Runtime Complexity proof of /tmp/tmpDARmM1/countstack2.pl

Runtime Complexity of the query pattern
countstack(g,a)
w.r.t. the given Prolog program could be shown to be BOUNDS(O(1), O(n^1)).

0 Prolog

↳1 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 178 ms)

↳2 CdtProblem

    ↳3 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳4 CdtProblem

    ↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 168 ms)

    ↳6 CdtProblem

    ↳7 SIsEmptyProof (⇔, 0 ms)

    ↳8 BOUNDS(O(1), O(1))

↳9 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 151 ms)

↳10 CdtProblem

    ↳11 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳12 CdtProblem

    ↳13 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 4 ms)

    ↳14 CdtProblem

(0) Obligation:

Clauses:

countstack(empty, 0).
countstack(S, X) :- ','(no(empty_stack(S)), ','(pop(S, nil), ','(popped(S, Pd), countstack(Pd, X)))).
countstack(S, s(X)) :- ','(no(empty_stack(S)), ','(pop(S, P), ','(no(empty_list(P)), ','(head(P, H), ','(tail(P, T), ','(popped(S, Pd), countstack(push(H, push(T, Pd)), X))))))).
pop(empty, X1).
pop(push(P, X2), P).
popped(empty, empty).
popped(push(X3, Pd), Pd).
head(nil, X4).
head(cons(H, X5), H).
tail(nil, nil).
tail(cons(X6, T), T).
empty_stack(empty).
empty_list(nil).
no(X) :- ','(X, ','(!, failure(a))).
no(X7).
failure(b).

Query: countstack(g,a)

