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

(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) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT 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(T5, .(X10, X11)), ','(reduce(X11, s(0), X10, X12), eq(T7, X12)))\n\nT5 is ground\nX10 is free; \nX11 is free; \nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(eq(T5, .(X10, X11)), ','(reduce(X11, s(0), X10, X12), eq(T7, X12))), SCOPE: 2, CLAUSE: 14\n\nT5 is ground\nX10 is free; \nX11 is free; \nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(reduce(T16, s(0), T15, X12), eq(T7, X12))\n\nT15 is ground\nT16 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: reduce(T16, s(0), T15, X12)\n\nT15 is ground\nT16 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: eq(T7, T19)\n\nT19 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 1 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 2 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 3 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 4 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 5\n\nT15 is ground\nT16 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 2 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 3 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 4 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 5\n\nT15 is ground\nT16 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: !_3 | reduce([], s(0), T25, X12), SCOPE: 3, CLAUSE: 3 | reduce([], s(0), T25, X12), SCOPE: 3, CLAUSE: 4 | reduce([], s(0), T25, X12), SCOPE: 3, CLAUSE: 5\n\nT25 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 3 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 4 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 5\n\nT15 is ground\nT16 is ground\nX12 is free; \nreduce(T16, s(0), T15, X12) !=? reduce([], X31, X32, [])", 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: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 3\n\nT15 is ground\nT16 is ground\nX12 is free; \nreduce(T16, s(0), T15, X12) !=? reduce([], X31, X32, [])", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 4 | reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 5\n\nT15 is ground\nT16 is ground\nX12 is free; \nreduce(T16, s(0), T15, X12) !=? reduce([], X31, X32, [])", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59)))\n\nT34 is ground\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 6 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 7 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(!_3, reduce(T35, s(0), 97, X59)) | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 7 | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(97), ','(!_3, reduce(T35, s(0), 97, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 7 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: reduce(T35, s(0), 97, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(!_3, reduce(T35, s(0), 101, X59)) | ','(vowel_h_w_y(101), ','(!_3, reduce(T35, s(0), 101, X59))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(101), ','(!_3, reduce(T35, s(0), 101, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(101), ','(!_3, reduce(T35, s(0), 101, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(101), ','(!_3, reduce(T35, s(0), 101, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(101), ','(!_3, reduce(T35, s(0), 101, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(101), ','(!_3, reduce(T35, s(0), 101, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 8 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)\nvowel_h_w_y(T34) !=? vowel_h_w_y(101)", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: reduce(T35, s(0), 101, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(!_3, reduce(T35, s(0), 105, X59)) | ','(vowel_h_w_y(105), ','(!_3, reduce(T35, s(0), 105, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(105), ','(!_3, reduce(T35, s(0), 105, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(105), ','(!_3, reduce(T35, s(0), 105, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(105), ','(!_3, reduce(T35, s(0), 105, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(105), ','(!_3, reduce(T35, s(0), 105, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 9 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)\nvowel_h_w_y(T34) !=? vowel_h_w_y(101)\nvowel_h_w_y(T34) !=? vowel_h_w_y(105)", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: reduce(T35, s(0), 105, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(!_3, reduce(T35, s(0), 111, X59)) | ','(vowel_h_w_y(111), ','(!_3, reduce(T35, s(0), 111, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(111), ','(!_3, reduce(T35, s(0), 111, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(111), ','(!_3, reduce(T35, s(0), 111, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(111), ','(!_3, reduce(T35, s(0), 111, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 10 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)\nvowel_h_w_y(T34) !=? vowel_h_w_y(101)\nvowel_h_w_y(T34) !=? vowel_h_w_y(105)\nvowel_h_w_y(T34) !=? vowel_h_w_y(111)", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: reduce(T35, s(0), 111, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(!_3, reduce(T35, s(0), 117, X59)) | ','(vowel_h_w_y(117), ','(!_3, reduce(T35, s(0), 117, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(117), ','(!_3, reduce(T35, s(0), 117, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(117), ','(!_3, reduce(T35, s(0), 117, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 11 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)\nvowel_h_w_y(T34) !=? vowel_h_w_y(101)\nvowel_h_w_y(T34) !=? vowel_h_w_y(105)\nvowel_h_w_y(T34) !=? vowel_h_w_y(111)\nvowel_h_w_y(T34) !=? vowel_h_w_y(117)", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: reduce(T35, s(0), 117, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: ','(!_3, reduce(T35, s(0), 104, X59)) | ','(vowel_h_w_y(104), ','(!_3, reduce(T35, s(0), 104, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(104), ','(!_3, reduce(T35, s(0), 104, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 12 | ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)\nvowel_h_w_y(T34) !=? vowel_h_w_y(101)\nvowel_h_w_y(T34) !=? vowel_h_w_y(105)\nvowel_h_w_y(T34) !=? vowel_h_w_y(111)\nvowel_h_w_y(T34) !=? vowel_h_w_y(117)\nvowel_h_w_y(T34) !=? vowel_h_w_y(104)", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: reduce(T35, s(0), 104, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(!_3, reduce(T35, s(0), 119, X59)) | ','(vowel_h_w_y(119), ','(!_3, reduce(T35, s(0), 119, X59))), SCOPE: 4, CLAUSE: 13\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(vowel_h_w_y(T34), ','(!_3, reduce(T35, s(0), T34, X59))), SCOPE: 4, CLAUSE: 13\n\nT34 is ground\nT35 is ground\nX59 is free; \nvowel_h_w_y(T34) !=? vowel_h_w_y(97)\nvowel_h_w_y(T34) !=? vowel_h_w_y(101)\nvowel_h_w_y(T34) !=? vowel_h_w_y(105)\nvowel_h_w_y(T34) !=? vowel_h_w_y(111)\nvowel_h_w_y(T34) !=? vowel_h_w_y(117)\nvowel_h_w_y(T34) !=? vowel_h_w_y(104)\nvowel_h_w_y(T34) !=? vowel_h_w_y(119)", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: reduce(T35, s(0), 119, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(!_3, reduce(T35, s(0), 121, X59))\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: reduce(T35, s(0), 121, X59)\n\nT35 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 4\n\nT15 is ground\nT16 is ground\nX12 is free; \nreduce(T16, s(0), T15, X12) !=? reduce([], X31, X32, [])", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: reduce(T16, s(0), T15, X12), SCOPE: 3, CLAUSE: 5\n\nT15 is ground\nT16 is ground\nX12 is free; \nreduce(T16, s(0), T15, X12) !=? reduce([], X31, X32, [])", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(!_3, reduce(T53, s(0), T52, X120))\n\nT52 is ground\nT53 is ground\nX120 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: reduce(T53, s(0), T52, X120)\n\nT52 is ground\nT53 is ground\nX120 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: reduce(T63, s(s(0)), T62, X146)\n\nT62 is ground\nT63 is ground\nX146 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 1 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 2 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 3 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 4 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nT63 is ground\nX146 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 2 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 3 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 4 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nT63 is ground\nX146 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: !_5 | reduce([], s(s(0)), T70, X146), SCOPE: 5, CLAUSE: 3 | reduce([], s(s(0)), T70, X146), SCOPE: 5, CLAUSE: 4 | reduce([], s(s(0)), T70, X146), SCOPE: 5, CLAUSE: 5\n\nT70 is ground\nX146 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 3 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 4 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nT63 is ground\nX146 is free; \nreduce(T63, s(s(0)), T62, X146) !=? reduce([], X162, X163, [])", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 3\n\nT62 is ground\nT63 is ground\nX146 is free; \nreduce(T63, s(s(0)), T62, X146) !=? reduce([], X162, X163, [])", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 4 | reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nT63 is ground\nX146 is free; \nreduce(T63, s(s(0)), T62, X146) !=? reduce([], X162, X163, [])", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190)))\n\nT79 is ground\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 6 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 7 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(!_5, reduce(T80, s(s(0)), 97, X190)) | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 7 | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(97), ','(!_5, reduce(T80, s(s(0)), 97, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 7 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: reduce(T80, s(s(0)), 97, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(!_5, reduce(T80, s(s(0)), 101, X190)) | ','(vowel_h_w_y(101), ','(!_5, reduce(T80, s(s(0)), 101, X190))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(101), ','(!_5, reduce(T80, s(s(0)), 101, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(101), ','(!_5, reduce(T80, s(s(0)), 101, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(101), ','(!_5, reduce(T80, s(s(0)), 101, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(101), ','(!_5, reduce(T80, s(s(0)), 101, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(101), ','(!_5, reduce(T80, s(s(0)), 101, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 8 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)\nvowel_h_w_y(T79) !=? vowel_h_w_y(101)", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: reduce(T80, s(s(0)), 101, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(!_5, reduce(T80, s(s(0)), 105, X190)) | ','(vowel_h_w_y(105), ','(!_5, reduce(T80, s(s(0)), 105, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(105), ','(!_5, reduce(T80, s(s(0)), 105, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(105), ','(!_5, reduce(T80, s(s(0)), 105, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(105), ','(!_5, reduce(T80, s(s(0)), 105, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(105), ','(!_5, reduce(T80, s(s(0)), 105, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 9 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)\nvowel_h_w_y(T79) !=? vowel_h_w_y(101)\nvowel_h_w_y(T79) !=? vowel_h_w_y(105)", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: reduce(T80, s(s(0)), 105, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(!_5, reduce(T80, s(s(0)), 111, X190)) | ','(vowel_h_w_y(111), ','(!_5, reduce(T80, s(s(0)), 111, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(111), ','(!_5, reduce(T80, s(s(0)), 111, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(111), ','(!_5, reduce(T80, s(s(0)), 111, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(111), ','(!