121, T22), 121, X73) → U38_GGA(T22, X73, reduce50_in_gga(T22, 121, X73))
REDUCE50_IN_GGA(.(121, T22), 121, X73) → REDUCE50_IN_GGA(T22, 121, X73)
REDUCE50_IN_GGA(.(T23, T24), T23, X130) → U39_GGA(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
REDUCE50_IN_GGA(.(T23, T24), T23, X130) → REDUCE50_IN_GGA(T24, T23, X130)
REDUCE50_IN_GGA(.(T25, T26), T25, X145) → U40_GGA(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
REDUCE50_IN_GGA(.(97, .(97, T32)), T29, .(97, X177)) → U41_GGA(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
REDUCE50_IN_GGA(.(97, .(97, T32)), T29, .(97, X177)) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE130_IN_GGA(.(97, T32), 97, X177) → U51_GGA(T32, X177, reduce130_in_gga(T32, 97, X177))
REDUCE130_IN_GGA(.(97, T32), 97, X177) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE130_IN_GGA(.(101, T32), 101, X177) → U52_GGA(T32, X177, reduce130_in_gga(T32, 101, X177))
REDUCE130_IN_GGA(.(101, T32), 101, X177) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE130_IN_GGA(.(105, T32), 105, X177) → U53_GGA(T32, X177, reduce130_in_gga(T32, 105, X177))
REDUCE130_IN_GGA(.(105, T32), 105, X177) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE130_IN_GGA(.(111, T32), 111, X177) → U54_GGA(T32, X177, reduce130_in_gga(T32, 111, X177))
REDUCE130_IN_GGA(.(111, T32), 111, X177) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE130_IN_GGA(.(117, T32), 117, X177) → U55_GGA(T32, X177, reduce130_in_gga(T32, 117, X177))
REDUCE130_IN_GGA(.(117, T32), 117, X177) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE130_IN_GGA(.(104, T32), 104, X177) → U56_GGA(T32, X177, reduce130_in_gga(T32, 104, X177))
REDUCE130_IN_GGA(.(104, T32), 104, X177) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE130_IN_GGA(.(119, T32), 119, X177) → U57_GGA(T32, X177, reduce130_in_gga(T32, 119, X177))
REDUCE130_IN_GGA(.(119, T32), 119, X177) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE130_IN_GGA(.(121, T32), 121, X177) → U58_GGA(T32, X177, reduce130_in_gga(T32, 121, X177))
REDUCE130_IN_GGA(.(121, T32), 121, X177) → REDUCE130_IN_GGA(T32, 121, X177)
REDUCE130_IN_GGA(.(T33, T34), T33, X234) → U59_GGA(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
REDUCE130_IN_GGA(.(T33, T34), T33, X234) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE130_IN_GGA(.(T35, T36), T35, X249) → U60_GGA(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
REDUCE50_IN_GGA(.(101, .(101, T32)), T29, .(101, X177)) → U42_GGA(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
REDUCE50_IN_GGA(.(101, .(101, T32)), T29, .(101, X177)) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE50_IN_GGA(.(105, .(105, T32)), T29, .(105, X177)) → U43_GGA(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
REDUCE50_IN_GGA(.(105, .(105, T32)), T29, .(105, X177)) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE50_IN_GGA(.(111, .(111, T32)), T29, .(111, X177)) → U44_GGA(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
REDUCE50_IN_GGA(.(111, .(111, T32)), T29, .(111, X177)) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE50_IN_GGA(.(117, .(117, T32)), T29, .(117, X177)) → U45_GGA(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
REDUCE50_IN_GGA(.(117, .(117, T32)), T29, .(117, X177)) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE50_IN_GGA(.(104, .(104, T32)), T29, .(104, X177)) → U46_GGA(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
REDUCE50_IN_GGA(.(104, .(104, T32)), T29, .(104, X177)) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE50_IN_GGA(.(119, .(119, T32)), T29, .(119, X177)) → U47_GGA(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
REDUCE50_IN_GGA(.(119, .(119, T32)), T29, .(119, X177)) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE50_IN_GGA(.(121, .(121, T32)), T29, .(121, X177)) → U48_GGA(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
REDUCE50_IN_GGA(.(121, .(121, T32)), T29, .(121, X177)) → REDUCE130_IN_GGA(T32, 121, X177)
REDUCE50_IN_GGA(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_GGA(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
REDUCE50_IN_GGA(.(T33, .(T33, T34)), T29, .(T33, X234)) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE50_IN_GGA(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_GGA(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
REDUCE7_IN_GGA(.(101, .(101, T22)), T19, .(101, X73)) → U12_GGA(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
REDUCE7_IN_GGA(.(101, .(101, T22)), T19, .(101, X73)) → REDUCE50_IN_GGA(T22, 101, X73)
REDUCE7_IN_GGA(.(105, .(105, T22)), T19, .(105, X73)) → U13_GGA(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
REDUCE7_IN_GGA(.(105, .(105, T22)), T19, .(105, X73)) → REDUCE50_IN_GGA(T22, 105, X73)
REDUCE7_IN_GGA(.(111, .(111, T22)), T19, .(111, X73)) → U14_GGA(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
REDUCE7_IN_GGA(.(111, .(111, T22)), T19, .(111, X73)) → REDUCE50_IN_GGA(T22, 111, X73)
REDUCE7_IN_GGA(.(117, .(117, T22)), T19, .(117, X73)) → U15_GGA(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
REDUCE7_IN_GGA(.(117, .(117, T22)), T19, .(117, X73)) → REDUCE50_IN_GGA(T22, 117, X73)
REDUCE7_IN_GGA(.(104, .(104, T22)), T19, .(104, X73)) → U16_GGA(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
REDUCE7_IN_GGA(.(104, .(104, T22)), T19, .(104, X73)) → REDUCE50_IN_GGA(T22, 104, X73)
REDUCE7_IN_GGA(.(119, .(119, T22)), T19, .(119, X73)) → U17_GGA(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
REDUCE7_IN_GGA(.(119, .(119, T22)), T19, .(119, X73)) → REDUCE50_IN_GGA(T22, 119, X73)
REDUCE7_IN_GGA(.(121, .(121, T22)), T19, .(121, X73)) → U18_GGA(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
REDUCE7_IN_GGA(.(121, .(121, T22)), T19, .(121, X73)) → REDUCE50_IN_GGA(T22, 121, X73)
REDUCE7_IN_GGA(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_GGA(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
REDUCE7_IN_GGA(.(T23, .(T23, T24)), T19, .(T23, X130)) → REDUCE50_IN_GGA(T24, T23, X130)
REDUCE7_IN_GGA(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_GGA(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
REDUCE7_IN_GGA(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
REDUCE7_IN_GGA(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE7_IN_GGA(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
REDUCE7_IN_GGA(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE7_IN_GGA(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
REDUCE7_IN_GGA(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE7_IN_GGA(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
REDUCE7_IN_GGA(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE7_IN_GGA(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
REDUCE7_IN_GGA(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE7_IN_GGA(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
REDUCE7_IN_GGA(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE7_IN_GGA(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
REDUCE7_IN_GGA(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE7_IN_GGA(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
REDUCE7_IN_GGA(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → REDUCE130_IN_GGA(T32, 121, X177)
REDUCE7_IN_GGA(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_GGA(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
REDUCE7_IN_GGA(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE7_IN_GGA(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_GGA(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
GOAL1_IN_GA(.(T7, T8), T42) → U62_GA(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
GOAL1_IN_GA(.(T7, T8), T42) → REDUCE7_IN_GGA(T8, T7, T42)

The TRS R consists of the following rules:

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

The argument filtering Pi contains the following mapping:
goal1_in_ga(x1, x2) = goal1_in_ga(x1)
.(x1, x2) = .(x1, x2)
U61_ga(x1, x2, x3, x4) = U61_ga(x4)
reduce7_in_gga(x1, x2, x3) = reduce7_in_gga(x1, x2)
[] = []
reduce7_out_gga(x1, x2, x3) = reduce7_out_gga(x3)
97 = 97
U1_gga(x1, x2, x3) = U1_gga(x3)
101 = 101
U2_gga(x1, x2, x3) = U2_gga(x3)
105 = 105
U3_gga(x1, x2, x3) = U3_gga(x3)
111 = 111
U4_gga(x1, x2, x3) = U4_gga(x3)
117 = 117
U5_gga(x1, x2, x3) = U5_gga(x3)
104 = 104
U6_gga(x1, x2, x3) = U6_gga(x3)
119 = 119
U7_gga(x1, x2, x3) = U7_gga(x3)
121 = 121
U8_gga(x1, x2, x3) = U8_gga(x3)
U9_gga(x1, x2, x3, x4) = U9_gga(x4)
U10_gga(x1, x2, x3, x4) = U10_gga(x4)
U11_gga(x1, x2, x3, x4) = U11_gga(x4)
reduce50_in_gga(x1, x2, x3) = reduce50_in_gga(x1, x2)
reduce50_out_gga(x1, x2, x3) = reduce50_out_gga(x3)
U31_gga(x1, x2, x3) = U31_gga(x3)
U32_gga(x1, x2, x3) = U32_gga(x3)
U33_gga(x1, x2, x3) = U33_gga(x3)
U34_gga(x1, x2, x3) = U34_gga(x3)
U35_gga(x1, x2, x3) = U35_gga(x3)
U36_gga(x1, x2, x3) = U36_gga(x3)
U37_gga(x1, x2, x3) = U37_gga(x3)
U38_gga(x1, x2, x3) = U38_gga(x3)
U39_gga(x1, x2, x3, x4) = U39_gga(x4)
U40_gga(x1, x2, x3, x4) = U40_gga(x4)
U41_gga(x1, x2, x3, x4) = U41_gga(x4)
reduce130_in_gga(x1, x2, x3) = reduce130_in_gga(x1, x2)
reduce130_out_gga(x1, x2, x3) = reduce130_out_gga(x3)
U51_gga(x1, x2, x3) = U51_gga(x3)
U52_gga(x1, x2, x3) = U52_gga(x3)
U53_gga(x1, x2, x3) = U53_gga(x3)
U54_gga(x1, x2, x3) = U54_gga(x3)
U55_gga(x1, x2, x3) = U55_gga(x3)
U56_gga(x1, x2, x3) = U56_gga(x3)
U57_gga(x1, x2, x3) = U57_gga(x3)
U58_gga(x1, x2, x3) = U58_gga(x3)
U59_gga(x1, x2, x3, x4) = U59_gga(x4)
U60_gga(x1, x2, x3, x4) = U60_gga(x4)
U42_gga(x1, x2, x3, x4) = U42_gga(x4)
U43_gga(x1, x2, x3, x4) = U43_gga(x4)
U44_gga(x1, x2, x3, x4) = U44_gga(x4)
U45_gga(x1, x2, x3, x4) = U45_gga(x4)
U46_gga(x1, x2, x3, x4) = U46_gga(x4)
U47_gga(x1, x2, x3, x4) = U47_gga(x4)
U48_gga(x1, x2, x3, x4) = U48_gga(x4)
U49_gga(x1, x2, x3, x4, x5) = U49_gga(x1, x5)
U50_gga(x1, x2, x3, x4, x5) = U50_gga(x1, x5)
U12_gga(x1, x2, x3, x4) = U12_gga(x4)
U13_gga(x1, x2, x3, x4) = U13_gga(x4)
U14_gga(x1, x2, x3, x4) = U14_gga(x4)
U15_gga(x1, x2, x3, x4) = U15_gga(x4)
U16_gga(x1, x2, x3, x4) = U16_gga(x4)
U17_gga(x1, x2, x3, x4) = U17_gga(x4)
U18_gga(x1, x2, x3, x4) = U18_gga(x4)
U19_gga(x1, x2, x3, x4, x5) = U19_gga(x1, x5)
U20_gga(x1, x2, x3, x4, x5) = U20_gga(x1, x5)
U21_gga(x1, x2, x3, x4, x5) = U21_gga(x1, x5)
U22_gga(x1, x2, x3, x4, x5) = U22_gga(x1, x5)
U23_gga(x1, x2, x3, x4, x5) = U23_gga(x1, x5)
U24_gga(x1, x2, x3, x4, x5) = U24_gga(x1, x5)
U25_gga(x1, x2, x3, x4, x5) = U25_gga(x1, x5)
U26_gga(x1, x2, x3, x4, x5) = U26_gga(x1, x5)
U27_gga(x1, x2, x3, x4, x5) = U27_gga(x1, x5)
U28_gga(x1, x2, x3, x4, x5) = U28_gga(x1, x5)
U29_gga(x1, x2, x3, x4, x5, x6) = U29_gga(x1, x2, x6)
U30_gga(x1, x2, x3, x4, x5, x6) = U30_gga(x1, x2, x6)
goal1_out_ga(x1, x2) = goal1_out_ga
U62_ga(x1, x2, x3, x4) = U62_ga(x4)
GOAL1_IN_GA(x1, x2) = GOAL1_IN_GA(x1)
U61_GA(x1, x2, x3, x4) = U61_GA(x4)
REDUCE7_IN_GGA(x1, x2, x3) = REDUCE7_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3) = U1_GGA(x3)
U2_GGA(x1, x2, x3) = U2_GGA(x3)
U3_GGA(x1, x2, x3) = U3_GGA(x3)
U4_GGA(x1, x2, x3) = U4_GGA(x3)
U5_GGA(x1, x2, x3) = U5_GGA(x3)
U6_GGA(x1, x2, x3) = U6_GGA(x3)
U7_GGA(x1, x2, x3) = U7_GGA(x3)
U8_GGA(x1, x2, x3) = U8_GGA(x3)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x4)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x4)
REDUCE50_IN_GGA(x1, x2, x3) = REDUCE50_IN_GGA(x1, x2)
U31_GGA(x1, x2, x3) = U31_GGA(x3)
U32_GGA(x1, x2, x3) = U32_GGA(x3)
U33_GGA(x1, x2, x3) = U33_GGA(x3)
U34_GGA(x1, x2, x3) = U34_GGA(x3)
U35_GGA(x1, x2, x3) = U35_GGA(x3)
U36_GGA(x1, x2, x3) = U36_GGA(x3)
U37_GGA(x1, x2, x3) = U37_GGA(x3)
U38_GGA(x1, x2, x3) = U38_GGA(x3)
U39_GGA(x1, x2, x3, x4) = U39_GGA(x4)
U40_GGA(x1, x2, x3, x4) = U40_GGA(x4)
U41_GGA(x1, x2, x3, x4) = U41_GGA(x4)
REDUCE130_IN_GGA(x1, x2, x3) = REDUCE130_IN_GGA(x1, x2)
U51_GGA(x1, x2, x3) = U51_GGA(x3)
U52_GGA(x1, x2, x3) = U52_GGA(x3)
U53_GGA(x1, x2, x3) = U53_GGA(x3)
U54_GGA(x1, x2, x3) = U54_GGA(x3)
U55_GGA(x1, x2, x3) = U55_GGA(x3)
U56_GGA(x1, x2, x3) = U56_GGA(x3)
U57_GGA(x1, x2, x3) = U57_GGA(x3)
U58_GGA(x1, x2, x3) = U58_GGA(x3)
U59_GGA(x1, x2, x3, x4) = U59_GGA(x4)
U60_GGA(x1, x2, x3, x4) = U60_GGA(x4)
U42_GGA(x1, x2, x3, x4) = U42_GGA(x4)
U43_GGA(x1, x2, x3, x4) = U43_GGA(x4)
U44_GGA(x1, x2, x3, x4) = U44_GGA(x4)
U45_GGA(x1, x2, x3, x4) = U45_GGA(x4)
U46_GGA(x1, x2, x3, x4) = U46_GGA(x4)
U47_GGA(x1, x2, x3, x4) = U47_GGA(x4)
U48_GGA(x1, x2, x3, x4) = U48_GGA(x4)
U49_GGA(x1, x2, x3, x4, x5) = U49_GGA(x1, x5)
U50_GGA(x1, x2, x3, x4, x5) = U50_GGA(x1, x5)
U12_GGA(x1, x2, x3, x4) = U12_GGA(x4)
U13_GGA(x1, x2, x3, x4) = U13_GGA(x4)
U14_GGA(x1, x2, x3, x4) = U14_GGA(x4)
U15_GGA(x1, x2, x3, x4) = U15_GGA(x4)
U16_GGA(x1, x2, x3, x4) = U16_GGA(x4)
U17_GGA(x1, x2, x3, x4) = U17_GGA(x4)
U18_GGA(x1, x2, x3, x4) = U18_GGA(x4)
U19_GGA(x1, x2, x3, x4, x5) = U19_GGA(x1, x5)
U20_GGA(x1, x2, x3, x4, x5) = U20_GGA(x1, x5)
U21_GGA(x1, x2, x3, x4, x5) = U21_GGA(x1, x5)
U22_GGA(x1, x2, x3, x4, x5) = U22_GGA(x1, x5)
U23_GGA(x1, x2, x3, x4, x5) = U23_GGA(x1, x5)
U24_GGA(x1, x2, x3, x4, x5) = U24_GGA(x1, x5)
U25_GGA(x1, x2, x3, x4, x5) = U25_GGA(x1, x5)
U26_GGA(x1, x2, x3, x4, x5) = U26_GGA(x1, x5)
U27_GGA(x1, x2, x3, x4, x5) = U27_GGA(x1, x5)
U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x1, x5)
U29_GGA(x1, x2, x3, x4, x5, x6) = U29_GGA(x1, x2, x6)
U30_GGA(x1, x2, x3, x4, x5, x6) = U30_GGA(x1, x2, x6)
U62_GA(x1, x2, x3, x4) = U62_GA(x4)