(1) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="2: countstack(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
3 [label="3: countstack(T1, T2), SCOPE: 1, CLAUSE: 0 | countstack(T1, T2), SCOPE: 1, CLAUSE: 1 | countstack(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true | countstack(empty, T2), SCOPE: 1, CLAUSE: 1 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: countstack(T1, T2), SCOPE: 1, CLAUSE: 1 | countstack(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground\ncountstack(T1, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: countstack(empty, T2), SCOPE: 1, CLAUSE: 1 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))) | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 2, CLAUSE: 13 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 2, CLAUSE: 14 | ?_2 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(','(call(empty_stack(empty)), ','(!_2, failure(a))), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))) | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 2, CLAUSE: 14 | ?_2 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(empty_stack(empty), ','(','(!_2, failure(a)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5))))) | ?_3 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 2, CLAUSE: 14 | ?_2 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(empty_stack(empty), ','(','(!_2, failure(a)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5))))), SCOPE: 4, CLAUSE: 11 | ?_4 | ?_3 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 2, CLAUSE: 14 | ?_2 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(','(!_2, failure(a)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))) | ?_4 | ?_3 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 2, CLAUSE: 14 | ?_2 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))) | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X12), countstack(X12, T5)))), SCOPE: 5, CLAUSE: 15 | ?_5 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ?_5 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9)))))))\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 6, CLAUSE: 13 | ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 6, CLAUSE: 14\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(','(call(empty_stack(empty)), ','(!_6, failure(a))), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))) | ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 6, CLAUSE: 14\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(empty_stack(empty), ','(','(!_6, failure(a)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9)))))))) | ?_7 | ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 6, CLAUSE: 14\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(empty_stack(empty), ','(','(!_6, failure(a)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9)))))))), SCOPE: 8, CLAUSE: 11 | ?_8 | ?_7 | ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 6, CLAUSE: 14\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(','(!_6, failure(a)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))) | ?_8 | ?_7 | ','(no(empty_stack(empty)), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 6, CLAUSE: 14\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(failure(a), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9)))))))\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(failure(a), ','(pop(empty, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(empty, X29), countstack(push(X27, push(X28, X29)), T9))))))), SCOPE: 9, CLAUSE: 15\n\nX26 is free\nX27 is free\nX28 is free\nX29 is free", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(no(empty_stack(T12)), ','(pop(T12, nil), ','(popped(T12, X37), countstack(X37, T14)))) | countstack(T12, T2), SCOPE: 1, CLAUSE: 2\n\nT12 is ground\nX37 is free\ncountstack(T12, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(no(empty_stack(T12)), ','(pop(T12, nil), ','(popped(T12, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 13 | ','(no(empty_stack(T12)), ','(pop(T12, nil), ','(popped(T12, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T12, T2), SCOPE: 1, CLAUSE: 2\n\nT12 is ground\nX37 is free\ncountstack(T12, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(','(call(empty_stack(T17)), ','(!_10, failure(a))), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))) | ','(no(empty_stack(T17)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T17, T2), SCOPE: 1, CLAUSE: 2\n\nT17 is ground\nX37 is free\ncountstack(T17, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(empty_stack(T17), ','(','(!_10, failure(a)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14))))) | ?_11 | ','(no(empty_stack(T17)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T17, T2), SCOPE: 1, CLAUSE: 2\n\nT17 is ground\nX37 is free\ncountstack(T17, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(empty_stack(T17), ','(','(!_10, failure(a)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14))))), SCOPE: 12, CLAUSE: 11 | ?_12 | ?_11 | ','(no(empty_stack(T17)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T17, T2), SCOPE: 1, CLAUSE: 2\n\nT17 is ground\nX37 is free\ncountstack(T17, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(','(!_10, failure(a)), ','(pop(empty, nil), ','(popped(empty, X37), countstack(X37, T14)))) | ?_12 | ?_11 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX37 is free\ncountstack(empty, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ?_12 | ?_11 | ','(no(empty_stack(T17)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T17, T2), SCOPE: 1, CLAUSE: 2\n\nT17 is ground\nX37 is free\ncountstack(T17, T2) !=? countstack(empty, 0)\nempty_stack(T17) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X37), countstack(X37, T14)))) | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX37 is free\ncountstack(empty, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X37), countstack(X37, T14)))), SCOPE: 13, CLAUSE: 15 | ?_13 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\nX37 is free\ncountstack(empty, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ?_13 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\ncountstack(empty, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\ncountstack(empty, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21)))))))\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 14, CLAUSE: 13 | ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 14, CLAUSE: 14\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(','(call(empty_stack(empty)), ','(!_14, failure(a))), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))) | ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 14, CLAUSE: 14\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(empty_stack(empty), ','(','(!_14, failure(a)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21)))))))) | ?_15 | ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 14, CLAUSE: 14\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(empty_stack(empty), ','(','(!_14, failure(a)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21)))))))), SCOPE: 16, CLAUSE: 11 | ?_16 | ?_15 | ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 14, CLAUSE: 14\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(','(!_14, failure(a)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))) | ?_16 | ?_15 | ','(no(empty_stack(empty)), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 14, CLAUSE: 14\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(failure(a), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21)))))))\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(failure(a), ','(pop(empty, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(empty, X54), countstack(push(X52, push(X53, X54)), T21))))))), SCOPE: 17, CLAUSE: 15\n\nX51 is free\nX52 is free\nX53 is free\nX54 is free", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ?_11 | ','(no(empty_stack(T17)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T17, T2), SCOPE: 1, CLAUSE: 2\n\nT17 is ground\nX37 is free\ncountstack(T17, T2) !=? countstack(empty, 0)\nempty_stack(T17) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(no(empty_stack(T17)), ','(pop(T17, nil), ','(popped(T17, X37), countstack(X37, T14)))), SCOPE: 10, CLAUSE: 14 | ?_10 | countstack(T17, T2), SCOPE: 1, CLAUSE: 2\n\nT17 is ground\nX37 is free\ncountstack(T17, T2) !=? countstack(empty, 0)\nempty_stack(T17) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(pop(T24, nil), ','(popped(T24, X37), countstack(X37, T14))) | ?