_5, reduce(T80, s(s(0)), 111, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 10 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)\nvowel_h_w_y(T79) !=? vowel_h_w_y(101)\nvowel_h_w_y(T79) !=? vowel_h_w_y(105)\nvowel_h_w_y(T79) !=? vowel_h_w_y(111)", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: reduce(T80, s(s(0)), 111, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(!_5, reduce(T80, s(s(0)), 117, X190)) | ','(vowel_h_w_y(117), ','(!_5, reduce(T80, s(s(0)), 117, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(117), ','(!_5, reduce(T80, s(s(0)), 117, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(117), ','(!_5, reduce(T80, s(s(0)), 117, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 11 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)\nvowel_h_w_y(T79) !=? vowel_h_w_y(101)\nvowel_h_w_y(T79) !=? vowel_h_w_y(105)\nvowel_h_w_y(T79) !=? vowel_h_w_y(111)\nvowel_h_w_y(T79) !=? vowel_h_w_y(117)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: reduce(T80, s(s(0)), 117, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(!_5, reduce(T80, s(s(0)), 104, X190)) | ','(vowel_h_w_y(104), ','(!_5, reduce(T80, s(s(0)), 104, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(104), ','(!_5, reduce(T80, s(s(0)), 104, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 12 | ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)\nvowel_h_w_y(T79) !=? vowel_h_w_y(101)\nvowel_h_w_y(T79) !=? vowel_h_w_y(105)\nvowel_h_w_y(T79) !=? vowel_h_w_y(111)\nvowel_h_w_y(T79) !=? vowel_h_w_y(117)\nvowel_h_w_y(T79) !=? vowel_h_w_y(104)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: reduce(T80, s(s(0)), 104, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(!_5, reduce(T80, s(s(0)), 119, X190)) | ','(vowel_h_w_y(119), ','(!_5, reduce(T80, s(s(0)), 119, X190))), SCOPE: 6, CLAUSE: 13\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(vowel_h_w_y(T79), ','(!_5, reduce(T80, s(s(0)), T79, X190))), SCOPE: 6, CLAUSE: 13\n\nT79 is ground\nT80 is ground\nX190 is free; \nvowel_h_w_y(T79) !=? vowel_h_w_y(97)\nvowel_h_w_y(T79) !=? vowel_h_w_y(101)\nvowel_h_w_y(T79) !=? vowel_h_w_y(105)\nvowel_h_w_y(T79) !=? vowel_h_w_y(111)\nvowel_h_w_y(T79) !=? vowel_h_w_y(117)\nvowel_h_w_y(T79) !=? vowel_h_w_y(104)\nvowel_h_w_y(T79) !=? vowel_h_w_y(119)", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: reduce(T80, s(s(0)), 119, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(!_5, reduce(T80, s(s(0)), 121, X190))\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: reduce(T80, s(s(0)), 121, X190)\n\nT80 is ground\nX190 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 4\n\nT62 is ground\nT63 is ground\nX146 is free; \nreduce(T63, s(s(0)), T62, X146) !=? reduce([], X162, X163, [])", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: reduce(T63, s(s(0)), T62, X146), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nT63 is ground\nX146 is free; \nreduce(T63, s(s(0)), T62, X146) !=? reduce([], X162, X163, [])", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ','(!_5, reduce(T98, s(s(0)), T97, X251))\n\nT97 is ground\nT98 is ground\nX251 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: reduce(T98, s(s(0)), T97, X251)\n\nT97 is ground\nT98 is ground\nX251 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: reduce(T108, s(s(s(0))), T107, X277)\n\nT107 is ground\nT108 is ground\nX277 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 1 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 2 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 3 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 4 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 5\n\nT107 is ground\nT108 is ground\nX277 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 2 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 3 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 4 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 5\n\nT107 is ground\nT108 is ground\nX277 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: !_7 | reduce([], s(s(s(0))), T115, X277), SCOPE: 7, CLAUSE: 3 | reduce([], s(s(s(0))), T115, X277), SCOPE: 7, CLAUSE: 4 | reduce([], s(s(s(0))), T115, X277), SCOPE: 7, CLAUSE: 5\n\nT115 is ground\nX277 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 3 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 4 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 5\n\nT107 is ground\nT108 is ground\nX277 is free; \nreduce(T108, s(s(s(0))), T107, X277) !=? reduce([], X293, X294, [])", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 3\n\nT107 is ground\nT108 is ground\nX277 is free; \nreduce(T108, s(s(s(0))), T107, X277) !=? reduce([], X293, X294, [])", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 4 | reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 5\n\nT107 is ground\nT108 is ground\nX277 is free; \nreduce(T108, s(s(s(0))), T107, X277) !=? reduce([], X293, X294, [])", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321)))\n\nT124 is ground\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 6 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 7 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 8 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(!_7, reduce(T125, s(s(s(0))), 97, X321)) | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 7 | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 8 | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(97), ','(!_7, reduce(T125, s(s(s(0))), 97, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 7 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 8 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: reduce(T125, s(s(s(0))), 97, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ','(!_7, reduce(T125, s(s(s(0))), 101, X321)) | ','(vowel_h_w_y(101), ','(!_7, reduce(T125, s(s(s(0))), 101, X321))), SCOPE: 8, CLAUSE: 8 | ','(vowel_h_w_y(101), ','(!_7, reduce(T125, s(s(s(0))), 101, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(101), ','(!_7, reduce(T125, s(s(s(0))), 101, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(101), ','(!_7, reduce(T125, s(s(s(0))), 101, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(101), ','(!_7, reduce(T125, s(s(s(0))), 101, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(101), ','(!_7, reduce(T125, s(s(s(0))), 101, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 8 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)\nvowel_h_w_y(T124) !=? vowel_h_w_y(101)", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: reduce(T125, s(s(s(0))), 101, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(!_7, reduce(T125, s(s(s(0))), 105, X321)) | ','(vowel_h_w_y(105), ','(!_7, reduce(T125, s(s(s(0))), 105, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(105), ','(!_7, reduce(T125, s(s(s(0))), 105, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(105), ','(!_7, reduce(T125, s(s(s(0))), 105, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(105), ','(!_7, reduce(T125, s(s(s(0))), 105, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(105), ','(!_7, reduce(T125, s(s(s(0))), 105, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 9 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)\nvowel_h_w_y(T124) !=? vowel_h_w_y(101)\nvowel_h_w_y(T124) !=? vowel_h_w_y(105)", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: reduce(T125, s(s(s(0))), 105, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(!_7, reduce(T125, s(s(s(0))), 111, X321)) | ','(vowel_h_w_y(111), ','(!_7, reduce(T125, s(s(s(0))), 111, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(111), ','(!_7, reduce(T125, s(s(s(0))), 111, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(111), ','(!_7, reduce(T125, s(s(s(0))), 111, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(111), ','(!_7, reduce(T125, s(s(s(0))), 111, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 10 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)\nvowel_h_w_y(T124) !=? vowel_h_w_y(101)\nvowel_h_w_y(T124) !=? vowel_h_w_y(105)\nvowel_h_w_y(T124) !=? vowel_h_w_y(111)", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: reduce(T125, s(s(s(0))), 111, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(!_7, reduce(T125, s(s(s(0))), 117, X321)) | ','(vowel_h_w_y(117), ','(!_7, reduce(T125, s(s(s(0))), 117, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(117), ','(!_7, reduce(T125, s(s(s(0))), 117, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(117), ','(!_7, reduce(T125, s(s(s(0))), 117, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 11 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)\nvowel_h_w_y(T124) !=? vowel_h_w_y(101)\nvowel_h_w_y(T124) !=? vowel_h_w_y(105)\nvowel_h_w_y(T124) !=? vowel_h_w_y(111)\nvowel_h_w_y(T124) !=? vowel_h_w_y(117)", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: reduce(T125, s(s(s(0))), 117, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(!_7, reduce(T125, s(s(s(0))), 104, X321)) | ','(vowel_h_w_y(104), ','(!_7, reduce(T125, s(s(s(0))), 104, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(104), ','(!_7, reduce(T125, s(s(s(0))), 104, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 12 | ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)\nvowel_h_w_y(T124) !=? vowel_h_w_y(101)\nvowel_h_w_y(T124) !=? vowel_h_w_y(105)\nvowel_h_w_y(T124) !=? vowel_h_w_y(111)\nvowel_h_w_y(T124) !=? vowel_h_w_y(117)\nvowel_h_w_y(T124) !=? vowel_h_w_y(104)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: reduce(T125, s(s(s(0))), 104, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: ','(!_7, reduce(T125, s(s(s(0))), 119, X321)) | ','(vowel_h_w_y(119), ','(!_7, reduce(T125, s(s(s(0))), 119, X321))), SCOPE: 8, CLAUSE: 13\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(vowel_h_w_y(T124), ','(!_7, reduce(T125, s(s(s(0))), T124, X321))), SCOPE: 8, CLAUSE: 13\n\nT124 is ground\nT125 is ground\nX321 is free; \nvowel_h_w_y(T124) !=? vowel_h_w_y(97)\nvowel_h_w_y(T124) !=? vowel_h_w_y(101)\nvowel_h_w_y(T124) !=? vowel_h_w_y(105)\nvowel_h_w_y(T124) !=? vowel_h_w_y(111)\nvowel_h_w_y(T124) !=? vowel_h_w_y(117)\nvowel_h_w_y(T124) !=? vowel_h_w_y(104)\nvowel_h_w_y(T124) !=? vowel_h_w_y(119)", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: reduce(T125, s(s(s(0))), 119, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(!_7, reduce(T125, s(s(s(0))), 121, X321))\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: reduce(T125, s(s(s(0))), 121, X321)\n\nT125 is ground\nX321 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 4\n\nT107 is ground\nT108 is ground\nX277 is free; \nreduce(T108, s(s(s(0))), T107, X277) !=? reduce([], X293, X294, [])", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: reduce(T108, s(s(s(0))), T107, X277), SCOPE: 7, CLAUSE: 5\n\nT107 is ground\nT108 is ground\nX277 is free; \nreduce(T108, s(s(s(0))), T107, X277) !=? reduce([], X293, X294, [])", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: ','(!_7, reduce(T143, s(s(s(0))), T142, X382))\n\nT142 is ground\nT143 is ground\nX382 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: reduce(T143, s(s(s(0))), T142, X382)\n\nT142 is ground\nT143 is ground\nX382 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: reduce(T153, s(s(s(s(0)))), T152, X408)\n\nT152 is ground\nT153 is ground\nX408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: reduce(T153, s(s(s(s(0)))), T152, X408), SCOPE: 9, CLAUSE: 1 | reduce(T153, s(s(s(s(0)))), T152, X408), SCOPE: 9, CLAUSE: 2 | reduce(T153, s(s(s(s(0)))), T152, X408), SCOPE: 9, CLAUSE: 3 | reduce(T153, s(s(s(s(0)))), T152, X408), SCOPE: 9, CLAUSE: 4 | reduce(T153, s(s(s(s(0)))), T152, X408), SCOPE: 9, CLAUSE: 5\n\nT152 is ground\nT153 is ground\nX408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: !_9 | reduce(T161, s(s(s(s(0)))), T162, X408), SCOPE: 9, CLAUSE: 2 | reduce(T161, s(s(s(s(0)))), T162, X408), SCOPE: 9, CLAUSE: 3 | reduce(T161, s(s(s(s(0)))), T162, X408), SCOPE: 9, CLAUSE: 4 | reduce(T161, s(s(s(s(0)))), T162, X408), SCOPE: 9, CLAUSE: 5\n\nT161 is ground\nT162 is ground\nX408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: eq(T7, T19), SCOPE: 10, CLAUSE: 14\n\nT19 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 143 [arrowhead = none ];
143 -> 2;