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

(6) Obligation:

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

GOAL1_IN_GA(.(T7, T8), T5) → U61_GA(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
GOAL1_IN_GA(.(T7, T8), T5) → REDUCE7_IN_GGA(T8, T7, X12)
REDUCE7_IN_GGA(.(97, T12), 97, X29) → U1_GGA(T12, X29, reduce7_in_gga(T12, 97, X29))
REDUCE7_IN_GGA(.(97, T12), 97, X29) → REDUCE7_IN_GGA(T12, 97, X29)
REDUCE7_IN_GGA(.(101, T12), 101, X29) → U2_GGA(T12, X29, reduce7_in_gga(T12, 101, X29))
REDUCE7_IN_GGA(.(101, T12), 101, X29) → REDUCE7_IN_GGA(T12, 101, X29)
REDUCE7_IN_GGA(.(105, T12), 105, X29) → U3_GGA(T12, X29, reduce7_in_gga(T12, 105, X29))
REDUCE7_IN_GGA(.(105, T12), 105, X29) → REDUCE7_IN_GGA(T12, 105, X29)
REDUCE7_IN_GGA(.(111, T12), 111, X29) → U4_GGA(T12, X29, reduce7_in_gga(T12, 111, X29))
REDUCE7_IN_GGA(.(111, T12), 111, X29) → REDUCE7_IN_GGA(T12, 111, X29)
REDUCE7_IN_GGA(.(117, T12), 117, X29) → U5_GGA(T12, X29, reduce7_in_gga(T12, 117, X29))
REDUCE7_IN_GGA(.(117, T12), 117, X29) → REDUCE7_IN_GGA(T12, 117, X29)
REDUCE7_IN_GGA(.(104, T12), 104, X29) → U6_GGA(T12, X29, reduce7_in_gga(T12, 104, X29))
REDUCE7_IN_GGA(.(104, T12), 104, X29) → REDUCE7_IN_GGA(T12, 104, X29)
REDUCE7_IN_GGA(.(119, T12), 119, X29) → U7_GGA(T12, X29, reduce7_in_gga(T12, 119, X29))
REDUCE7_IN_GGA(.(119, T12), 119, X29) → REDUCE7_IN_GGA(T12, 119, X29)
REDUCE7_IN_GGA(.(121, T12), 121, X29) → U8_GGA(T12, X29, reduce7_in_gga(T12, 121, X29))
REDUCE7_IN_GGA(.(121, T12), 121, X29) → REDUCE7_IN_GGA(T12, 121, X29)
REDUCE7_IN_GGA(.(T13, T14), T13, X38) → U9_GGA(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
REDUCE7_IN_GGA(.(T13, T14), T13, X38) → REDUCE7_IN_GGA(T14, T13, X38)
REDUCE7_IN_GGA(.(T15, T16), T15, X47) → U10_GGA(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
REDUCE7_IN_GGA(.(97, .(97, T22)), T19, .(97, X73)) → U11_GGA(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
REDUCE7_IN_GGA(.(97, .(97, T22)), T19, .(97, X73)) → REDUCE50_IN_GGA(T22, 97, X73)
REDUCE50_IN_GGA(.(97, T22), 97, X73) → U31_GGA(T22, X73, reduce50_in_gga(T22, 97, X73))
REDUCE50_IN_GGA(.(97, T22), 97, X73) → REDUCE50_IN_GGA(T22, 97, X73)
REDUCE50_IN_GGA(.(101, T22), 101, X73) → U32_GGA(T22, X73, reduce50_in_gga(T22, 101, X73))
REDUCE50_IN_GGA(.(101, T22), 101, X73) → REDUCE50_IN_GGA(T22, 101, X73)
REDUCE50_IN_GGA(.(105, T22), 105, X73) → U33_GGA(T22, X73, reduce50_in_gga(T22, 105, X73))
REDUCE50_IN_GGA(.(105, T22), 105, X73) → REDUCE50_IN_GGA(T22, 105, X73)
REDUCE50_IN_GGA(.(111, T22), 111, X73) → U34_GGA(T22, X73, reduce50_in_gga(T22, 111, X73))
REDUCE50_IN_GGA(.(111, T22), 111, X73) → REDUCE50_IN_GGA(T22, 111, X73)
REDUCE50_IN_GGA(.(117, T22), 117, X73) → U35_GGA(T22, X73, reduce50_in_gga(T22, 117, X73))
REDUCE50_IN_GGA(.(117, T22), 117, X73) → REDUCE50_IN_GGA(T22, 117, X73)
REDUCE50_IN_GGA(.(104, T22), 104, X73) → U36_GGA(T22, X73, reduce50_in_gga(T22, 104, X73))
REDUCE50_IN_GGA(.(104, T22), 104, X73) → REDUCE50_IN_GGA(T22, 104, X73)
REDUCE50_IN_GGA(.(119, T22), 119, X73) → U37_GGA(T22, X73, reduce50_in_gga(T22, 119, X73))
REDUCE50_IN_GGA(.(119, T22), 119, X73) → REDUCE50_IN_GGA(T22, 119, X73)
REDUCE50_IN_GGA(.(121, T22), 121, X73) → U38_GGA(T22, X73, reduce50_in_gga(T22, 121, X73))
REDUCE50_IN_GGA(.(121, T22), 121, X73) → REDUCE50_IN_GGA(T22, 121, X73)
REDUCE50_IN_GGA(.(T23, T24), T23, X130) → U39_GGA(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
REDUCE50_IN_GGA(.(T23, T24), T23, X130) → REDUCE50_IN_GGA(T24, T23, X130)
REDUCE50_IN_GGA(.(T25, T26), T25, X145) → U40_GGA(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
REDUCE50_IN_GGA(.(97, .(97, T32)), T29, .(97, X177)) → U41_GGA(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
REDUCE50_IN_GGA(.(97, .(97, T32)), T29, .(97, X177)) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE130_IN_GGA(.(97, T32), 97, X177) → U51_GGA(T32, X177, reduce130_in_gga(T32, 97, X177))
REDUCE130_IN_GGA(.(97, T32), 97, X177) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE130_IN_GGA(.(101, T32), 101, X177) → U52_GGA(T32, X177, reduce130_in_gga(T32, 101, X177))
REDUCE130_IN_GGA(.(101, T32), 101, X177) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE130_IN_GGA(.(105, T32), 105, X177) → U53_GGA(T32, X177, reduce130_in_gga(T32, 105, X177))
REDUCE130_IN_GGA(.(105, T32), 105, X177) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE130_IN_GGA(.(111, T32), 111, X177) → U54_GGA(T32, X177, reduce130_in_gga(T32, 111, X177))
REDUCE130_IN_GGA(.(111, T32), 111, X177) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE130_IN_GGA(.(117, T32), 117, X177) → U55_GGA(T32, X177, reduce130_in_gga(T32, 117, X177))
REDUCE130_IN_GGA(.(117, T32), 117, X177) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE130_IN_GGA(.(104, T32), 104, X177) → U56_GGA(T32, X177, reduce130_in_gga(T32, 104, X177))
REDUCE130_IN_GGA(.(104, T32), 104, X177) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE130_IN_GGA(.(119, T32), 119, X177) → U57_GGA(T32, X177, reduce130_in_gga(T32, 119, X177))
REDUCE130_IN_GGA(.(119, T32), 119, X177) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE130_IN_GGA(.(121, T32), 121, X177) → U58_GGA(T32, X177, reduce130_in_gga(T32, 121, X177))
REDUCE130_IN_GGA(.(121, T32), 121, X177) → REDUCE130_IN_GGA(T32, 121, X177)
REDUCE130_IN_GGA(.(T33, T34), T33, X234) → U59_GGA(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
REDUCE130_IN_GGA(.(T33, T34), T33, X234) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE130_IN_GGA(.(T35, T36), T35, X249) → U60_GGA(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
REDUCE50_IN_GGA(.(101, .(101, T32)), T29, .(101, X177)) → U42_GGA(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
REDUCE50_IN_GGA(.(101, .(101, T32)), T29, .(101, X177)) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE50_IN_GGA(.(105, .(105, T32)), T29, .(105, X177)) → U43_GGA(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