_10 | countstack(T24, T2), SCOPE: 1, CLAUSE: 2\n\nT24 is ground\nX37 is free\ncountstack(T24, T2) !=? countstack(empty, 0)\nempty_stack(T24) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(pop(T24, nil), ','(popped(T24, X37), countstack(X37, T14))), SCOPE: 18, CLAUSE: 3 | ','(pop(T24, nil), ','(popped(T24, X37), countstack(X37, T14))), SCOPE: 18, CLAUSE: 4 | ?_18 | ?_10 | countstack(T24, T2), SCOPE: 1, CLAUSE: 2\n\nT24 is ground\nX37 is free\ncountstack(T24, T2) !=? countstack(empty, 0)\nempty_stack(T24) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(pop(T24, nil), ','(popped(T24, X37), countstack(X37, T14))), SCOPE: 18, CLAUSE: 4 | ?_18 | ?_10 | countstack(T24, T2), SCOPE: 1, CLAUSE: 2\n\nT24 is ground\nX37 is free\ncountstack(T24, T2) !=? countstack(empty, 0)\nempty_stack(T24) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ','(popped(push(nil, T30), X37), countstack(X37, T14)) | ?_18 | ?_10 | countstack(push(nil, T30), T2), SCOPE: 1, CLAUSE: 2\n\nT30 is ground\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ?_18 | ?_10 | countstack(T24, T2), SCOPE: 1, CLAUSE: 2\n\nT24 is ground\nX66 is free\nX67 is free\ncountstack(T24, T2) !=? countstack(empty, 0)\nempty_stack(T24) !=? empty_stack(empty)\npop(T24, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(popped(push(nil, T30), X37), countstack(X37, T14)), SCOPE: 19, CLAUSE: 5 | ','(popped(push(nil, T30), X37), countstack(X37, T14)), SCOPE: 19, CLAUSE: 6 | ?_19 | ?_18 | ?_10 | countstack(push(nil, T30), T2), SCOPE: 1, CLAUSE: 2\n\nT30 is ground\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(popped(push(nil, T30), X37), countstack(X37, T14)), SCOPE: 19, CLAUSE: 6 | ?_19 | ?_18 | ?_10 | countstack(push(nil, T30), T2), SCOPE: 1, CLAUSE: 2\n\nT30 is ground\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: countstack(T33, T14) | ?_19 | ?_18 | ?_10 | countstack(push(nil, T33), T2), SCOPE: 1, CLAUSE: 2\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: countstack(T33, T14)\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ?_19 | ?_18 | ?_10 | countstack(push(nil, T33), T2), SCOPE: 1, CLAUSE: 2\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ?_18 | ?_10 | countstack(push(nil, T33), T2), SCOPE: 1, CLAUSE: 2\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ?_10 | countstack(push(nil, T33), T2), SCOPE: 1, CLAUSE: 2\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: countstack(push(nil, T33), T2), SCOPE: 1, CLAUSE: 2\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(no(empty_stack(push(nil, T38))), ','(pop(push(nil, T38), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T38), X87), countstack(push(X85, push(X86, X87)), T40)))))))\n\nT38 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(no(empty_stack(push(nil, T38))), ','(pop(push(nil, T38), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T38), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 13 | ','(no(empty_stack(push(nil, T38))), ','(pop(push(nil, T38), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T38), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT38 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(','(call(empty_stack(push(nil, T43))), ','(!_20, failure(a))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))) | ','(no(empty_stack(push(nil, T43))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT43 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(empty_stack(push(nil, T43)), ','(','(!_20, failure(a)), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40)))))))) | ?_21 | ','(no(empty_stack(push(nil, T43))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT43 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(empty_stack(push(nil, T43)), ','(','(!_20, failure(a)), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40)))))))), SCOPE: 22, CLAUSE: 11 | ?_22 | ?_21 | ','(no(empty_stack(push(nil, T43))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT43 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ?_22 | ?_21 | ','(no(empty_stack(push(nil, T43))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT43 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: ?_21 | ','(no(empty_stack(push(nil, T43))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT43 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(no(empty_stack(push(nil, T43))), ','(pop(push(nil, T43), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T43), X87), countstack(push(X85, push(X86, X87)), T40))))))), SCOPE: 20, CLAUSE: 14\n\nT43 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(pop(push(nil, T46), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T46), X87), countstack(push(X85, push(X86, X87)), T40))))))\n\nT46 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(pop(push(nil, T46), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T46), X87), countstack(push(X85, push(X86, X87)), T40)))))), SCOPE: 23, CLAUSE: 3 | ','(pop(push(nil, T46), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T46), X87), countstack(push(X85, push(X86, X87)), T40)))))), SCOPE: 23, CLAUSE: 4\n\nT46 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(pop(push(nil, T46), X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(push(nil, T46), X87), countstack(push(X85, push(X86, X87)), T40)))))), SCOPE: 23, CLAUSE: 4\n\nT46 is ground\nX84 is free\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40)))))\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 24, CLAUSE: 13 | ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 24, CLAUSE: 14\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ','(','(call(empty_list(nil)), ','(!_24, failure(a))), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))) | ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 24, CLAUSE: 14\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(empty_list(nil), ','(','(!_24, failure(a)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40)))))) | ?_25 | ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 24, CLAUSE: 14\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(empty_list(nil), ','(','(!_24, failure(a)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40)))))), SCOPE: 26, CLAUSE: 12 | ?_26 | ?_25 | ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 24, CLAUSE: 14\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(','(!_24, failure(a)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))) | ?_26 | ?_25 | ','(no(empty_list(nil)), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 24, CLAUSE: 14\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(failure(a), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40)))))\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(failure(a), ','(head(nil, X85), ','(tail(nil, X86), ','(popped(push(nil, T49), X87), countstack(push(X85, push(X86, X87)), T40))))), SCOPE: 27, CLAUSE: 15\n\nT49 is ground\nX85 is free\nX86 is free\nX87 is free", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ?_10 | countstack(T24, T2), SCOPE: 1, CLAUSE: 2\n\nT24 is ground\nX66 is free\nX67 is free\ncountstack(T24, T2) !=? countstack(empty, 0)\nempty_stack(T24) !=? empty_stack(empty)\npop(T24, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: countstack(T24, T2), SCOPE: 1, CLAUSE: 2\n\nT24 is ground\nX66 is free\nX67 is free\ncountstack(T24, T2) !=? countstack(empty, 0)\nempty_stack(T24) !=? empty_stack(empty)\npop(T24, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(no(empty_stack(T54)), ','(pop(T54, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T54, X117), countstack(push(X115, push(X116, X117)), T56)))))))\n\nT54 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T54, T2) !=? countstack(empty, 0)\nempty_stack(T54) !=? empty_stack(empty)\npop(T54, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(no(empty_stack(T54)), ','(pop(T54, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T54, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 13 | ','(no(empty_stack(T54)), ','(pop(T54, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T54, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT54 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T54, T2) !=? countstack(empty, 0)\nempty_stack(T54) !=? empty_stack(empty)\npop(T54, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: ','(','(call(empty_stack(T59)), ','(!_28, failure(a))), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))) | ','(no(empty_stack(T59)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT59 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T59, T2) !