144 [label="ONLY EVAL with clause\ngoal(X8, X9) :- ','(eq(X8, .(X10, X11)), ','(reduce(X11, s(0), X10, X12), eq(X9, X12))).\nand substitution\nT1 -> T5\nX8 -> T5\nT2 -> T7\nX9 -> T7\nT6 -> T7", fontsize=14, style = filled, fillcolor = white];
2 -> 144 [arrowhead = none ];
144 -> 3;

145 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 145 [arrowhead = none ];
145 -> 4;

146 [label="EVAL with clause\neq(X15, X15).\nand substitution\nT5 -> .(T15, T16)\nX15 -> .(T15, T16)\nX10 -> T15\nX11 -> T16\nT14 -> .(T15, T16)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 146 [arrowhead = none ];
146 -> 5;

147 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 147 [arrowhead = none ];
147 -> 6;

148 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
5 -> 148 [arrowhead = none ];
148 -> 7;

149 [label="SPLIT 2\nnew knowledge:\nT19 is ground\nreplacements:\nX12 -> T19", fontsize=14, style = filled, fillcolor = violet];
5 -> 149 [arrowhead = none ];
149 -> 8;

150 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 150 [arrowhead = none ];
150 -> 9;

151 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 151 [arrowhead = none ];
151 -> 139;

152 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
9 -> 152 [arrowhead = none ];
152 -> 10;

153 [label="EVAL with clause\nreduce([], X31, X32, []) :- !_3.\nand substitution\nT16 -> []\nX31 -> s(0)\nT15 -> T25\nX32 -> T25\nX12 -> []", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 153 [arrowhead = none ];
153 -> 11;

154 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 154 [arrowhead = none ];
154 -> 12;

155 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 155 [arrowhead = none ];
155 -> 13;

156 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 156 [arrowhead = none ];
156 -> 15;

157 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 157 [arrowhead = none ];
157 -> 16;

158 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 158 [arrowhead = none ];
158 -> 14;

159 [label="EVAL with clause\nreduce(.(X55, X56), X57, X55, X58) :- ','(vowel_h_w_y(X55), ','(!_3, reduce(X56, X57, X55, X58))).\nand substitution\nX55 -> T34\nX56 -> T35\nT16 -> .(T34, T35)\nX57 -> s(0)\nT15 -> T34\nX12 -> X59\nX58 -> X59", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 159 [arrowhead = none ];
159 -> 17;

160 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 160 [arrowhead = none ];
160 -> 18;

161 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 161 [arrowhead = none ];
161 -> 44;

162 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 162 [arrowhead = none ];
162 -> 45;

163 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 163 [arrowhead = none ];
163 -> 19;

164 [label="EVAL with clause\nvowel_h_w_y(97).\nand substitution\nT34 -> 97", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 164 [arrowhead = none ];
164 -> 20;

165 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 165 [arrowhead = none ];
165 -> 21;

166 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 166 [arrowhead = none ];
166 -> 22;

167 [label="EVAL with clause\nvowel_h_w_y(101).\nand substitution\nT34 -> 101", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 167 [arrowhead = none ];
167 -> 23;

168 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 168 [arrowhead = none ];
168 -> 24;

169 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 97\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
22 -> 169 [arrowhead = none , style=dashed];
169 -> 7[style=dashed];

170 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 170 [arrowhead = none ];
170 -> 25;

171 [label="EVAL with clause\nvowel_h_w_y(105).\nand substitution\nT34 -> 105", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 171 [arrowhead = none ];
171 -> 26;

172 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 172 [arrowhead = none ];
172 -> 27;

173 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 101\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
25 -> 173 [arrowhead = none , style=dashed];
173 -> 7[style=dashed];

174 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
26 -> 174 [arrowhead = none ];
174 -> 28;

175 [label="EVAL with clause\nvowel_h_w_y(111).\nand substitution\nT34 -> 111", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 175 [arrowhead = none ];
175 -> 29;

176 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 176 [arrowhead = none ];
176 -> 30;

177 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 105\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
28 -> 177 [arrowhead = none , style=dashed];
177 -> 7[style=dashed];

178 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 178 [arrowhead = none ];
178 -> 31;

179 [label="EVAL with clause\nvowel_h_w_y(117).\nand substitution\nT34 -> 117", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 179 [arrowhead = none ];
179 -> 32;

180 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 180 [arrowhead = none ];
180 -> 33;

181 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 111\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
31 -> 181 [arrowhead = none , style=dashed];
181 -> 7[style=dashed];

182 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
32 -> 182 [arrowhead = none ];
182 -> 34;

183 [label="EVAL with clause\nvowel_h_w_y(104).\nand substitution\nT34 -> 104", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 183 [arrowhead = none ];
183 -> 35;

184 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 184 [arrowhead = none ];
184 -> 36;

185 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 117\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
34 -> 185 [arrowhead = none , style=dashed];
185 -> 7[style=dashed];

186 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 186 [arrowhead = none ];
186 -> 37;

187 [label="EVAL with clause\nvowel_h_w_y(119).\nand substitution\nT34 -> 119", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 187 [arrowhead = none ];
187 -> 38;

188 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 188 [arrowhead = none ];
188 -> 39;

189 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 104\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
37 -> 189 [arrowhead = none , style=dashed];
189 -> 7[style=dashed];

190 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 190 [arrowhead = none ];
190 -> 40;

191 [label="EVAL with clause\nvowel_h_w_y(121).\nand substitution\nT34 -> 121", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 191 [arrowhead = none ];
191 -> 41;

192 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 192 [arrowhead = none ];
192 -> 42;

193 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 119\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
40 -> 193 [arrowhead = none , style=dashed];
193 -> 7[style=dashed];

194 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 194 [arrowhead = none ];
194 -> 43;

195 [label="INSTANCE with matching:\nT16 -> T35\nT15 -> 121\nX12 -> X59", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 195 [arrowhead = none , style=dashed];
195 -> 7[style=dashed];

196 [label="EVAL with clause\nreduce(.(X116, X117), X118, X116, X119) :- ','(!_3, reduce(X117, X118, X116, X119)).\nand substitution\nX116 -> T52\nX117 -> T53\nT16 -> .(T52, T53)\nX118 -> s(0)\nT15 -> T52\nX12 -> X120\nX119 -> X120", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 196 [arrowhead = none ];
196 -> 46;

197 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 197 [arrowhead = none ];
197 -> 47;

198 [label="EVAL with clause\nreduce(.(X141, X142), X143, X144, .(X141, X145)) :- reduce(X142, s(X143), X141, X145).\nand substitution\nX141 -> T62\nX142 -> T63\nT16 -> .(T62, T63)\nX143 -> s(0)\nT15 -> T64\nX144 -> T64\nX145 -> X146\nX12 -> .(T62, X146)", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 198 [arrowhead = none ];
198 -> 49;

199 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 199 [arrowhead = none ];
199 -> 50;

200 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 200 [arrowhead = none ];
200 -> 48;

201 [label="INSTANCE with matching:\nT16 -> T53\nT15 -> T52\nX12 -> X120", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 201 [arrowhead = none , style=dashed];
201 -> 7[style=dashed];

202 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 202 [arrowhead = none ];
202 -> 51;

203 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
51 -> 203 [arrowhead = none ];
203 -> 52;

204 [label="EVAL with clause\nreduce([], X162, X163, []) :- !_5.\nand substitution\nT63 -> []\nX162 -> s(s(0))\nT62 -> T70\nX163 -> T70\nX146 -> []", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 204 [arrowhead = none ];
204 -> 53;

205 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 205 [arrowhead = none ];
205 -> 54;

206 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 206 [arrowhead = none ];
206 -> 55;

207 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 207 [arrowhead = none ];
207 -> 57;

208 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 208 [arrowhead = none ];
208 -> 58;

209 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 209 [arrowhead = none ];
209 -> 56;

210 [label="EVAL with clause\nreduce(.(X186, X187), X188, X186, X189) :- ','(vowel_h_w_y(X186), ','(!_5, reduce(X187, X188, X186, X189))).\nand substitution\nX186 -> T79\nX187 -> T80\nT63 -> .(T79, T80)\nX188 -> s(s(0))\nT62 -> T79\nX146 -> X190\nX189 -> X190", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 210 [arrowhead = none ];
210 -> 59;

211 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 211 [arrowhead = none ];
211 -> 60;

212 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 212 [arrowhead = none ];
212 -> 86;

213 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 213 [arrowhead = none ];
213 -> 87;

214 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
59 -> 214 [arrowhead = none ];
214 -> 61;

215 [label="EVAL with clause\nvowel_h_w_y(97).\nand substitution\nT79 -> 97", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 215 [arrowhead = none ];
215 -> 62;

216 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 216 [arrowhead = none ];
216 -> 63;