REDUCE50_IN_GGA(.(105, .(105, T32)), T29, .(105, X177)) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE50_IN_GGA(.(111, .(111, T32)), T29, .(111, X177)) → U44_GGA(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
REDUCE50_IN_GGA(.(111, .(111, T32)), T29, .(111, X177)) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE50_IN_GGA(.(117, .(117, T32)), T29, .(117, X177)) → U45_GGA(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
REDUCE50_IN_GGA(.(117, .(117, T32)), T29, .(117, X177)) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE50_IN_GGA(.(104, .(104, T32)), T29, .(104, X177)) → U46_GGA(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
REDUCE50_IN_GGA(.(104, .(104, T32)), T29, .(104, X177)) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE50_IN_GGA(.(119, .(119, T32)), T29, .(119, X177)) → U47_GGA(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
REDUCE50_IN_GGA(.(119, .(119, T32)), T29, .(119, X177)) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE50_IN_GGA(.(121, .(121, T32)), T29, .(121, X177)) → U48_GGA(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
REDUCE50_IN_GGA(.(121, .(121, T32)), T29, .(121, X177)) → REDUCE130_IN_GGA(T32, 121, X177)
REDUCE50_IN_GGA(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_GGA(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
REDUCE50_IN_GGA(.(T33, .(T33, T34)), T29, .(T33, X234)) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE50_IN_GGA(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_GGA(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
REDUCE7_IN_GGA(.(101, .(101, T22)), T19, .(101, X73)) → U12_GGA(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
REDUCE7_IN_GGA(.(101, .(101, T22)), T19, .(101, X73)) → REDUCE50_IN_GGA(T22, 101, X73)
REDUCE7_IN_GGA(.(105, .(105, T22)), T19, .(105, X73)) → U13_GGA(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
REDUCE7_IN_GGA(.(105, .(105, T22)), T19, .(105, X73)) → REDUCE50_IN_GGA(T22, 105, X73)
REDUCE7_IN_GGA(.(111, .(111, T22)), T19, .(111, X73)) → U14_GGA(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
REDUCE7_IN_GGA(.(111, .(111, T22)), T19, .(111, X73)) → REDUCE50_IN_GGA(T22, 111, X73)
REDUCE7_IN_GGA(.(117, .(117, T22)), T19, .(117, X73)) → U15_GGA(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
REDUCE7_IN_GGA(.(117, .(117, T22)), T19, .(117, X73)) → REDUCE50_IN_GGA(T22, 117, X73)
REDUCE7_IN_GGA(.(104, .(104, T22)), T19, .(104, X73)) → U16_GGA(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
REDUCE7_IN_GGA(.(104, .(104, T22)), T19, .(104, X73)) → REDUCE50_IN_GGA(T22, 104, X73)
REDUCE7_IN_GGA(.(119, .(119, T22)), T19, .(119, X73)) → U17_GGA(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
REDUCE7_IN_GGA(.(119, .(119, T22)), T19, .(119, X73)) → REDUCE50_IN_GGA(T22, 119, X73)
REDUCE7_IN_GGA(.(121, .(121, T22)), T19, .(121, X73)) → U18_GGA(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
REDUCE7_IN_GGA(.(121, .(121, T22)), T19, .(121, X73)) → REDUCE50_IN_GGA(T22, 121, X73)
REDUCE7_IN_GGA(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_GGA(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
REDUCE7_IN_GGA(.(T23, .(T23, T24)), T19, .(T23, X130)) → REDUCE50_IN_GGA(T24, T23, X130)
REDUCE7_IN_GGA(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_GGA(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
REDUCE7_IN_GGA(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
REDUCE7_IN_GGA(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE7_IN_GGA(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
REDUCE7_IN_GGA(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE7_IN_GGA(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
REDUCE7_IN_GGA(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE7_IN_GGA(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
REDUCE7_IN_GGA(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE7_IN_GGA(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
REDUCE7_IN_GGA(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE7_IN_GGA(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
REDUCE7_IN_GGA(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE7_IN_GGA(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
REDUCE7_IN_GGA(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE7_IN_GGA(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_GGA(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
REDUCE7_IN_GGA(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → REDUCE130_IN_GGA(T32, 121, X177)
REDUCE7_IN_GGA(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_GGA(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
REDUCE7_IN_GGA(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE7_IN_GGA(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_GGA(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
GOAL1_IN_GA(.(T7, T8), T42) → U62_GA(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
GOAL1_IN_GA(.(T7, T8), T42) → REDUCE7_IN_GGA(T8, T7, T42)

The TRS R consists of the following rules:

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 91 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

REDUCE130_IN_GGA(.(T33, T34), T33, X234) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE130_IN_GGA(.(97, T32), 97, X177) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE130_IN_GGA(.(101, T32), 101, X177) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE130_IN_GGA(.(105, T32), 105, X177) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE130_IN_GGA(.(111, T32), 111, X177) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE130_IN_GGA(.(117, T32), 117, X177) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE130_IN_GGA(.(104, T32), 104, X177) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE130_IN_GGA(.(119, T32), 119, X177) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE130_IN_GGA(.(121, T32), 121, X177) → REDUCE130_IN_GGA(T32, 121, X177)

The TRS R consists of the following rules:

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

(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:

REDUCE130_IN_GGA(.(T33, T34), T33, X234) → REDUCE130_IN_GGA(T34, T33, X234)
REDUCE130_IN_GGA(.(97, T32), 97, X177) → REDUCE130_IN_GGA(T32, 97, X177)
REDUCE130_IN_GGA(.(101, T32), 101, X177) → REDUCE130_IN_GGA(T32, 101, X177)
REDUCE130_IN_GGA(.(105, T32), 105, X177) → REDUCE130_IN_GGA(T32, 105, X177)
REDUCE130_IN_GGA(.(111, T32), 111, X177) → REDUCE130_IN_GGA(T32, 111, X177)
REDUCE130_IN_GGA(.(117, T32), 117, X177) → REDUCE130_IN_GGA(T32, 117, X177)
REDUCE130_IN_GGA(.(104, T32), 104, X177) → REDUCE130_IN_GGA(T32, 104, X177)
REDUCE130_IN_GGA(.(119, T32), 119, X177) → REDUCE130_IN_GGA(T32, 119, X177)
REDUCE130_IN_GGA(.(121, T32), 121, X177) → REDUCE130_IN_GGA(T32, 121, X177)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
97 = 97
101 = 101
105 = 105
111 = 111
117 = 117
104 = 104
119 = 119
121 = 121
REDUCE130_IN_GGA(x1, x2, x3) = REDUCE130_IN_GGA(x1, x2)

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:

REDUCE130_IN_GGA(.(T33, T34), T33) → REDUCE130_IN_GGA(T34, T33)
REDUCE130_IN_GGA(.(97, T32), 97) → REDUCE130_IN_GGA(T32, 97)
REDUCE130_IN_GGA(.(101, T32), 101) → REDUCE130_IN_GGA(T32, 101)
REDUCE130_IN_GGA(.(105, T32), 105) → REDUCE130_IN_GGA(T32, 105)
REDUCE130_IN_GGA(.(111, T32), 111) → REDUCE130_IN_GGA(T32, 111)
REDUCE130_IN_GGA(.(117, T32), 117) → REDUCE130_IN_GGA(T32, 117)
REDUCE130_IN_GGA(.(104, T32), 104) → REDUCE130_IN_GGA(T32, 104)
REDUCE130_IN_GGA(.(119, T32), 119) → REDUCE130_IN_GGA(T32, 119)
REDUCE130_IN_GGA(.(121, T32), 121) → REDUCE130_IN_GGA(T32, 121)

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:

REDUCE130_IN_GGA(.(T33, T34), T33) → REDUCE130_IN_GGA(T34, T33)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(97, T32), 97) → REDUCE130_IN_GGA(T32, 97)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(101, T32), 101) → REDUCE130_IN_GGA(T32, 101)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(105, T32), 105) → REDUCE130_IN_GGA(T32, 105)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(111, T32), 111) → REDUCE130_IN_GGA(T32, 111)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(117, T32), 117) → REDUCE130_IN_GGA(T32, 117)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(104, T32), 104) → REDUCE130_IN_GGA(T32, 104)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(119, T32), 119) → REDUCE130_IN_GGA(T32, 119)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE130_IN_GGA(.(121, T32), 121) → REDUCE130_IN_GGA(T32, 121)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

(15) TRUE

(16) Obligation:

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

REDUCE50_IN_GGA(.(T23, T24), T23, X130) → REDUCE50_IN_GGA(T24, T23, X130)
REDUCE50_IN_GGA(.(97, T22), 97, X73) → REDUCE50_IN_GGA(T22, 97, X73)
REDUCE50_IN_GGA(.(101, T22), 101, X73) → REDUCE50_IN_GGA(T22, 101, X73)
REDUCE50_IN_GGA(.(105, T22), 105, X73) → REDUCE50_IN_GGA(T22, 105, X73)
REDUCE50_IN_GGA(.(111, T22), 111, X73) → REDUCE50_IN_GGA(T22, 111, X73)
REDUCE50_IN_GGA(.(117, T22), 117, X73) → REDUCE50_IN_GGA(T22, 117, X73)
REDUCE50_IN_GGA(.(104, T22), 104, X73) → REDUCE50_IN_GGA(T22, 104, X73)
REDUCE50_IN_GGA(.(119, T22), 119, X73) → REDUCE50_IN_GGA(T22, 119, X73)
REDUCE50_IN_GGA(.(121, T22), 121, X73) → REDUCE50_IN_GGA(T22, 121, X73)

The TRS R consists of the following rules:

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

(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:

REDUCE50_IN_GGA(.(T23, T24), T23, X130) → REDUCE50_IN_GGA(T24, T23, X130)
REDUCE50_IN_GGA(.(97, T22), 97, X73) → REDUCE50_IN_GGA(T22, 97, X73)
REDUCE50_IN_GGA(.(101, T22), 101, X73) → REDUCE50_IN_GGA(T22, 101, X73)
REDUCE50_IN_GGA(.(105, T22), 105, X73) → REDUCE50_IN_GGA(T22, 105, X73)
REDUCE50_IN_GGA(.(111, T22), 111, X73) → REDUCE50_IN_GGA(T22, 111, X73)
REDUCE50_IN_GGA(.(117, T22), 117, X73) → REDUCE50_IN_GGA(T22, 117, X73)
REDUCE50_IN_GGA(.(104, T22), 104, X73) → REDUCE50_IN_GGA(T22, 104, X73)
REDUCE50_IN_GGA(.(119, T22), 119, X73) → REDUCE50_IN_GGA(T22, 119, X73)
REDUCE50_IN_GGA(.(121, T22), 121, X73) → REDUCE50_IN_GGA(T22, 121, X73)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
97 = 97
101 = 101
105 = 105
111 = 111
117 = 117
104 = 104
119 = 119
121 = 121
REDUCE50_IN_GGA(x1, x2, x3) = REDUCE50_IN_GGA(x1, x2)

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:

REDUCE50_IN_GGA(.(T23, T24), T23) → REDUCE50_IN_GGA(T24, T23)
REDUCE50_IN_GGA(.(97, T22), 97) → REDUCE50_IN_GGA(T22, 97)
REDUCE50_IN_GGA(.(101, T22), 101) → REDUCE50_IN_GGA(T22, 101)
REDUCE50_IN_GGA(.(105, T22), 105) → REDUCE50_IN_GGA(T22, 105)
REDUCE50_IN_GGA(.(111, T22), 111) → REDUCE50_IN_GGA(T22, 111)
REDUCE50_IN_GGA(.(117, T22), 117) → REDUCE50_IN_GGA(T22, 117)
REDUCE50_IN_GGA(.(104, T22), 104) → REDUCE50_IN_GGA(T22, 104)
REDUCE50_IN_GGA(.(119, T22), 119) → REDUCE50_IN_GGA(T22, 119)
REDUCE50_IN_GGA(.(121, T22), 121) → REDUCE50_IN_GGA(T22, 121)

R is empty.
Q is empty.
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:

REDUCE50_IN_GGA(.(T23, T24), T23) → REDUCE50_IN_GGA(T24, T23)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(97, T22), 97) → REDUCE50_IN_GGA(T22, 97)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(101, T22), 101) → REDUCE50_IN_GGA(T22, 101)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(105, T22), 105) → REDUCE50_IN_GGA(T22, 105)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(111, T22), 111) → REDUCE50_IN_GGA(T22, 111)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(117, T22), 117) → REDUCE50_IN_GGA(T22, 117)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(104, T22), 104) → REDUCE50_IN_GGA(T22, 104)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(119, T22), 119) → REDUCE50_IN_GGA(T22, 119)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE50_IN_GGA(.(121, T22), 121) → REDUCE50_IN_GGA(T22, 121)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

(22) TRUE

(23) Obligation:

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

REDUCE7_IN_GGA(.(T13, T14), T13, X38) → REDUCE7_IN_GGA(T14, T13, X38)
REDUCE7_IN_GGA(.(97, T12), 97, X29) → REDUCE7_IN_GGA(T12, 97, X29)
REDUCE7_IN_GGA(.(101, T12), 101, X29) → REDUCE7_IN_GGA(T12, 101, X29)
REDUCE7_IN_GGA(.(105, T12), 105, X29) → REDUCE7_IN_GGA(T12, 105, X29)
REDUCE7_IN_GGA(.(111, T12), 111, X29) → REDUCE7_IN_GGA(T12, 111, X29)
REDUCE7_IN_GGA(.(117, T12), 117, X29) → REDUCE7_IN_GGA(T12, 117, X29)
REDUCE7_IN_GGA(.(104, T12), 104, X29) → REDUCE7_IN_GGA(T12, 104, X29)
REDUCE7_IN_GGA(.(119, T12), 119, X29) → REDUCE7_IN_GGA(T12, 119, X29)
REDUCE7_IN_GGA(.(121, T12), 121, X29) → REDUCE7_IN_GGA(T12, 121, X29)

The TRS R consists of the following rules:

goal1_in_ga(.(T7, T8), T5) → U61_ga(T7, T8, T5, reduce7_in_gga(T8, T7, X12))
reduce7_in_gga([], T10, []) → reduce7_out_gga([], T10, [])
reduce7_in_gga(.(97, T12), 97, X29) → U1_gga(T12, X29, reduce7_in_gga(T12, 97, X29))
reduce7_in_gga(.(101, T12), 101, X29) → U2_gga(T12, X29, reduce7_in_gga(T12, 101, X29))
reduce7_in_gga(.(105, T12), 105, X29) → U3_gga(T12, X29, reduce7_in_gga(T12, 105, X29))
reduce7_in_gga(.(111, T12), 111, X29) → U4_gga(T12, X29, reduce7_in_gga(T12, 111, X29))
reduce7_in_gga(.(117, T12), 117, X29) → U5_gga(T12, X29, reduce7_in_gga(T12, 117, X29))
reduce7_in_gga(.(104, T12), 104, X29) → U6_gga(T12, X29, reduce7_in_gga(T12, 104, X29))
reduce7_in_gga(.(119, T12), 119, X29) → U7_gga(T12, X29, reduce7_in_gga(T12, 119, X29))
reduce7_in_gga(.(121, T12), 121, X29) → U8_gga(T12, X29, reduce7_in_gga(T12, 121, X29))
reduce7_in_gga(.(T13, T14), T13, X38) → U9_gga(T13, T14, X38, reduce7_in_gga(T14, T13, X38))
reduce7_in_gga(.(T15, T16), T15, X47) → U10_gga(T15, T16, X47, reduce7_in_gga(T16, T15, X47))
reduce7_in_gga(.(T20, []), T19, .(T20, [])) → reduce7_out_gga(.(T20, []), T19, .(T20, []))
reduce7_in_gga(.(97, .(97, T22)), T19, .(97, X73)) → U11_gga(T22, T19, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga([], T20, []) → reduce50_out_gga([], T20, [])
reduce50_in_gga(.(97, T22), 97, X73) → U31_gga(T22, X73, reduce50_in_gga(T22, 97, X73))
reduce50_in_gga(.(101, T22), 101, X73) → U32_gga(T22, X73, reduce50_in_gga(T22, 101, X73))
reduce50_in_gga(.(105, T22), 105, X73) → U33_gga(T22, X73, reduce50_in_gga(T22, 105, X73))
reduce50_in_gga(.(111, T22), 111, X73) → U34_gga(T22, X73, reduce50_in_gga(T22, 111, X73))
reduce50_in_gga(.(117, T22), 117, X73) → U35_gga(T22, X73, reduce50_in_gga(T22, 117, X73))
reduce50_in_gga(.(104, T22), 104, X73) → U36_gga(T22, X73, reduce50_in_gga(T22, 104, X73))
reduce50_in_gga(.(119, T22), 119, X73) → U37_gga(T22, X73, reduce50_in_gga(T22, 119, X73))
reduce50_in_gga(.(121, T22), 121, X73) → U38_gga(T22, X73, reduce50_in_gga(T22, 121, X73))
reduce50_in_gga(.(T23, T24), T23, X130) → U39_gga(T23, T24, X130, reduce50_in_gga(T24, T23, X130))
reduce50_in_gga(.(T25, T26), T25, X145) → U40_gga(T25, T26, X145, reduce50_in_gga(T26, T25, X145))
reduce50_in_gga(.(T30, []), T29, .(T30, [])) → reduce50_out_gga(.(T30, []), T29, .(T30, []))
reduce50_in_gga(.(97, .(97, T32)), T29, .(97, X177)) → U41_gga(T32, T29, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga([], T30, []) → reduce130_out_gga([], T30, [])
reduce130_in_gga(.(97, T32), 97, X177) → U51_gga(T32, X177, reduce130_in_gga(T32, 97, X177))
reduce130_in_gga(.(101, T32), 101, X177) → U52_gga(T32, X177, reduce130_in_gga(T32, 101, X177))
reduce130_in_gga(.(105, T32), 105, X177) → U53_gga(T32, X177, reduce130_in_gga(T32, 105, X177))
reduce130_in_gga(.(111, T32), 111, X177) → U54_gga(T32, X177, reduce130_in_gga(T32, 111, X177))
reduce130_in_gga(.(117, T32), 117, X177) → U55_gga(T32, X177, reduce130_in_gga(T32, 117, X177))
reduce130_in_gga(.(104, T32), 104, X177) → U56_gga(T32, X177, reduce130_in_gga(T32, 104, X177))
reduce130_in_gga(.(119, T32), 119, X177) → U57_gga(T32, X177, reduce130_in_gga(T32, 119, X177))
reduce130_in_gga(.(121, T32), 121, X177) → U58_gga(T32, X177, reduce130_in_gga(T32, 121, X177))
reduce130_in_gga(.(T33, T34), T33, X234) → U59_gga(T33, T34, X234, reduce130_in_gga(T34, T33, X234))
reduce130_in_gga(.(T35, T36), T35, X249) → U60_gga(T35, T36, X249, reduce130_in_gga(T36, T35, X249))
reduce130_in_gga(.(T41, T40), T39, .(T41, [])) → reduce130_out_gga(.(T41, T40), T39, .(T41, []))
U60_gga(T35, T36, X249, reduce130_out_gga(T36, T35, X249)) → reduce130_out_gga(.(T35, T36), T35, X249)
U59_gga(T33, T34, X234, reduce130_out_gga(T34, T33, X234)) → reduce130_out_gga(.(T33, T34), T33, X234)
U58_gga(T32, X177, reduce130_out_gga(T32, 121, X177)) → reduce130_out_gga(.(121, T32), 121, X177)
U57_gga(T32, X177, reduce130_out_gga(T32, 119, X177)) → reduce130_out_gga(.(119, T32), 119, X177)
U56_gga(T32, X177, reduce130_out_gga(T32, 104, X177)) → reduce130_out_gga(.(104, T32), 104, X177)
U55_gga(T32, X177, reduce130_out_gga(T32, 117, X177)) → reduce130_out_gga(.(117, T32), 117, X177)
U54_gga(T32, X177, reduce130_out_gga(T32, 111, X177)) → reduce130_out_gga(.(111, T32), 111, X177)
U53_gga(T32, X177, reduce130_out_gga(T32, 105, X177)) → reduce130_out_gga(.(105, T32), 105, X177)
U52_gga(T32, X177, reduce130_out_gga(T32, 101, X177)) → reduce130_out_gga(.(101, T32), 101, X177)
U51_gga(T32, X177, reduce130_out_gga(T32, 97, X177)) → reduce130_out_gga(.(97, T32), 97, X177)
U41_gga(T32, T29, X177, reduce130_out_gga(T32, 97, X177)) → reduce50_out_gga(.(97, .(97, T32)), T29, .(97, X177))
reduce50_in_gga(.(101, .(101, T32)), T29, .(101, X177)) → U42_gga(T32, T29, X177, reduce130_in_gga(T32, 101, X177))
U42_gga(T32, T29, X177, reduce130_out_gga(T32, 101, X177)) → reduce50_out_gga(.(101, .(101, T32)), T29, .(101, X177))
reduce50_in_gga(.(105, .(105, T32)), T29, .(105, X177)) → U43_gga(T32, T29, X177, reduce130_in_gga(T32, 105, X177))
U43_gga(T32, T29, X177, reduce130_out_gga(T32, 105, X177)) → reduce50_out_gga(.(105, .(105, T32)), T29, .(105, X177))
reduce50_in_gga(.(111, .(111, T32)), T29, .(111, X177)) → U44_gga(T32, T29, X177, reduce130_in_gga(T32, 111, X177))
U44_gga(T32, T29, X177, reduce130_out_gga(T32, 111, X177)) → reduce50_out_gga(.(111, .(111, T32)), T29, .(111, X177))
reduce50_in_gga(.(117, .(117, T32)), T29, .(117, X177)) → U45_gga(T32, T29, X177, reduce130_in_gga(T32, 117, X177))
U45_gga(T32, T29, X177, reduce130_out_gga(T32, 117, X177)) → reduce50_out_gga(.(117, .(117, T32)), T29, .(117, X177))
reduce50_in_gga(.(104, .(104, T32)), T29, .(104, X177)) → U46_gga(T32, T29, X177, reduce130_in_gga(T32, 104, X177))
U46_gga(T32, T29, X177, reduce130_out_gga(T32, 104, X177)) → reduce50_out_gga(.(104, .(104, T32)), T29, .(104, X177))
reduce50_in_gga(.(119, .(119, T32)), T29, .(119, X177)) → U47_gga(T32, T29, X177, reduce130_in_gga(T32, 119, X177))
U47_gga(T32, T29, X177, reduce130_out_gga(T32, 119, X177)) → reduce50_out_gga(.(119, .(119, T32)), T29, .(119, X177))
reduce50_in_gga(.(121, .(121, T32)), T29, .(121, X177)) → U48_gga(T32, T29, X177, reduce130_in_gga(T32, 121, X177))
U48_gga(T32, T29, X177, reduce130_out_gga(T32, 121, X177)) → reduce50_out_gga(.(121, .(121, T32)), T29, .(121, X177))
reduce50_in_gga(.(T33, .(T33, T34)), T29, .(T33, X234)) → U49_gga(T33, T34, T29, X234, reduce130_in_gga(T34, T33, X234))
U49_gga(T33, T34, T29, X234, reduce130_out_gga(T34, T33, X234)) → reduce50_out_gga(.(T33, .(T33, T34)), T29, .(T33, X234))
reduce50_in_gga(.(T35, .(T35, T36)), T29, .(T35, X249)) → U50_gga(T35, T36, T29, X249, reduce130_in_gga(T36, T35, X249))
U50_gga(T35, T36, T29, X249, reduce130_out_gga(T36, T35, X249)) → reduce50_out_gga(.(T35, .(T35, T36)), T29, .(T35, X249))