=? countstack(empty, 0)\nempty_stack(T59) !=? empty_stack(empty)\npop(T59, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: ','(empty_stack(T59), ','(','(!_28, failure(a)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56)))))))) | ?_29 | ','(no(empty_stack(T59)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT59 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T59, T2) !=? countstack(empty, 0)\nempty_stack(T59) !=? empty_stack(empty)\npop(T59, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(empty_stack(T59), ','(','(!_28, failure(a)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56)))))))), SCOPE: 30, CLAUSE: 11 | ?_30 | ?_29 | ','(no(empty_stack(T59)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT59 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T59, T2) !=? countstack(empty, 0)\nempty_stack(T59) !=? empty_stack(empty)\npop(T59, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: ?_30 | ?_29 | ','(no(empty_stack(T59)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT59 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T59, T2) !=? countstack(empty, 0)\nempty_stack(T59) !=? empty_stack(empty)\npop(T59, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: ?_29 | ','(no(empty_stack(T59)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT59 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T59, T2) !=? countstack(empty, 0)\nempty_stack(T59) !=? empty_stack(empty)\npop(T59, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(no(empty_stack(T59)), ','(pop(T59, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T59, X117), countstack(push(X115, push(X116, X117)), T56))))))), SCOPE: 28, CLAUSE: 14\n\nT59 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T59, T2) !=? countstack(empty, 0)\nempty_stack(T59) !=? empty_stack(empty)\npop(T59, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(pop(T62, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T62, X117), countstack(push(X115, push(X116, X117)), T56))))))\n\nT62 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T62, T2) !=? countstack(empty, 0)\nempty_stack(T62) !=? empty_stack(empty)\npop(T62, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: ','(pop(T62, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T62, X117), countstack(push(X115, push(X116, X117)), T56)))))), SCOPE: 31, CLAUSE: 3 | ','(pop(T62, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T62, X117), countstack(push(X115, push(X116, X117)), T56)))))), SCOPE: 31, CLAUSE: 4\n\nT62 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T62, T2) !=? countstack(empty, 0)\nempty_stack(T62) !=? empty_stack(empty)\npop(T62, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(pop(T62, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(T62, X117), countstack(push(X115, push(X116, X117)), T56)))))), SCOPE: 31, CLAUSE: 4\n\nT62 is ground\nX66 is free\nX67 is free\nX114 is free\nX115 is free\nX116 is free\nX117 is free\ncountstack(T62, T2) !=? countstack(empty, 0)\nempty_stack(T62) !=? empty_stack(empty)\npop(T62, nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: ','(no(empty_list(T67)), ','(head(T67, X115), ','(tail(T67, X116), ','(popped(push(T67, T68), X117), countstack(push(X115, push(X116, X117)), T56)))))\n\nT67 is ground\nT68 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T67, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(no(empty_list(T67)), ','(head(T67, X115), ','(tail(T67, X116), ','(popped(push(T67, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 13 | ','(no(empty_list(T67)), ','(head(T67, X115), ','(tail(T67, X116), ','(popped(push(T67, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT67 is ground\nT68 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T67, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: ','(','(call(empty_list(T71)), ','(!_32, failure(a))), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))) | ','(no(empty_list(T71)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT68 is ground\nT71 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T71, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(empty_list(T71), ','(','(!_32, failure(a)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56)))))) | ?_33 | ','(no(empty_list(T71)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT68 is ground\nT71 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T71, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: ','(empty_list(T71), ','(','(!_32, failure(a)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56)))))), SCOPE: 34, CLAUSE: 12 | ?_34 | ?_33 | ','(no(empty_list(T71)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT68 is ground\nT71 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T71, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: ?_34 | ?_33 | ','(no(empty_list(T71)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT68 is ground\nT71 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T71, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ?_33 | ','(no(empty_list(T71)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT68 is ground\nT71 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T71, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: ','(no(empty_list(T71)), ','(head(T71, X115), ','(tail(T71, X116), ','(popped(push(T71, T68), X117), countstack(push(X115, push(X116, X117)), T56))))), SCOPE: 32, CLAUSE: 14\n\nT68 is ground\nT71 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T71, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(head(T74, X115), ','(tail(T74, X116), ','(popped(push(T74, T68), X117), countstack(push(X115, push(X116, X117)), T56))))\n\nT68 is ground\nT74 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T74, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: ','(head(T74, X115), ','(tail(T74, X116), ','(popped(push(T74, T68), X117), countstack(push(X115, push(X116, X117)), T56)))), SCOPE: 35, CLAUSE: 7 | ','(head(T74, X115), ','(tail(T74, X116), ','(popped(push(T74, T68), X117), countstack(push(X115, push(X116, X117)), T56)))), SCOPE: 35, CLAUSE: 8\n\nT68 is ground\nT74 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T74, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: ','(head(T74, X115), ','(tail(T74, X116), ','(popped(push(T74, T68), X117), countstack(push(X115, push(X116, X117)), T56)))), SCOPE: 35, CLAUSE: 8\n\nT68 is ground\nT74 is ground\nX66 is free\nX67 is free\nX115 is free\nX116 is free\nX117 is free\npop(push(T74, T68), nil) !=? pop(push(X66, X67), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: ','(tail(cons(T79, T80), X116), ','(popped(push(cons(T79, T80), T68), X117), countstack(push(T79, push(X116, X117)), T56)))\n\nT68 is ground\nT79 is ground\nT80 is ground\nX116 is free\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: ','(tail(cons(T79, T80), X116), ','(popped(push(cons(T79, T80), T68), X117), countstack(push(T79, push(X116, X117)), T56))), SCOPE: 36, CLAUSE: 9 | ','(tail(cons(T79, T80), X116), ','(popped(push(cons(T79, T80), T68), X117), countstack(push(T79, push(X116, X117)), T56))), SCOPE: 36, CLAUSE: 10\n\nT68 is ground\nT79 is ground\nT80 is ground\nX116 is free\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: ','(tail(cons(T79, T80), X116), ','(popped(push(cons(T79, T80), T68), X117), countstack(push(T79, push(X116, X117)), T56))), SCOPE: 36, CLAUSE: 10\n\nT68 is ground\nT79 is ground\nT80 is ground\nX116 is free\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(popped(push(cons(T85, T86), T68), X117), countstack(push(T85, push(T86, X117)), T56))\n\nT68 is ground\nT85 is ground\nT86 is ground\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(popped(push(cons(T85, T86), T68), X117), countstack(push(T85, push(T86, X117)), T56)), SCOPE: 37, CLAUSE: 5 | ','(popped(push(cons(T85, T86), T68), X117), countstack(push(T85, push(T86, X117)), T56)), SCOPE: 37, CLAUSE: 6\n\nT68 is ground\nT85 is ground\nT86 is ground\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: ','(popped(push(cons(T85, T86), T68), X117), countstack(push(T85, push(T86, X117)), T56)), SCOPE: 37, CLAUSE: 6\n\nT68 is ground\nT85 is ground\nT86 is ground\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: countstack(push(T93, push(T94, T95)), T56)\n\nT93 is ground\nT94 is ground\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 205 [arrowhead = none ];
205 -> 3;