217 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 217 [arrowhead = none ];
217 -> 64;

218 [label="EVAL with clause\nvowel_h_w_y(101).\nand substitution\nT79 -> 101", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 218 [arrowhead = none ];
218 -> 65;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 219 [arrowhead = none ];
219 -> 66;

220 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 97\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
64 -> 220 [arrowhead = none , style=dashed];
220 -> 49[style=dashed];

221 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 221 [arrowhead = none ];
221 -> 67;

222 [label="EVAL with clause\nvowel_h_w_y(105).\nand substitution\nT79 -> 105", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 222 [arrowhead = none ];
222 -> 68;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 223 [arrowhead = none ];
223 -> 69;

224 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 101\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 224 [arrowhead = none , style=dashed];
224 -> 49[style=dashed];

225 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
68 -> 225 [arrowhead = none ];
225 -> 70;

226 [label="EVAL with clause\nvowel_h_w_y(111).\nand substitution\nT79 -> 111", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 226 [arrowhead = none ];
226 -> 71;

227 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 227 [arrowhead = none ];
227 -> 72;

228 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 105\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
70 -> 228 [arrowhead = none , style=dashed];
228 -> 49[style=dashed];

229 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 229 [arrowhead = none ];
229 -> 73;

230 [label="EVAL with clause\nvowel_h_w_y(117).\nand substitution\nT79 -> 117", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 230 [arrowhead = none ];
230 -> 74;

231 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 231 [arrowhead = none ];
231 -> 75;

232 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 111\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
73 -> 232 [arrowhead = none , style=dashed];
232 -> 49[style=dashed];

233 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
74 -> 233 [arrowhead = none ];
233 -> 76;

234 [label="EVAL with clause\nvowel_h_w_y(104).\nand substitution\nT79 -> 104", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 234 [arrowhead = none ];
234 -> 77;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 235 [arrowhead = none ];
235 -> 78;

236 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 117\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
76 -> 236 [arrowhead = none , style=dashed];
236 -> 49[style=dashed];

237 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 237 [arrowhead = none ];
237 -> 79;

238 [label="EVAL with clause\nvowel_h_w_y(119).\nand substitution\nT79 -> 119", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 238 [arrowhead = none ];
238 -> 80;

239 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 239 [arrowhead = none ];
239 -> 81;

240 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 104\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
79 -> 240 [arrowhead = none , style=dashed];
240 -> 49[style=dashed];

241 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 241 [arrowhead = none ];
241 -> 82;

242 [label="EVAL with clause\nvowel_h_w_y(121).\nand substitution\nT79 -> 121", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 242 [arrowhead = none ];
242 -> 83;

243 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 243 [arrowhead = none ];
243 -> 84;

244 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 119\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
82 -> 244 [arrowhead = none , style=dashed];
244 -> 49[style=dashed];

245 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 245 [arrowhead = none ];
245 -> 85;

246 [label="INSTANCE with matching:\nT63 -> T80\nT62 -> 121\nX146 -> X190", fontsize=14, style = filled, fillcolor = lightgrey];
85 -> 246 [arrowhead = none , style=dashed];
246 -> 49[style=dashed];

247 [label="EVAL with clause\nreduce(.(X247, X248), X249, X247, X250) :- ','(!_5, reduce(X248, X249, X247, X250)).\nand substitution\nX247 -> T97\nX248 -> T98\nT63 -> .(T97, T98)\nX249 -> s(s(0))\nT62 -> T97\nX146 -> X251\nX250 -> X251", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 247 [arrowhead = none ];
247 -> 88;

248 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 248 [arrowhead = none ];
248 -> 89;

249 [label="EVAL with clause\nreduce(.(X272, X273), X274, X275, .(X272, X276)) :- reduce(X273, s(X274), X272, X276).\nand substitution\nX272 -> T107\nX273 -> T108\nT63 -> .(T107, T108)\nX274 -> s(s(0))\nT62 -> T109\nX275 -> T109\nX276 -> X277\nX146 -> .(T107, X277)", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 249 [arrowhead = none ];
249 -> 91;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 250 [arrowhead = none ];
250 -> 92;

251 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 251 [arrowhead = none ];
251 -> 90;

252 [label="INSTANCE with matching:\nT63 -> T98\nT62 -> T97\nX146 -> X251", fontsize=14, style = filled, fillcolor = lightgrey];
90 -> 252 [arrowhead = none , style=dashed];
252 -> 49[style=dashed];

253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 253 [arrowhead = none ];
253 -> 93;

254 [label="BACKTRACK\nfor clause: reduce(X1, s(s(s(s(0)))), X2, []) :- !because of non-unification", fontsize=14, style = filled, fillcolor = white];
93 -> 254 [arrowhead = none ];
254 -> 94;

255 [label="EVAL with clause\nreduce([], X293, X294, []) :- !_7.\nand substitution\nT108 -> []\nX293 -> s(s(s(0)))\nT107 -> T115\nX294 -> T115\nX277 -> []", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 255 [arrowhead = none ];
255 -> 95;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 256 [arrowhead = none ];
256 -> 96;

257 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 257 [arrowhead = none ];
257 -> 97;

258 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 258 [arrowhead = none ];
258 -> 99;

259 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 259 [arrowhead = none ];
259 -> 100;

260 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 260 [arrowhead = none ];
260 -> 98;

261 [label="EVAL with clause\nreduce(.(X317, X318), X319, X317, X320) :- ','(vowel_h_w_y(X317), ','(!_7, reduce(X318, X319, X317, X320))).\nand substitution\nX317 -> T124\nX318 -> T125\nT108 -> .(T124, T125)\nX319 -> s(s(s(0)))\nT107 -> T124\nX277 -> X321\nX320 -> X321", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 261 [arrowhead = none ];
261 -> 101;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 262 [arrowhead = none ];
262 -> 102;

263 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
100 -> 263 [arrowhead = none ];
263 -> 128;

264 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
100 -> 264 [arrowhead = none ];
264 -> 129;

265 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
101 -> 265 [arrowhead = none ];
265 -> 103;

266 [label="EVAL with clause\nvowel_h_w_y(97).\nand substitution\nT124 -> 97", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 266 [arrowhead = none ];
266 -> 104;

267 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 267 [arrowhead = none ];
267 -> 105;

268 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
104 -> 268 [arrowhead = none ];
268 -> 106;

269 [label="EVAL with clause\nvowel_h_w_y(101).\nand substitution\nT124 -> 101", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 269 [arrowhead = none ];
269 -> 107;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 270 [arrowhead = none ];
270 -> 108;

271 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 97\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
106 -> 271 [arrowhead = none , style=dashed];
271 -> 91[style=dashed];

272 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 272 [arrowhead = none ];
272 -> 109;

273 [label="EVAL with clause\nvowel_h_w_y(105).\nand substitution\nT124 -> 105", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 273 [arrowhead = none ];
273 -> 110;

274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 274 [arrowhead = none ];
274 -> 111;

275 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 101\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 275 [arrowhead = none , style=dashed];
275 -> 91[style=dashed];

276 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 276 [arrowhead = none ];
276 -> 112;

277 [label="EVAL with clause\nvowel_h_w_y(111).\nand substitution\nT124 -> 111", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 277 [arrowhead = none ];
277 -> 113;

278 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 278 [arrowhead = none ];
278 -> 114;

279 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 105\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
112 -> 279 [arrowhead = none , style=dashed];
279 -> 91[style=dashed];

280 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 280 [arrowhead = none ];
280 -> 115;

281 [label="EVAL with clause\nvowel_h_w_y(117).\nand substitution\nT124 -> 117", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 281 [arrowhead = none ];
281 -> 116;

282 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 282 [arrowhead = none ];
282 -> 117;

283 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 111\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 283 [arrowhead = none , style=dashed];
283 -> 91[style=dashed];

284 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 284 [arrowhead = none ];
284 -> 118;

285 [label="EVAL with clause\nvowel_h_w_y(104).\nand substitution\nT124 -> 104", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 285 [arrowhead = none ];
285 -> 119;

286 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 286 [arrowhead = none ];
286 -> 120;

287 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 117\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
118 -> 287 [arrowhead = none , style=dashed];
287 -> 91[style=dashed];

288 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 288 [arrowhead = none ];
288 -> 121;

289 [label="EVAL with clause\nvowel_h_w_y(119).\nand substitution\nT124 -> 119", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 289 [arrowhead = none ];
289 -> 122;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 290 [arrowhead = none ];
290 -> 123;

291 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 104\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
121 -> 291 [arrowhead = none , style=dashed];
291 -> 91[style=dashed];

292 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 292 [arrowhead = none ];
292 -> 124;

293 [label="EVAL with clause\nvowel_h_w_y(121).\nand substitution\nT124 -> 121", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 293 [arrowhead = none ];
293 -> 125;

294 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 294 [arrowhead = none ];
294 -> 126;

295 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 119\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
124 -> 295 [arrowhead = none , style=dashed];
295 -> 91[style=dashed];

296 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 296 [arrowhead = none ];
296 -> 127;

297 [label="INSTANCE with matching:\nT108 -> T125\nT107 -> 121\nX277 -> X321", fontsize=14, style = filled, fillcolor = lightgrey];
127 -> 297 [arrowhead = none , style=dashed];
297 -> 91[style=dashed];

298 [label="EVAL with clause\nreduce(.(X378, X379), X380, X378, X381) :- ','(!_7, reduce(X379, X380, X378, X381)).\nand substitution\nX378 -> T142\nX379 -> T143\nT108 -> .(T142, T143)\nX380 -> s(s(s(0)))\nT107 -> T142\nX277 -> X382\nX381 -> X382", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 298 [arrowhead = none ];
298 -> 130;

299 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 299 [arrowhead = none ];
299 -> 131;

300 [label="EVAL with clause\nreduce(.(X403, X404), X405, X406, .(X403, X407)) :- reduce(X404, s(X405), X403, X407).\nand substitution\nX403 -> T152\nX404 -> T153\nT108 -> .(T152, T153)\nX405 -> s(s(s(0)))\nT107 -> T154\nX406 -> T154\nX407 -> X408\nX277 -> .(T152, X408)", fontsize=14, style = filled, fillcolor = lightblue];
129 -> 300 [arrowhead = none ];
300 -> 133;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
129 -> 301 [arrowhead = none ];
301 -> 134;