reduce50_in_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, []))) → reduce50_out_gga(.(T39, .(T41, T40)), T29, .(T39, .(T41, [])))
U40_gga(T25, T26, X145, reduce50_out_gga(T26, T25, X145)) → reduce50_out_gga(.(T25, T26), T25, X145)
U39_gga(T23, T24, X130, reduce50_out_gga(T24, T23, X130)) → reduce50_out_gga(.(T23, T24), T23, X130)
U38_gga(T22, X73, reduce50_out_gga(T22, 121, X73)) → reduce50_out_gga(.(121, T22), 121, X73)
U37_gga(T22, X73, reduce50_out_gga(T22, 119, X73)) → reduce50_out_gga(.(119, T22), 119, X73)
U36_gga(T22, X73, reduce50_out_gga(T22, 104, X73)) → reduce50_out_gga(.(104, T22), 104, X73)
U35_gga(T22, X73, reduce50_out_gga(T22, 117, X73)) → reduce50_out_gga(.(117, T22), 117, X73)
U34_gga(T22, X73, reduce50_out_gga(T22, 111, X73)) → reduce50_out_gga(.(111, T22), 111, X73)
U33_gga(T22, X73, reduce50_out_gga(T22, 105, X73)) → reduce50_out_gga(.(105, T22), 105, X73)
U32_gga(T22, X73, reduce50_out_gga(T22, 101, X73)) → reduce50_out_gga(.(101, T22), 101, X73)
U31_gga(T22, X73, reduce50_out_gga(T22, 97, X73)) → reduce50_out_gga(.(97, T22), 97, X73)
U11_gga(T22, T19, X73, reduce50_out_gga(T22, 97, X73)) → reduce7_out_gga(.(97, .(97, T22)), T19, .(97, X73))
reduce7_in_gga(.(101, .(101, T22)), T19, .(101, X73)) → U12_gga(T22, T19, X73, reduce50_in_gga(T22, 101, X73))
U12_gga(T22, T19, X73, reduce50_out_gga(T22, 101, X73)) → reduce7_out_gga(.(101, .(101, T22)), T19, .(101, X73))
reduce7_in_gga(.(105, .(105, T22)), T19, .(105, X73)) → U13_gga(T22, T19, X73, reduce50_in_gga(T22, 105, X73))
U13_gga(T22, T19, X73, reduce50_out_gga(T22, 105, X73)) → reduce7_out_gga(.(105, .(105, T22)), T19, .(105, X73))
reduce7_in_gga(.(111, .(111, T22)), T19, .(111, X73)) → U14_gga(T22, T19, X73, reduce50_in_gga(T22, 111, X73))
U14_gga(T22, T19, X73, reduce50_out_gga(T22, 111, X73)) → reduce7_out_gga(.(111, .(111, T22)), T19, .(111, X73))
reduce7_in_gga(.(117, .(117, T22)), T19, .(117, X73)) → U15_gga(T22, T19, X73, reduce50_in_gga(T22, 117, X73))
U15_gga(T22, T19, X73, reduce50_out_gga(T22, 117, X73)) → reduce7_out_gga(.(117, .(117, T22)), T19, .(117, X73))
reduce7_in_gga(.(104, .(104, T22)), T19, .(104, X73)) → U16_gga(T22, T19, X73, reduce50_in_gga(T22, 104, X73))
U16_gga(T22, T19, X73, reduce50_out_gga(T22, 104, X73)) → reduce7_out_gga(.(104, .(104, T22)), T19, .(104, X73))
reduce7_in_gga(.(119, .(119, T22)), T19, .(119, X73)) → U17_gga(T22, T19, X73, reduce50_in_gga(T22, 119, X73))
U17_gga(T22, T19, X73, reduce50_out_gga(T22, 119, X73)) → reduce7_out_gga(.(119, .(119, T22)), T19, .(119, X73))
reduce7_in_gga(.(121, .(121, T22)), T19, .(121, X73)) → U18_gga(T22, T19, X73, reduce50_in_gga(T22, 121, X73))
U18_gga(T22, T19, X73, reduce50_out_gga(T22, 121, X73)) → reduce7_out_gga(.(121, .(121, T22)), T19, .(121, X73))
reduce7_in_gga(.(T23, .(T23, T24)), T19, .(T23, X130)) → U19_gga(T23, T24, T19, X130, reduce50_in_gga(T24, T23, X130))
U19_gga(T23, T24, T19, X130, reduce50_out_gga(T24, T23, X130)) → reduce7_out_gga(.(T23, .(T23, T24)), T19, .(T23, X130))
reduce7_in_gga(.(T25, .(T25, T26)), T19, .(T25, X145)) → U20_gga(T25, T26, T19, X145, reduce50_in_gga(T26, T25, X145))
U20_gga(T25, T26, T19, X145, reduce50_out_gga(T26, T25, X145)) → reduce7_out_gga(.(T25, .(T25, T26)), T19, .(T25, X145))
reduce7_in_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, []))) → reduce7_out_gga(.(T29, .(T30, [])), T19, .(T29, .(T30, [])))
reduce7_in_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177))) → U21_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 97, X177))
U21_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 97, X177)) → reduce7_out_gga(.(T29, .(97, .(97, T32))), T19, .(T29, .(97, X177)))
reduce7_in_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177))) → U22_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 101, X177))
U22_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 101, X177)) → reduce7_out_gga(.(T29, .(101, .(101, T32))), T19, .(T29, .(101, X177)))
reduce7_in_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177))) → U23_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 105, X177))
U23_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 105, X177)) → reduce7_out_gga(.(T29, .(105, .(105, T32))), T19, .(T29, .(105, X177)))
reduce7_in_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177))) → U24_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 111, X177))
U24_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 111, X177)) → reduce7_out_gga(.(T29, .(111, .(111, T32))), T19, .(T29, .(111, X177)))
reduce7_in_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177))) → U25_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 117, X177))
U25_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 117, X177)) → reduce7_out_gga(.(T29, .(117, .(117, T32))), T19, .(T29, .(117, X177)))
reduce7_in_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177))) → U26_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 104, X177))
U26_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 104, X177)) → reduce7_out_gga(.(T29, .(104, .(104, T32))), T19, .(T29, .(104, X177)))
reduce7_in_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177))) → U27_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 119, X177))
U27_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 119, X177)) → reduce7_out_gga(.(T29, .(119, .(119, T32))), T19, .(T29, .(119, X177)))
reduce7_in_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177))) → U28_gga(T29, T32, T19, X177, reduce130_in_gga(T32, 121, X177))
U28_gga(T29, T32, T19, X177, reduce130_out_gga(T32, 121, X177)) → reduce7_out_gga(.(T29, .(121, .(121, T32))), T19, .(T29, .(121, X177)))
reduce7_in_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234))) → U29_gga(T29, T33, T34, T19, X234, reduce130_in_gga(T34, T33, X234))
U29_gga(T29, T33, T34, T19, X234, reduce130_out_gga(T34, T33, X234)) → reduce7_out_gga(.(T29, .(T33, .(T33, T34))), T19, .(T29, .(T33, X234)))
reduce7_in_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249))) → U30_gga(T29, T35, T36, T19, X249, reduce130_in_gga(T36, T35, X249))
U30_gga(T29, T35, T36, T19, X249, reduce130_out_gga(T36, T35, X249)) → reduce7_out_gga(.(T29, .(T35, .(T35, T36))), T19, .(T29, .(T35, X249)))
reduce7_in_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, [])))) → reduce7_out_gga(.(T29, .(T39, .(T41, T40))), T19, .(T29, .(T39, .(T41, []))))
U10_gga(T15, T16, X47, reduce7_out_gga(T16, T15, X47)) → reduce7_out_gga(.(T15, T16), T15, X47)
U9_gga(T13, T14, X38, reduce7_out_gga(T14, T13, X38)) → reduce7_out_gga(.(T13, T14), T13, X38)
U8_gga(T12, X29, reduce7_out_gga(T12, 121, X29)) → reduce7_out_gga(.(121, T12), 121, X29)
U7_gga(T12, X29, reduce7_out_gga(T12, 119, X29)) → reduce7_out_gga(.(119, T12), 119, X29)
U6_gga(T12, X29, reduce7_out_gga(T12, 104, X29)) → reduce7_out_gga(.(104, T12), 104, X29)
U5_gga(T12, X29, reduce7_out_gga(T12, 117, X29)) → reduce7_out_gga(.(117, T12), 117, X29)
U4_gga(T12, X29, reduce7_out_gga(T12, 111, X29)) → reduce7_out_gga(.(111, T12), 111, X29)
U3_gga(T12, X29, reduce7_out_gga(T12, 105, X29)) → reduce7_out_gga(.(105, T12), 105, X29)
U2_gga(T12, X29, reduce7_out_gga(T12, 101, X29)) → reduce7_out_gga(.(101, T12), 101, X29)
U1_gga(T12, X29, reduce7_out_gga(T12, 97, X29)) → reduce7_out_gga(.(97, T12), 97, X29)
U61_ga(T7, T8, T5, reduce7_out_gga(T8, T7, X12)) → goal1_out_ga(.(T7, T8), T5)
goal1_in_ga(.(T7, T8), T42) → U62_ga(T7, T8, T42, reduce7_in_gga(T8, T7, T42))
U62_ga(T7, T8, T42, reduce7_out_gga(T8, T7, T42)) → goal1_out_ga(.(T7, T8), T42)