206 [label="EVAL with clause\ncountstack(empty, 0).\nand substitutionT1 -> empty,\nT2 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
3 -> 206 [arrowhead = none ];
206 -> 5;

207 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 207 [arrowhead = none ];
207 -> 7;

208 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 208 [arrowhead = none ];
208 -> 9;

209 [label="ONLY EVAL with clause\ncountstack(X35, X36) :- ','(no(empty_stack(X35)), ','(pop(X35, nil), ','(popped(X35, X37), countstack(X37, X36)))).\nand substitutionT1 -> T12,\nX35 -> T12,\nT2 -> T14,\nX36 -> T14,\nT13 -> T14", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 209 [arrowhead = none ];
209 -> 51;

210 [label="ONLY EVAL with clause\ncountstack(X10, X11) :- ','(no(empty_stack(X10)), ','(pop(X10, nil), ','(popped(X10, X12), countstack(X12, X11)))).\nand substitutionX10 -> empty,\nT2 -> T5,\nX11 -> T5,\nT4 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 210 [arrowhead = none ];
210 -> 11;

211 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
11 -> 211 [arrowhead = none ];
211 -> 13;

212 [label="ONLY EVAL with clause\nno(X15) :- ','(call(X15), ','(!_2, failure(a))).\nand substitutionX15 -> empty_stack(empty)", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 212 [arrowhead = none ];
212 -> 15;

213 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 213 [arrowhead = none ];
213 -> 16;

214 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 214 [arrowhead = none ];
214 -> 17;

215 [label="ONLY EVAL with clause\nempty_stack(empty).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 215 [arrowhead = none ];
215 -> 19;

216 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 216 [arrowhead = none ];
216 -> 21;

217 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
21 -> 217 [arrowhead = none ];
217 -> 23;

218 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 218 [arrowhead = none ];
218 -> 24;

219 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 219 [arrowhead = none ];
219 -> 27;

220 [label="EVAL with clause\ncountstack(X24, s(X25)) :- ','(no(empty_stack(X24)), ','(pop(X24, X26), ','(no(empty_list(X26)), ','(head(X26, X27), ','(tail(X26, X28), ','(popped(X24, X29), countstack(push(X27, push(X28, X29)), X25))))))).\nand substitutionX24 -> empty,\nX25 -> T9,\nT2 -> s(T9),\nT8 -> T9", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 220 [arrowhead = none ];
220 -> 32;

221 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 221 [arrowhead = none ];
221 -> 33;

222 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
32 -> 222 [arrowhead = none ];
222 -> 34;

223 [label="ONLY EVAL with clause\nno(X32) :- ','(call(X32), ','(!_6, failure(a))).\nand substitutionX32 -> empty_stack(empty)", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 223 [arrowhead = none ];
223 -> 37;

224 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
37 -> 224 [arrowhead = none ];
224 -> 39;

225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 225 [arrowhead = none ];
225 -> 40;

226 [label="ONLY EVAL with clause\nempty_stack(empty).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 226 [arrowhead = none ];
226 -> 42;

227 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 227 [arrowhead = none ];
227 -> 43;

228 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 228 [arrowhead = none ];
228 -> 45;

229 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
45 -> 229 [arrowhead = none ];
229 -> 47;

230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
51 -> 230 [arrowhead = none ];
230 -> 53;

231 [label="ONLY EVAL with clause\nno(X40) :- ','(call(X40), ','(!_10, failure(a))).\nand substitutionT12 -> T17,\nX40 -> empty_stack(T17)", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 231 [arrowhead = none ];
231 -> 54;

232 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 232 [arrowhead = none ];
232 -> 57;

233 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
57 -> 233 [arrowhead = none ];
233 -> 58;

234 [label="EVAL with clause\nempty_stack(empty).\nand substitutionT17 -> empty", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 234 [arrowhead = none ];
234 -> 59;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 235 [arrowhead = none ];
235 -> 60;

236 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 236 [arrowhead = none ];
236 -> 61;

237 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 237 [arrowhead = none ];
237 -> 89;

238 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
61 -> 238 [arrowhead = none ];
238 -> 62;

239 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 239 [arrowhead = none ];
239 -> 63;

240 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
63 -> 240 [arrowhead = none ];
240 -> 64;

241 [label="EVAL with clause\ncountstack(X49, s(X50)) :- ','(no(empty_stack(X49)), ','(pop(X49, X51), ','(no(empty_list(X51)), ','(head(X51, X52), ','(tail(X51, X53), ','(popped(X49, X54), countstack(push(X52, push(X53, X54)), X50))))))).\nand substitutionX49 -> empty,\nX50 -> T21,\nT2 -> s(T21),\nT20 -> T21", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 241 [arrowhead = none ];
241 -> 68;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 242 [arrowhead = none ];
242 -> 70;

243 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 243 [arrowhead = none ];
243 -> 72;

244 [label="ONLY EVAL with clause\nno(X57) :- ','(call(X57), ','(!_14, failure(a))).\nand substitutionX57 -> empty_stack(empty)", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 244 [arrowhead = none ];
244 -> 78;

245 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
78 -> 245 [arrowhead = none ];
245 -> 81;

246 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
81 -> 246 [arrowhead = none ];
246 -> 82;

247 [label="ONLY EVAL with clause\nempty_stack(empty).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 247 [arrowhead = none ];
247 -> 83;