302 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 302 [arrowhead = none ];
302 -> 132;

303 [label="INSTANCE with matching:\nT108 -> T143\nT107 -> T142\nX277 -> X382", fontsize=14, style = filled, fillcolor = lightgrey];
132 -> 303 [arrowhead = none , style=dashed];
303 -> 91[style=dashed];

304 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 304 [arrowhead = none ];
304 -> 135;

305 [label="ONLY EVAL with clause\nreduce(X420, s(s(s(s(0)))), X421, []) :- !_9.\nand substitution\nT153 -> T161\nX420 -> T161\nT152 -> T162\nX421 -> T162\nX408 -> []", fontsize=14, style = filled, fillcolor = white];
135 -> 305 [arrowhead = none ];
305 -> 136;

306 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 306 [arrowhead = none ];
306 -> 137;

307 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 307 [arrowhead = none ];
307 -> 138;

308 [label="EVAL with clause\neq(X424, X424).\nand substitution\nT7 -> T165\nX424 -> T165\nT19 -> T165", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 308 [arrowhead = none ];
308 -> 140;

309 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 309 [arrowhead = none ];
309 -> 141;

310 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 310 [arrowhead = none ];
310 -> 142;

}

(2) Obligation:

Triples:

reduce7(.(97, T35), 97, X59) :- reduce7(T35, 97, X59).
reduce7(.(101, T35), 101, X59) :- reduce7(T35, 101, X59).
reduce7(.(105, T35), 105, X59) :- reduce7(T35, 105, X59).
reduce7(.(111, T35), 111, X59) :- reduce7(T35, 111, X59).
reduce7(.(117, T35), 117, X59) :- reduce7(T35, 117, X59).
reduce7(.(104, T35), 104, X59) :- reduce7(T35, 104, X59).
reduce7(.(119, T35), 119, X59) :- reduce7(T35, 119, X59).
reduce7(.(121, T35), 121, X59) :- reduce7(T35, 121, X59).
reduce7(.(T52, T53), T52, X120) :- reduce7(T53, T52, X120).
reduce7(.(T62, T63), T64, .(T62, X146)) :- reduce49(T63, T62, X146).
reduce49(.(97, T80), 97, X190) :- reduce49(T80, 97, X190).
reduce49(.(101, T80), 101, X190) :- reduce49(T80, 101, X190).
reduce49(.(105, T80), 105, X190) :- reduce49(T80, 105, X190).
reduce49(.(111, T80), 111, X190) :- reduce49(T80, 111, X190).
reduce49(.(117, T80), 117, X190) :- reduce49(T80, 117, X190).
reduce49(.(104, T80), 104, X190) :- reduce49(T80, 104, X190).
reduce49(.(119, T80), 119, X190) :- reduce49(T80, 119, X190).
reduce49(.(121, T80), 121, X190) :- reduce49(T80, 121, X190).
reduce49(.(T97, T98), T97, X251) :- reduce49(T98, T97, X251).
reduce49(.(T107, T108), T109, .(T107, X277)) :- reduce91(T108, T107, X277).
reduce91(.(97, T125), 97, X321) :- reduce91(T125, 97, X321).
reduce91(.(101, T125), 101, X321) :- reduce91(T125, 101, X321).
reduce91(.(105, T125), 105, X321) :- reduce91(T125, 105, X321).
reduce91(.(111, T125), 111, X321) :- reduce91(T125, 111, X321).
reduce91(.(117, T125), 117, X321) :- reduce91(T125, 117, X321).
reduce91(.(104, T125), 104, X321) :- reduce91(T125, 104, X321).
reduce91(.(119, T125), 119, X321) :- reduce91(T125, 119, X321).
reduce91(.(121, T125), 121, X321) :- reduce91(T125, 121, X321).
reduce91(.(T142, T143), T142, X382) :- reduce91(T143, T142, X382).
goal1(.(T15, T16), T7) :- reduce7(T16, T15, X12).

Clauses:

reducec7([], T25, []).
reducec7(.(97, T35), 97, X59) :- reducec7(T35, 97, X59).
reducec7(.(101, T35), 101, X59) :- reducec7(T35, 101, X59).
reducec7(.(105, T35), 105, X59) :- reducec7(T35, 105, X59).
reducec7(.(111, T35), 111, X59) :- reducec7(T35, 111, X59).
reducec7(.(117, T35), 117, X59) :- reducec7(T35, 117, X59).
reducec7(.(104, T35), 104, X59) :- reducec7(T35, 104, X59).
reducec7(.(119, T35), 119, X59) :- reducec7(T35, 119, X59).
reducec7(.(121, T35), 121, X59) :- reducec7(T35, 121, X59).
reducec7(.(T52, T53), T52, X120) :- reducec7(T53, T52, X120).
reducec7(.(T62, T63), T64, .(T62, X146)) :- reducec49(T63, T62, X146).
reducec49([], T70, []).
reducec49(.(97, T80), 97, X190) :- reducec49(T80, 97, X190).
reducec49(.(101, T80), 101, X190) :- reducec49(T80, 101, X190).
reducec49(.(105, T80), 105, X190) :- reducec49(T80, 105, X190).
reducec49(.(111, T80), 111, X190) :- reducec49(T80, 111, X190).
reducec49(.(117, T80), 117, X190) :- reducec49(T80, 117, X190).
reducec49(.(104, T80), 104, X190) :- reducec49(T80, 104, X190).
reducec49(.(119, T80), 119, X190) :- reducec49(T80, 119, X190).
reducec49(.(121, T80), 121, X190) :- reducec49(T80, 121, X190).
reducec49(.(T97, T98), T97, X251) :- reducec49(T98, T97, X251).
reducec49(.(T107, T108), T109, .(T107, X277)) :- reducec91(T108, T107, X277).
reducec91([], T115, []).
reducec91(.(97, T125), 97, X321) :- reducec91(T125, 97, X321).
reducec91(.(101, T125), 101, X321) :- reducec91(T125, 101, X321).
reducec91(.(105, T125), 105, X321) :- reducec91(T125, 105, X321).
reducec91(.(111, T125), 111, X321) :- reducec91(T125, 111, X321).
reducec91(.(117, T125), 117, X321) :- reducec91(T125, 117, X321).
reducec91(.(104, T125), 104, X321) :- reducec91(T125, 104, X321).
reducec91(.(119, T125), 119, X321) :- reducec91(T125, 119, X321).
reducec91(.(121, T125), 121, X321) :- reducec91(T125, 121, X321).
reducec91(.(T142, T143), T142, X382) :- reducec91(T143, T142, X382).
reducec91(.(T162, T161), T154, .(T162, [])).

Afs:

goal1(x1, x2)  =  goal1(x1)

(3) TriplesToPiDPProof (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)
reduce49_in: (b,b,f)
reduce91_in: (b,b,f)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