(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:

REDUCE7_IN_GGA(.(T13, T14), T13, X38) → REDUCE7_IN_GGA(T14, T13, X38)
REDUCE7_IN_GGA(.(97, T12), 97, X29) → REDUCE7_IN_GGA(T12, 97, X29)
REDUCE7_IN_GGA(.(101, T12), 101, X29) → REDUCE7_IN_GGA(T12, 101, X29)
REDUCE7_IN_GGA(.(105, T12), 105, X29) → REDUCE7_IN_GGA(T12, 105, X29)
REDUCE7_IN_GGA(.(111, T12), 111, X29) → REDUCE7_IN_GGA(T12, 111, X29)
REDUCE7_IN_GGA(.(117, T12), 117, X29) → REDUCE7_IN_GGA(T12, 117, X29)
REDUCE7_IN_GGA(.(104, T12), 104, X29) → REDUCE7_IN_GGA(T12, 104, X29)
REDUCE7_IN_GGA(.(119, T12), 119, X29) → REDUCE7_IN_GGA(T12, 119, X29)
REDUCE7_IN_GGA(.(121, T12), 121, X29) → REDUCE7_IN_GGA(T12, 121, X29)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
97 = 97
101 = 101
105 = 105
111 = 111
117 = 117
104 = 104
119 = 119
121 = 121
REDUCE7_IN_GGA(x1, x2, x3) = REDUCE7_IN_GGA(x1, x2)

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:

REDUCE7_IN_GGA(.(T13, T14), T13) → REDUCE7_IN_GGA(T14, T13)
REDUCE7_IN_GGA(.(97, T12), 97) → REDUCE7_IN_GGA(T12, 97)
REDUCE7_IN_GGA(.(101, T12), 101) → REDUCE7_IN_GGA(T12, 101)
REDUCE7_IN_GGA(.(105, T12), 105) → REDUCE7_IN_GGA(T12, 105)
REDUCE7_IN_GGA(.(111, T12), 111) → REDUCE7_IN_GGA(T12, 111)
REDUCE7_IN_GGA(.(117, T12), 117) → REDUCE7_IN_GGA(T12, 117)
REDUCE7_IN_GGA(.(104, T12), 104) → REDUCE7_IN_GGA(T12, 104)
REDUCE7_IN_GGA(.(119, T12), 119) → REDUCE7_IN_GGA(T12, 119)
REDUCE7_IN_GGA(.(121, T12), 121) → REDUCE7_IN_GGA(T12, 121)

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

(28) 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:

REDUCE7_IN_GGA(.(T13, T14), T13) → REDUCE7_IN_GGA(T14, T13)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(97, T12), 97) → REDUCE7_IN_GGA(T12, 97)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(101, T12), 101) → REDUCE7_IN_GGA(T12, 101)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(105, T12), 105) → REDUCE7_IN_GGA(T12, 105)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(111, T12), 111) → REDUCE7_IN_GGA(T12, 111)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(117, T12), 117) → REDUCE7_IN_GGA(T12, 117)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(104, T12), 104) → REDUCE7_IN_GGA(T12, 104)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(119, T12), 119) → REDUCE7_IN_GGA(T12, 119)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
REDUCE7_IN_GGA(.(121, T12), 121) → REDUCE7_IN_GGA(T12, 121)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (SOUND transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) TRUE

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) TRUE

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) TRUE