248 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 248 [arrowhead = none ];
248 -> 84;

249 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 249 [arrowhead = none ];
249 -> 86;

250 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
86 -> 250 [arrowhead = none ];
250 -> 87;

251 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 251 [arrowhead = none ];
251 -> 91;

252 [label="ONLY EVAL with clause\nno(X60).\nand substitutionT17 -> T24,\nX60 -> empty_stack(T24)", fontsize=14, style = filled, fillcolor = lightblue];
91 -> 252 [arrowhead = none ];
252 -> 92;

253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
92 -> 253 [arrowhead = none ];
253 -> 94;

254 [label="BACKTRACK\nfor clause: pop(empty, X1)\nwith clash: (empty_stack(T24), empty_stack(empty))", fontsize=14, style = filled, fillcolor = lightgreen];
94 -> 254 [arrowhead = none ];
254 -> 96;

255 [label="EVAL with clause\npop(push(X66, X67), X66).\nand substitutionX66 -> nil,\nX67 -> T30,\nT24 -> push(nil, T30),\nT29 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 255 [arrowhead = none ];
255 -> 99;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
96 -> 256 [arrowhead = none ];
256 -> 101;

257 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
99 -> 257 [arrowhead = none ];
257 -> 102;

258 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 258 [arrowhead = none ];
258 -> 149;

259 [label="BACKTRACK\nfor clause: popped(empty, empty)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 259 [arrowhead = none ];
259 -> 103;

260 [label="ONLY EVAL with clause\npopped(push(X72, X73), X73).\nand substitutionX72 -> nil,\nT30 -> T33,\nX73 -> T33,\nX37 -> T33", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 260 [arrowhead = none ];
260 -> 104;

261 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 261 [arrowhead = none ];
261 -> 105;

262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 262 [arrowhead = none ];
262 -> 106;

263 [label="INSTANCE with matching:\nT1 -> T33\nT2 -> T14", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 263 [arrowhead = none , style=dashed];
263 -> 2[style=dashed];

264 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
106 -> 264 [arrowhead = none ];
264 -> 107;

265 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 265 [arrowhead = none ];
265 -> 108;

266 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 266 [arrowhead = none ];
266 -> 109;

267 [label="EVAL with clause\ncountstack(X82, s(X83)) :- ','(no(empty_stack(X82)), ','(pop(X82, X84), ','(no(empty_list(X84)), ','(head(X84, X85), ','(tail(X84, X86), ','(popped(X82, X87), countstack(push(X85, push(X86, X87)), X83))))))).\nand substitutionT33 -> T38,\nX82 -> push(nil, T38),\nX83 -> T40,\nT2 -> s(T40),\nT39 -> T40", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 267 [arrowhead = none ];
267 -> 110;

268 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
109 -> 268 [arrowhead = none ];
268 -> 111;

269 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
110 -> 269 [arrowhead = none ];
269 -> 114;

270 [label="ONLY EVAL with clause\nno(X90) :- ','(call(X90), ','(!_20, failure(a))).\nand substitutionT38 -> T43,\nX90 -> empty_stack(push(nil, T43))", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 270 [arrowhead = none ];
270 -> 116;

271 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
116 -> 271 [arrowhead = none ];
271 -> 117;

272 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
117 -> 272 [arrowhead = none ];
272 -> 119;

273 [label="BACKTRACK\nfor clause: empty_stack(empty)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 273 [arrowhead = none ];
273 -> 121;

274 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
121 -> 274 [arrowhead = none ];
274 -> 122;

275 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 275 [arrowhead = none ];
275 -> 123;

276 [label="ONLY EVAL with clause\nno(X93).\nand substitutionT43 -> T46,\nX93 -> empty_stack(push(nil, T46))", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 276 [arrowhead = none ];
276 -> 128;

277 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
128 -> 277 [arrowhead = none ];
277 -> 131;

278 [label="BACKTRACK\nfor clause: pop(empty, X1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 278 [arrowhead = none ];
278 -> 133;

279 [label="ONLY EVAL with clause\npop(push(X99, X100), X99).\nand substitutionX99 -> nil,\nT46 -> T49,\nX100 -> T49,\nX84 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 279 [arrowhead = none ];
279 -> 136;

280 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
136 -> 280 [arrowhead = none ];
280 -> 138;

281 [label="ONLY EVAL with clause\nno(X103) :- ','(call(X103), ','(!_24, failure(a))).\nand substitutionX103 -> empty_list(nil)", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 281 [arrowhead = none ];
281 -> 140;

282 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
140 -> 282 [arrowhead = none ];
282 -> 141;

283 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
141 -> 283 [arrowhead = none ];
283 -> 142;

284 [label="ONLY EVAL with clause\nempty_list(nil).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 284 [arrowhead = none ];
284 -> 143;

285 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 285 [arrowhead = none ];
285 -> 144;

286 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
144 -> 286 [arrowhead = none ];
286 -> 146;

287 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
146 -> 287 [arrowhead = none ];
287 -> 147;

288 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 288 [arrowhead = none ];
288 -> 151;

289 [label="EVAL with clause\ncountstack(X112, s(X113)) :- ','(no(empty_stack(X112)), ','(pop(X112, X114), ','(no(empty_list(X114)), ','(head(X114, X115), ','(tail(X114, X116), ','(popped(X112, X117), countstack(push(X115, push(X116, X117)), X113))))))).\nand substitutionT24 -> T54,\nX112 -> T54,\nX113 -> T56,\nT2 -> s(T56),\nT55 -> T56", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 289 [arrowhead = none ];
289 -> 161;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 290 [arrowhead = none ];
290 -> 163;