GOAL1_IN_GA(.(T15, T16), T7) → U30_GA(T15, T16, T7, reduce7_in_gga(T16, T15, X12))
GOAL1_IN_GA(.(T15, T16), T7) → REDUCE7_IN_GGA(T16, T15, X12)
REDUCE7_IN_GGA(.(97, T35), 97, X59) → U1_GGA(T35, X59, reduce7_in_gga(T35, 97, X59))
REDUCE7_IN_GGA(.(97, T35), 97, X59) → REDUCE7_IN_GGA(T35, 97, X59)
REDUCE7_IN_GGA(.(101, T35), 101, X59) → U2_GGA(T35, X59, reduce7_in_gga(T35, 101, X59))
REDUCE7_IN_GGA(.(101, T35), 101, X59) → REDUCE7_IN_GGA(T35, 101, X59)
REDUCE7_IN_GGA(.(105, T35), 105, X59) → U3_GGA(T35, X59, reduce7_in_gga(T35, 105, X59))
REDUCE7_IN_GGA(.(105, T35), 105, X59) → REDUCE7_IN_GGA(T35, 105, X59)
REDUCE7_IN_GGA(.(111, T35), 111, X59) → U4_GGA(T35, X59, reduce7_in_gga(T35, 111, X59))
REDUCE7_IN_GGA(.(111, T35), 111, X59) → REDUCE7_IN_GGA(T35, 111, X59)
REDUCE7_IN_GGA(.(117, T35), 117, X59) → U5_GGA(T35, X59, reduce7_in_gga(T35, 117, X59))
REDUCE7_IN_GGA(.(117, T35), 117, X59) → REDUCE7_IN_GGA(T35, 117, X59)
REDUCE7_IN_GGA(.(104, T35), 104, X59) → U6_GGA(T35, X59, reduce7_in_gga(T35, 104, X59))
REDUCE7_IN_GGA(.(104, T35), 104, X59) → REDUCE7_IN_GGA(T35, 104, X59)
REDUCE7_IN_GGA(.(119, T35), 119, X59) → U7_GGA(T35, X59, reduce7_in_gga(T35, 119, X59))
REDUCE7_IN_GGA(.(119, T35), 119, X59) → REDUCE7_IN_GGA(T35, 119, X59)
REDUCE7_IN_GGA(.(121, T35), 121, X59) → U8_GGA(T35, X59, reduce7_in_gga(T35, 121, X59))
REDUCE7_IN_GGA(.(121, T35), 121, X59) → REDUCE7_IN_GGA(T35, 121, X59)
REDUCE7_IN_GGA(.(T52, T53), T52, X120) → U9_GGA(T52, T53, X120, reduce7_in_gga(T53, T52, X120))
REDUCE7_IN_GGA(.(T52, T53), T52, X120) → REDUCE7_IN_GGA(T53, T52, X120)
REDUCE7_IN_GGA(.(T62, T63), T64, .(T62, X146)) → U10_GGA(T62, T63, T64, X146, reduce49_in_gga(T63, T62, X146))
REDUCE7_IN_GGA(.(T62, T63), T64, .(T62, X146)) → REDUCE49_IN_GGA(T63, T62, X146)
REDUCE49_IN_GGA(.(97, T80), 97, X190) → U11_GGA(T80, X190, reduce49_in_gga(T80, 97, X190))
REDUCE49_IN_GGA(.(97, T80), 97, X190) → REDUCE49_IN_GGA(T80, 97, X190)
REDUCE49_IN_GGA(.(101, T80), 101, X190) → U12_GGA(T80, X190, reduce49_in_gga(T80, 101, X190))
REDUCE49_IN_GGA(.(101, T80), 101, X190) → REDUCE49_IN_GGA(T80, 101, X190)
REDUCE49_IN_GGA(.(105, T80), 105, X190) → U13_GGA(T80, X190, reduce49_in_gga(T80, 105, X190))
REDUCE49_IN_GGA(.(105, T80), 105, X190) → REDUCE49_IN_GGA(T80, 105, X190)
REDUCE49_IN_GGA(.(111, T80), 111, X190) → U14_GGA(T80, X190, reduce49_in_gga(T80, 111, X190))
REDUCE49_IN_GGA(.(111, T80), 111, X190) → REDUCE49_IN_GGA(T80, 111, X190)
REDUCE49_IN_GGA(.(117, T80), 117, X190) → U15_GGA(T80, X190, reduce49_in_gga(T80, 117, X190))
REDUCE49_IN_GGA(.(117, T80), 117, X190) → REDUCE49_IN_GGA(T80, 117, X190)
REDUCE49_IN_GGA(.(104, T80), 104, X190) → U16_GGA(T80, X190, reduce49_in_gga(T80, 104, X190))
REDUCE49_IN_GGA(.(104, T80), 104, X190) → REDUCE49_IN_GGA(T80, 104, X190)
REDUCE49_IN_GGA(.(119, T80), 119, X190) → U17_GGA(T80, X190, reduce49_in_gga(T80, 119, X190))
REDUCE49_IN_GGA(.(119, T80), 119, X190) → REDUCE49_IN_GGA(T80, 119, X190)
REDUCE49_IN_GGA(.(121, T80), 121, X190) → U18_GGA(T80, X190, reduce49_in_gga(T80, 121, X190))
REDUCE49_IN_GGA(.(121, T80), 121, X190) → REDUCE49_IN_GGA(T80, 121, X190)
REDUCE49_IN_GGA(.(T97, T98), T97, X251) → U19_GGA(T97, T98, X251, reduce49_in_gga(T98, T97, X251))
REDUCE49_IN_GGA(.(T97, T98), T97, X251) → REDUCE49_IN_GGA(T98, T97, X251)
REDUCE49_IN_GGA(.(T107, T108), T109, .(T107, X277)) → U20_GGA(T107, T108, T109, X277, reduce91_in_gga(T108, T107, X277))
REDUCE49_IN_GGA(.(T107, T108), T109, .(T107, X277)) → REDUCE91_IN_GGA(T108, T107, X277)
REDUCE91_IN_GGA(.(97, T125), 97, X321) → U21_GGA(T125, X321, reduce91_in_gga(T125, 97, X321))
REDUCE91_IN_GGA(.(97, T125), 97, X321) → REDUCE91_IN_GGA(T125, 97, X321)
REDUCE91_IN_GGA(.(101, T125), 101, X321) → U22_GGA(T125, X321, reduce91_in_gga(T125, 101, X321))
REDUCE91_IN_GGA(.(101, T125), 101, X321) → REDUCE91_IN_GGA(T125, 101, X321)
REDUCE91_IN_GGA(.(105, T125), 105, X321) → U23_GGA(T125, X321, reduce91_in_gga(T125, 105, X321))
REDUCE91_IN_GGA(.(105, T125), 105, X321) → REDUCE91_IN_GGA(T125, 105, X321)
REDUCE91_IN_GGA(.(111, T125), 111, X321) → U24_GGA(T125, X321, reduce91_in_gga(T125, 111, X321))
REDUCE91_IN_GGA(.(111, T125), 111, X321) → REDUCE91_IN_GGA(T125, 111, X321)
REDUCE91_IN_GGA(.(117, T125), 117, X321) → U25_GGA(T125, X321, reduce91_in_gga(T125, 117, X321))
REDUCE91_IN_GGA(.(117, T125), 117, X321) → REDUCE91_IN_GGA(T125, 117, X321)
REDUCE91_IN_GGA(.(104, T125), 104, X321) → U26_GGA(T125, X321, reduce91_in_gga(T125, 104, X321))
REDUCE91_IN_GGA(.(104, T125), 104, X321) → REDUCE91_IN_GGA(T125, 104, X321)
REDUCE91_IN_GGA(.(119, T125), 119, X321) → U27_GGA(T125, X321, reduce91_in_gga(T125, 119, X321))
REDUCE91_IN_GGA(.(119, T125), 119, X321) → REDUCE91_IN_GGA(T125, 119, X321)
REDUCE91_IN_GGA(.(121, T125), 121, X321) → U28_GGA(T125, X321, reduce91_in_gga(T125, 121, X321))
REDUCE91_IN_GGA(.(121, T125), 121, X321) → REDUCE91_IN_GGA(T125, 121, X321)
REDUCE91_IN_GGA(.(T142, T143), T142, X382) → U29_GGA(T142, T143, X382, reduce91_in_gga(T143, T142, X382))
REDUCE91_IN_GGA(.(T142, T143), T142, X382) → REDUCE91_IN_GGA(T143, T142, X382)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
reduce7_in_gga(x1, x2, x3)  =  reduce7_in_gga(x1, x2)
97  =  97
101  =  101
105  =  105
111  =  111
117  =  117
104  =  104
119  =  119
121  =  121
reduce49_in_gga(x1, x2, x3)  =  reduce49_in_gga(x1, x2)
reduce91_in_gga(x1, x2, x3)  =  reduce91_in_gga(x1, x2)
GOAL1_IN_GA(x1, x2)  =  GOAL1_IN_GA(x1)
U30_GA(x1, x2, x3, x4)  =  U30_GA(x1, x2, x4)
REDUCE7_IN_GGA(x1, x2, x3)  =  REDUCE7_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3)  =  U1_GGA(x1, x3)
U2_GGA(x1, x2, x3)  =  U2_GGA(x1, x3)
U3_GGA(x1, x2, x3)  =  U3_GGA(x1, x3)
U4_GGA(x1, x2, x3)  =  U4_GGA(x1, x3)
U5_GGA(x1, x2, x3)  =  U5_GGA(x1, x3)
U6_GGA(x1, x2, x3)  =  U6_GGA(x1, x3)
U7_GGA(x1, x2, x3)  =  U7_GGA(x1, x3)
U8_GGA(x1, x2, x3)  =  U8_GGA(x1, x3)
U9_GGA(x1, x2, x3, x4)  =  U9_GGA(x1, x2, x4)
U10_GGA(x1, x2, x3, x4, x5)  =  U10_GGA(x1, x2, x3, x5)
REDUCE49_IN_GGA(x1, x2, x3)  =  REDUCE49_IN_GGA(x1, x2)
U11_GGA(x1, x2, x3)  =  U11_GGA(x1, x3)
U12_GGA(x1, x2, x3)  =  U12_GGA(x1, x3)
U13_GGA(x1, x2, x3)  =  U13_GGA(x1, x3)
U14_GGA(x1, x2, x3)  =  U14_GGA(x1, x3)
U15_GGA(x1, x2, x3)  =  U15_GGA(x1, x3)
U16_GGA(x1, x2, x3)  =  U16_GGA(x1, x3)
U17_GGA(x1, x2, x3)  =  U17_GGA(x1, x3)
U18_GGA(x1, x2, x3)  =  U18_GGA(x1, x3)
U19_GGA(x1, x2, x3, x4)  =  U19_GGA(x1, x2, x4)
U20_GGA(x1, x2, x3, x4, x5)  =  U20_GGA(x1, x2, x3, x5)
REDUCE91_IN_GGA(x1, x2, x3)  =  REDUCE91_IN_GGA(x1, x2)
U21_GGA(x1, x2, x3)  =  U21_GGA(x1, x3)
U22_GGA(x1, x2, x3)  =  U22_GGA(x1, x3)
U23_GGA(x1, x2, x3)  =  U23_GGA(x1, x3)
U24_GGA(x1, x2, x3)  =  U24_GGA(x1, x3)
U25_GGA(x1, x2, x3)  =  U25_GGA(x1, x3)
U26_GGA(x1, x2, x3)  =  U26_GGA(x1, x3)
U27_GGA(x1, x2, x3)  =  U27_GGA(x1, x3)
U28_GGA(x1, x2, x3)  =  U28_GGA(x1, x3)
U29_GGA(x1, x2, x3, x4)  =  U29_GGA(x1, x2, x4)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

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

GOAL1_IN_GA(.(T15, T16), T7) → U30_GA(T15, T16, T7, reduce7_in_gga(T16, T15, X12))
GOAL1_IN_GA(.(T15, T16), T7) → REDUCE7_IN_GGA(T16, T15, X12)
REDUCE7_IN_GGA(.(97, T35), 97, X59) → U1_GGA(T35, X59, reduce7_in_gga(T35, 97, X59))
REDUCE7_IN_GGA(.(97, T35), 97, X59) → REDUCE7_IN_GGA(T35, 97, X59)
REDUCE7_IN_GGA(.(101, T35), 101, X59) → U2_GGA(T35, X59, reduce7_in_gga(T35, 101, X59))
REDUCE7_IN_GGA(.(101, T35), 101, X59) → REDUCE7_IN_GGA(T35, 101, X59)
REDUCE7_IN_GGA(.(105, T35), 105, X59) → U3_GGA(T35, X59, reduce7_in_gga(T35, 105, X59))
REDUCE7_IN_GGA(.(105, T35), 105, X59) → REDUCE7_IN_GGA(T35, 105, X59)
REDUCE7_IN_GGA(.(111, T35), 111, X59) → U4_GGA(T35, X59, reduce7_in_gga(T35, 111, X59))
REDUCE7_IN_GGA(.(111, T35), 111, X59) → REDUCE7_IN_GGA(T35, 111, X59)
REDUCE7_IN_GGA(.(117, T35), 117, X59) → U5_GGA(T35, X59, reduce7_in_gga(T35, 117, X59))
REDUCE7_IN_GGA(.(117, T35), 117, X59) → REDUCE7_IN_GGA(T35, 117, X59)
REDUCE7_IN_GGA(.(104, T35), 104, X59) → U6_GGA(T35, X59, reduce7_in_gga(T35, 104, X59))
REDUCE7_IN_GGA(.(104, T35), 104, X59) → REDUCE7_IN_GGA(T35, 104, X59)
REDUCE7_IN_GGA(.(119, T35), 119, X59) → U7_GGA(T35, X59, reduce7_in_gga(T35, 119, X59))
REDUCE7_IN_GGA(.(119, T35), 119, X59) → REDUCE7_IN_GGA(T35, 119, X59)
REDUCE7_IN_GGA(.(121, T35), 121, X59) → U8_GGA(T35, X59, reduce7_in_gga(T35, 121, X59))
REDUCE7_IN_GGA(.(121, T35), 121, X59) → REDUCE7_IN_GGA(T35, 121, X59)
REDUCE7_IN_GGA(.(T52, T53), T52, X120) → U9_GGA(T52, T53, X120, reduce7_in_gga(T53, T52, X120))
REDUCE7_IN_GGA(.(T52, T53), T52, X120) → REDUCE7_IN_GGA(T53, T52, X120)
REDUCE7_IN_GGA(.(T62, T63), T64, .(T62, X146)) → U10_GGA(T62, T63, T64, X146, reduce49_in_gga(T63, T62, X146))
REDUCE7_IN_GGA(.(T62, T63), T64, .(T62, X146)) → REDUCE49_IN_GGA(T63, T62, X146)
REDUCE49_IN_GGA(.(97, T80), 97, X190) → U11_GGA(T80, X190, reduce49_in_gga(T80, 97, X190))
REDUCE49_IN_GGA(.(97, T80), 97, X190) → REDUCE49_IN_GGA(T80, 97, X190)
REDUCE49_IN_GGA(.(101, T80), 101, X190) → U12_GGA(T80, X190, reduce49_in_gga(T80, 101, X190))
REDUCE49_IN_GGA(.(101, T80), 101, X190) → REDUCE49_IN_GGA(T80, 101, X190)
REDUCE49_IN_GGA(.(105, T80), 105, X190) → U13_GGA(T80, X190, reduce49_in_gga(T80, 105, X190))
REDUCE49_IN_GGA(.(105, T80), 105, X190) → REDUCE49_IN_GGA(T80, 105, X190)
REDUCE49_IN_GGA(.(111, T80), 111, X190) → U14_GGA(T80, X190, reduce49_in_gga(T80, 111, X190))
REDUCE49_IN_GGA(.(111, T80), 111, X190) → REDUCE49_IN_GGA(T80, 111, X190)
REDUCE49_IN_GGA(.(117, T80), 117, X190) → U15_GGA(T80, X190, reduce49_in_gga(T80, 117, X190))
REDUCE49_IN_GGA(.(117, T80), 117, X190) → REDUCE49_IN_GGA(T80, 117, X190)
REDUCE49_IN_GGA(.(104, T80), 104, X190) → U16_GGA(T80, X190, reduce49_in_gga(T80, 104, X190))
REDUCE49_IN_GGA(.(104, T80), 104, X190) → REDUCE49_IN_GGA(T80, 104, X190)
REDUCE49_IN_GGA(.(119, T80), 119, X190) → U17_GGA(T80, X190, reduce49_in_gga(T80, 119, X190))
REDUCE49_IN_GGA(.(119, T80), 119, X190) → REDUCE49_IN_GGA(T80, 119, X190)
REDUCE49_IN_GGA(.(121, T80), 121, X190) → U18_GGA(T80, X190, reduce49_in_gga(T80, 121, X190))
REDUCE49_IN_GGA(.(121, T80), 121, X190) → REDUCE49_IN_GGA(T80, 121, X190)
REDUCE49_IN_GGA(.(T97, T98), T97, X251) → U19_GGA(T97, T98, X251, reduce49_in_gga(T98, T97, X251))
REDUCE49_IN_GGA(.(T97, T98), T97, X251) → REDUCE49_IN_GGA(T98, T97, X251)
REDUCE49_IN_GGA(.(T107, T108), T109, .(T107, X277)) → U20_GGA(T107, T108, T109, X277, reduce91_in_gga(T108, T107, X277))
REDUCE49_IN_GGA(.(T107, T108), T109, .(T107, X277)) → REDUCE91_IN_GGA(T108, T107, X277)
REDUCE91_IN_GGA(.(97, T125), 97, X321) → U21_GGA(T125, X321, reduce91_in_gga(T125, 97, X321))
REDUCE91_IN_GGA(.(97, T125), 97, X321) → REDUCE91_IN_GGA(T125, 97, X321)
REDUCE91_IN_GGA(.(101, T125), 101, X321) → U22_GGA(T125, X321, reduce91_in_gga(T125, 101, X321))
REDUCE91_IN_GGA(.(101, T125), 101, X321) → REDUCE91_IN_GGA(T125, 101, X321)
REDUCE91_IN_GGA(.(105, T125), 105, X321) → U23_GGA(T125, X321, reduce91_in_gga(T125, 105, X321))
REDUCE91_IN_GGA(.(105, T125), 105, X321) → REDUCE91_IN_GGA(T125, 105, X321)
REDUCE91_IN_GGA(.(111, T125), 111, X321) → U24_GGA(T125, X321, reduce91_in_gga(T125, 111, X321))
REDUCE91_IN_GGA(.(111, T125), 111, X321) → REDUCE91_IN_GGA(T125, 111, X321)
REDUCE91_IN_GGA(.(117, T125), 117, X321) → U25_GGA(T125, X321, reduce91_in_gga(T125, 117, X321))
REDUCE91_IN_GGA(.(117, T125), 117, X321) → REDUCE91_IN_GGA(T125, 117, X321)
REDUCE91_IN_GGA(.(104, T125), 104, X321) → U26_GGA(T125, X321, reduce91_in_gga(T125, 104, X321))
REDUCE91_IN_GGA(.(104, T125), 104, X321) → REDUCE91_IN_GGA(T125, 104, X321)
REDUCE91_IN_GGA(.(119, T125), 119, X321) → U27_GGA(T125, X321, reduce91_in_gga(T125, 119, X321))
REDUCE91_IN_GGA(.(119, T125), 119, X321) → REDUCE91_IN_GGA(T125, 119, X321)
REDUCE91_IN_GGA(.(121, T125), 121, X321) → U28_GGA(T125, X321, reduce91_in_gga(T125, 121, X321))
REDUCE91_IN_GGA(.(121, T125), 121, X321) → REDUCE91_IN_GGA(T125, 121, X321)
REDUCE91_IN_GGA(.(T142, T143), T142, X382) → U29_GGA(T142, T143, X382, reduce91_in_gga(T143, T142, X382))
REDUCE91_IN_GGA(.(T142, T143), T142, X382) → REDUCE91_IN_GGA(T143, T142, X382)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
reduce7_in_gga(x1, x2, x3)  =  reduce7_in_gga(x1, x2)
97  =  97
101  =  101
105  =  105
111  =  111
117  =  117
104  =  104
119  =  119
121  =  121
reduce49_in_gga(x1, x2, x3)  =  reduce49_in_gga(x1, x2)
reduce91_in_gga(x1, x2, x3)  =  reduce91_in_gga(x1, x2)
GOAL1_IN_GA(x1, x2)  =  GOAL1_IN_GA(x1)
U30_GA(x1, x2, x3, x4)  =  U30_GA(x1, x2, x4)
REDUCE7_IN_GGA(x1, x2, x3)  =  REDUCE7_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3)  =  U1_GGA(x1, x3)
U2_GGA(x1, x2, x3)  =  U2_GGA(x1, x3)
U3_GGA(x1, x2, x3)  =  U3_GGA(x1, x3)
U4_GGA(x1, x2, x3)  =  U4_GGA(x1, x3)
U5_GGA(x1, x2, x3)  =  U5_GGA(x1, x3)
U6_GGA(x1, x2, x3)  =  U6_GGA(x1, x3)
U7_GGA(x1, x2, x3)  =  U7_GGA(x1, x3)
U8_GGA(x1, x2, x3)  =  U8_GGA(x1, x3)
U9_GGA(x1, x2, x3, x4)  =  U9_GGA(x1, x2, x4)
U10_GGA(x1, x2, x3, x4, x5)  =  U10_GGA(x1, x2, x3, x5)
REDUCE49_IN_GGA(x1, x2, x3)  =  REDUCE49_IN_GGA(x1, x2)
U11_GGA(x1, x2, x3)  =  U11_GGA(x1, x3)
U12_GGA(x1, x2, x3)  =  U12_GGA(x1, x3)
U13_GGA(x1, x2, x3)  =  U13_GGA(x1, x3)
U14_GGA(x1, x2, x3)  =  U14_GGA(x1, x3)
U15_GGA(x1, x2, x3)  =  U15_GGA(x1, x3)
U16_GGA(x1, x2, x3)  =  U16_GGA(x1, x3)
U17_GGA(x1, x2, x3)  =  U17_GGA(x1, x3)
U18_GGA(x1, x2, x3)  =  U18_GGA(x1, x3)
U19_GGA(x1, x2, x3, x4)  =  U19_GGA(x1, x2, x4)
U20_GGA(x1, x2, x3, x4, x5)  =  U20_GGA(x1, x2, x3, x5)
REDUCE91_IN_GGA(x1, x2, x3)  =  REDUCE91_IN_GGA(x1, x2)
U21_GGA(x1, x2, x3)  =  U21_GGA(x1, x3)
U22_GGA(x1, x2, x3)  =  U22_GGA(x1, x3)
U23_GGA(x1, x2, x3)  =  U23_GGA(x1, x3)
U24_GGA(x1, x2, x3)  =  U24_GGA(x1, x3)
U25_GGA(x1, x2, x3)  =  U25_GGA(x1, x3)
U26_GGA(x1, x2, x3)  =  U26_GGA(x1, x3)
U27_GGA(x1, x2, x3)  =  U27_GGA(x1, x3)
U28_GGA(x1, x2, x3)  =  U28_GGA(x1, x3)
U29_GGA(x1, x2, x3, x4)  =  U29_GGA(x1, x2, x4)