291 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 291 [arrowhead = none ];
291 -> 164;

292 [label="ONLY EVAL with clause\nno(X120) :- ','(call(X120), ','(!_28, failure(a))).\nand substitutionT54 -> T59,\nX120 -> empty_stack(T59)", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 292 [arrowhead = none ];
292 -> 168;

293 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
168 -> 293 [arrowhead = none ];
293 -> 169;

294 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
169 -> 294 [arrowhead = none ];
294 -> 172;

295 [label="BACKTRACK\nfor clause: empty_stack(empty)\nwith clash: (empty_stack(T59), empty_stack(empty))", fontsize=14, style = filled, fillcolor = lightgreen];
172 -> 295 [arrowhead = none ];
295 -> 175;

296 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
175 -> 296 [arrowhead = none ];
296 -> 176;

297 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
176 -> 297 [arrowhead = none ];
297 -> 177;

298 [label="ONLY EVAL with clause\nno(X123).\nand substitutionT59 -> T62,\nX123 -> empty_stack(T62)", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 298 [arrowhead = none ];
298 -> 181;

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
181 -> 299 [arrowhead = none ];
299 -> 182;

300 [label="BACKTRACK\nfor clause: pop(empty, X1)\nwith clash: (empty_stack(T62), empty_stack(empty))", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 300 [arrowhead = none ];
300 -> 183;

301 [label="EVAL with clause\npop(push(X130, X131), X130).\nand substitutionX130 -> T67,\nX131 -> T68,\nT62 -> push(T67, T68),\nX114 -> T67", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 301 [arrowhead = none ];
301 -> 185;

302 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 302 [arrowhead = none ];
302 -> 186;

303 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
185 -> 303 [arrowhead = none ];
303 -> 187;

304 [label="ONLY EVAL with clause\nno(X134) :- ','(call(X134), ','(!_32, failure(a))).\nand substitutionT67 -> T71,\nX134 -> empty_list(T71)", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 304 [arrowhead = none ];
304 -> 188;

305 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
188 -> 305 [arrowhead = none ];
305 -> 189;

306 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
189 -> 306 [arrowhead = none ];
306 -> 190;

307 [label="BACKTRACK\nfor clause: empty_list(nil)\nwith clash: (pop(push(T71, T68), nil), pop(push(X66, X67), X66))", fontsize=14, style = filled, fillcolor = lightgreen];
190 -> 307 [arrowhead = none ];
307 -> 191;

308 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
191 -> 308 [arrowhead = none ];
308 -> 192;

309 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 309 [arrowhead = none ];
309 -> 193;

310 [label="ONLY EVAL with clause\nno(X137).\nand substitutionT71 -> T74,\nX137 -> empty_list(T74)", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 310 [arrowhead = none ];
310 -> 194;

311 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
194 -> 311 [arrowhead = none ];
311 -> 195;

312 [label="BACKTRACK\nfor clause: head(nil, X4)\nwith clash: (pop(push(T74, T68), nil), pop(push(X66, X67), X66))", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 312 [arrowhead = none ];
312 -> 196;

313 [label="EVAL with clause\nhead(cons(X144, X145), X144).\nand substitutionX144 -> T79,\nX145 -> T80,\nT74 -> cons(T79, T80),\nX115 -> T79", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 313 [arrowhead = none ];
313 -> 197;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 314 [arrowhead = none ];
314 -> 198;

315 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
197 -> 315 [arrowhead = none ];
315 -> 199;

316 [label="BACKTRACK\nfor clause: tail(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 316 [arrowhead = none ];
316 -> 200;

317 [label="ONLY EVAL with clause\ntail(cons(X150, X151), X151).\nand substitutionT79 -> T85,\nX150 -> T85,\nT80 -> T86,\nX151 -> T86,\nX116 -> T86", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 317 [arrowhead = none ];
317 -> 201;

318 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
201 -> 318 [arrowhead = none ];
318 -> 202;

319 [label="BACKTRACK\nfor clause: popped(empty, empty)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
202 -> 319 [arrowhead = none ];
319 -> 203;

320 [label="ONLY EVAL with clause\npopped(push(X156, X157), X157).\nand substitutionT85 -> T93,\nT86 -> T94,\nX156 -> cons(T93, T94),\nT68 -> T95,\nX157 -> T95,\nX117 -> T95", fontsize=14, style = filled, fillcolor = lightblue];
203 -> 320 [arrowhead = none ];
320 -> 204;

321 [label="INSTANCE with matching:\nT1 -> push(T93, push(T94, T95))\nT2 -> T56", fontsize=14, style = filled, fillcolor = lightgrey];
204 -> 321 [arrowhead = none , style=dashed];
321 -> 2[style=dashed];

}

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(empty) → f2_out1(0)
f2_in(push(nil, z0)) → U1(f104_in(z0), push(nil, z0))
f2_in(push(cons(z0, z1), z2)) → U2(f2_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2))
U1(f104_out1(z0), push(nil, z1)) → f2_out1(z0)
U1(f104_out5(z0), push(nil, z1)) → f2_out1(z0)
U2(f2_out1(z0), push(cons(z1, z2), z3)) → f2_out1(s(z0))
f104_in(z0) → U3(f2_in(z0), f106_in(z0), z0)
U3(f2_out1(z0), z1, z2) → f104_out1(z0)
U3(z0, f106_out4(z1), z2) → f104_out5(z1)