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

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 33 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

REDUCE91_IN_GGA(.(T142, T143), T142, X382) → REDUCE91_IN_GGA(T143, T142, X382)
REDUCE91_IN_GGA(.(97, T125), 97, X321) → REDUCE91_IN_GGA(T125, 97, X321)
REDUCE91_IN_GGA(.(101, T125), 101, X321) → REDUCE91_IN_GGA(T125, 101, X321)
REDUCE91_IN_GGA(.(105, T125), 105, X321) → REDUCE91_IN_GGA(T125, 105, X321)
REDUCE91_IN_GGA(.(111, T125), 111, X321) → REDUCE91_IN_GGA(T125, 111, X321)
REDUCE91_IN_GGA(.(117, T125), 117, X321) → REDUCE91_IN_GGA(T125, 117, X321)
REDUCE91_IN_GGA(.(104, T125), 104, X321) → REDUCE91_IN_GGA(T125, 104, X321)
REDUCE91_IN_GGA(.(119, T125), 119, X321) → REDUCE91_IN_GGA(T125, 119, X321)
REDUCE91_IN_GGA(.(121, T125), 121, X321) → REDUCE91_IN_GGA(T125, 121, X321)

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
REDUCE91_IN_GGA(x1, x2, x3)  =  REDUCE91_IN_GGA(x1, x2)

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

(8) PiDPToQDPProof (SOUND transformation)

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

(9) Obligation:

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

REDUCE91_IN_GGA(.(T142, T143), T142) → REDUCE91_IN_GGA(T143, T142)
REDUCE91_IN_GGA(.(97, T125), 97) → REDUCE91_IN_GGA(T125, 97)
REDUCE91_IN_GGA(.(101, T125), 101) → REDUCE91_IN_GGA(T125, 101)
REDUCE91_IN_GGA(.(105, T125), 105) → REDUCE91_IN_GGA(T125, 105)
REDUCE91_IN_GGA(.(111, T125), 111) → REDUCE91_IN_GGA(T125, 111)
REDUCE91_IN_GGA(.(117, T125), 117) → REDUCE91_IN_GGA(T125, 117)
REDUCE91_IN_GGA(.(104, T125), 104) → REDUCE91_IN_GGA(T125, 104)
REDUCE91_IN_GGA(.(119, T125), 119) → REDUCE91_IN_GGA(T125, 119)
REDUCE91_IN_GGA(.(121, T125), 121) → REDUCE91_IN_GGA(T125, 121)

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

(10) 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:

• REDUCE91_IN_GGA(.(T142, T143), T142) → REDUCE91_IN_GGA(T143, T142)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(97, T125), 97) → REDUCE91_IN_GGA(T125, 97)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(101, T125), 101) → REDUCE91_IN_GGA(T125, 101)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(105, T125), 105) → REDUCE91_IN_GGA(T125, 105)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(111, T125), 111) → REDUCE91_IN_GGA(T125, 111)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(117, T125), 117) → REDUCE91_IN_GGA(T125, 117)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(104, T125), 104) → REDUCE91_IN_GGA(T125, 104)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(119, T125), 119) → REDUCE91_IN_GGA(T125, 119)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE91_IN_GGA(.(121, T125), 121) → REDUCE91_IN_GGA(T125, 121)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

(11) YES

(12) Obligation:

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

REDUCE49_IN_GGA(.(T97, T98), T97, X251) → REDUCE49_IN_GGA(T98, T97, X251)
REDUCE49_IN_GGA(.(97, T80), 97, X190) → REDUCE49_IN_GGA(T80, 97, X190)
REDUCE49_IN_GGA(.(101, T80), 101, X190) → REDUCE49_IN_GGA(T80, 101, X190)
REDUCE49_IN_GGA(.(105, T80), 105, X190) → REDUCE49_IN_GGA(T80, 105, X190)
REDUCE49_IN_GGA(.(111, T80), 111, X190) → REDUCE49_IN_GGA(T80, 111, X190)
REDUCE49_IN_GGA(.(117, T80), 117, X190) → REDUCE49_IN_GGA(T80, 117, X190)
REDUCE49_IN_GGA(.(104, T80), 104, X190) → REDUCE49_IN_GGA(T80, 104, X190)
REDUCE49_IN_GGA(.(119, T80), 119, X190) → REDUCE49_IN_GGA(T80, 119, X190)
REDUCE49_IN_GGA(.(121, T80), 121, X190) → REDUCE49_IN_GGA(T80, 121, X190)

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
REDUCE49_IN_GGA(x1, x2, x3)  =  REDUCE49_IN_GGA(x1, x2)

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

(13) PiDPToQDPProof (SOUND transformation)

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

(14) Obligation:

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

REDUCE49_IN_GGA(.(T97, T98), T97) → REDUCE49_IN_GGA(T98, T97)
REDUCE49_IN_GGA(.(97, T80), 97) → REDUCE49_IN_GGA(T80, 97)
REDUCE49_IN_GGA(.(101, T80), 101) → REDUCE49_IN_GGA(T80, 101)
REDUCE49_IN_GGA(.(105, T80), 105) → REDUCE49_IN_GGA(T80, 105)
REDUCE49_IN_GGA(.(111, T80), 111) → REDUCE49_IN_GGA(T80, 111)
REDUCE49_IN_GGA(.(117, T80), 117) → REDUCE49_IN_GGA(T80, 117)
REDUCE49_IN_GGA(.(104, T80), 104) → REDUCE49_IN_GGA(T80, 104)
REDUCE49_IN_GGA(.(119, T80), 119) → REDUCE49_IN_GGA(T80, 119)
REDUCE49_IN_GGA(.(121, T80), 121) → REDUCE49_IN_GGA(T80, 121)

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

(15) 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:

• REDUCE49_IN_GGA(.(T97, T98), T97) → REDUCE49_IN_GGA(T98, T97)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(97, T80), 97) → REDUCE49_IN_GGA(T80, 97)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(101, T80), 101) → REDUCE49_IN_GGA(T80, 101)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(105, T80), 105) → REDUCE49_IN_GGA(T80, 105)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(111, T80), 111) → REDUCE49_IN_GGA(T80, 111)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(117, T80), 117) → REDUCE49_IN_GGA(T80, 117)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(104, T80), 104) → REDUCE49_IN_GGA(T80, 104)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(119, T80), 119) → REDUCE49_IN_GGA(T80, 119)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE49_IN_GGA(.(121, T80), 121) → REDUCE49_IN_GGA(T80, 121)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

(16) YES

(17) Obligation:

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

REDUCE7_IN_GGA(.(T52, T53), T52, X120) → REDUCE7_IN_GGA(T53, T52, X120)
REDUCE7_IN_GGA(.(97, T35), 97, X59) → REDUCE7_IN_GGA(T35, 97, X59)
REDUCE7_IN_GGA(.(101, T35), 101, X59) → REDUCE7_IN_GGA(T35, 101, X59)
REDUCE7_IN_GGA(.(105, T35), 105, X59) → REDUCE7_IN_GGA(T35, 105, X59)
REDUCE7_IN_GGA(.(111, T35), 111, X59) → REDUCE7_IN_GGA(T35, 111, X59)
REDUCE7_IN_GGA(.(117, T35), 117, X59) → REDUCE7_IN_GGA(T35, 117, X59)
REDUCE7_IN_GGA(.(104, T35), 104, X59) → REDUCE7_IN_GGA(T35, 104, X59)
REDUCE7_IN_GGA(.(119, T35), 119, X59) → REDUCE7_IN_GGA(T35, 119, X59)
REDUCE7_IN_GGA(.(121, T35), 121, X59) → REDUCE7_IN_GGA(T35, 121, X59)

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

(18) PiDPToQDPProof (SOUND transformation)

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

(19) Obligation:

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

REDUCE7_IN_GGA(.(T52, T53), T52) → REDUCE7_IN_GGA(T53, T52)
REDUCE7_IN_GGA(.(97, T35), 97) → REDUCE7_IN_GGA(T35, 97)
REDUCE7_IN_GGA(.(101, T35), 101) → REDUCE7_IN_GGA(T35, 101)
REDUCE7_IN_GGA(.(105, T35), 105) → REDUCE7_IN_GGA(T35, 105)
REDUCE7_IN_GGA(.(111, T35), 111) → REDUCE7_IN_GGA(T35, 111)
REDUCE7_IN_GGA(.(117, T35), 117) → REDUCE7_IN_GGA(T35, 117)
REDUCE7_IN_GGA(.(104, T35), 104) → REDUCE7_IN_GGA(T35, 104)
REDUCE7_IN_GGA(.(119, T35), 119) → REDUCE7_IN_GGA(T35, 119)
REDUCE7_IN_GGA(.(121, T35), 121) → REDUCE7_IN_GGA(T35, 121)

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

(20) 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(.(T52, T53), T52) → REDUCE7_IN_GGA(T53, T52)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(97, T35), 97) → REDUCE7_IN_GGA(T35, 97)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(101, T35), 101) → REDUCE7_IN_GGA(T35, 101)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(105, T35), 105) → REDUCE7_IN_GGA(T35, 105)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(111, T35), 111) → REDUCE7_IN_GGA(T35, 111)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(117, T35), 117) → REDUCE7_IN_GGA(T35, 117)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(104, T35), 104) → REDUCE7_IN_GGA(T35, 104)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(119, T35), 119) → REDUCE7_IN_GGA(T35, 119)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

• REDUCE7_IN_GGA(.(121, T35), 121) → REDUCE7_IN_GGA(T35, 121)
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2

(21) YES