Tuples:

F2_IN(push(nil, z0)) → c1(U1'(f104_in(z0), push(nil, z0)), F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(U2'(f2_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2)), F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(U3'(f2_in(z0), f106_in(z0), z0), F2_IN(z0))

S tuples:

F2_IN(push(nil, z0)) → c1(U1'(f104_in(z0), push(nil, z0)), F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(U2'(f2_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2)), F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(U3'(f2_in(z0), f106_in(z0), z0), F2_IN(z0))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, f104_in, U3

Defined Pair Symbols:

F2_IN, F104_IN

Compound Symbols:

c1, c2, c6

(3) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(empty) → f2_out1(0)
f2_in(push(nil, z0)) → U1(f104_in(z0), push(nil, z0))
f2_in(push(cons(z0, z1), z2)) → U2(f2_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2))
U1(f104_out1(z0), push(nil, z1)) → f2_out1(z0)
U1(f104_out5(z0), push(nil, z1)) → f2_out1(z0)
U2(f2_out1(z0), push(cons(z1, z2), z3)) → f2_out1(s(z0))
f104_in(z0) → U3(f2_in(z0), f106_in(z0), z0)
U3(f2_out1(z0), z1, z2) → f104_out1(z0)
U3(z0, f106_out4(z1), z2) → f104_out5(z1)

Tuples:

F2_IN(push(nil, z0)) → c1(F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(F2_IN(z0))

S tuples:

F2_IN(push(nil, z0)) → c1(F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(F2_IN(z0))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, f104_in, U3

Defined Pair Symbols:

F2_IN, F104_IN

Compound Symbols:

c1, c2, c6

(5) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

F2_IN(push(nil, z0)) → c1(F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(F2_IN(z0))

We considered the (Usable) Rules:none
And the Tuples:

F2_IN(push(nil, z0)) → c1(F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(F2_IN(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(F104_IN(x₁)) = [1] + [2]x₁
POL(F2_IN(x₁)) = [2]x₁
POL(c1(x₁)) = x₁
POL(c2(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(cons(x₁, x₂)) = [1] + x₁ + x₂
POL(nil) = [2]
POL(push(x₁, x₂)) = x₁ + x₂

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(empty) → f2_out1(0)
f2_in(push(nil, z0)) → U1(f104_in(z0), push(nil, z0))
f2_in(push(cons(z0, z1), z2)) → U2(f2_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2))
U1(f104_out1(z0), push(nil, z1)) → f2_out1(z0)
U1(f104_out5(z0), push(nil, z1)) → f2_out1(z0)
U2(f2_out1(z0), push(cons(z1, z2), z3)) → f2_out1(s(z0))
f104_in(z0) → U3(f2_in(z0), f106_in(z0), z0)
U3(f2_out1(z0), z1, z2) → f104_out1(z0)
U3(z0, f106_out4(z1), z2) → f104_out5(z1)

Tuples:

F2_IN(push(nil, z0)) → c1(F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(F2_IN(z0))

S tuples:none
K tuples:

F2_IN(push(nil, z0)) → c1(F104_IN(z0))
F2_IN(push(cons(z0, z1), z2)) → c2(F2_IN(push(z0, push(z1, z2))))
F104_IN(z0) → c6(F2_IN(z0))

Defined Rule Symbols:

f2_in, U1, U2, f104_in, U3

Defined Pair Symbols:

F2_IN, F104_IN

Compound Symbols:

c1, c2, c6

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))

(9) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: countstack(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: countstack(T1, T2), SCOPE: 1, CLAUSE: 0 | countstack(T1, T2), SCOPE: 1, CLAUSE: 1 | countstack(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | countstack(empty, T2), SCOPE: 1, CLAUSE: 1 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: countstack(T1, T2), SCOPE: 1, CLAUSE: 1 | countstack(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground\ncountstack(T1, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: countstack(empty, T2), SCOPE: 1, CLAUSE: 1 | countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: countstack(empty, T2), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: countstack(empty, T2), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10))))\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 2, CLAUSE: 13 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 2, CLAUSE: 14\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(','(call(empty_stack(empty)), ','(!_2, failure(a))), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))) | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 2, CLAUSE: 14\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(empty_stack(empty), ','(','(!_2, failure(a)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10))))) | ?_3 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 2, CLAUSE: 14\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(empty_stack(empty), ','(','(!_2, failure(a)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10))))), SCOPE: 4, CLAUSE: 11 | ?_4 | ?_3 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 2, CLAUSE: 14\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(','(!_2, failure(a)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))) | ?_4 | ?_3 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 2, CLAUSE: 14\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10))))\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X20), countstack(X20, T10)))), SCOPE: 5, CLAUSE: 15\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14)))))))\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 6, CLAUSE: 13 | ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 6, CLAUSE: 14\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(','(call(empty_stack(empty)), ','(!_6, failure(a))), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))) | ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 6, CLAUSE: 14\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(empty_stack(empty), ','(','(!_6, failure(a)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14)))))))) | ?_7 | ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 6, CLAUSE: 14\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(empty_stack(empty), ','(','(!_6, failure(a)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14)))))))), SCOPE: 8, CLAUSE: 11 | ?_8 | ?_7 | ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 6, CLAUSE: 14\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(','(!_6, failure(a)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))) | ?_8 | ?_7 | ','(no(empty_stack(empty)), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 6, CLAUSE: 14\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(failure(a), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14)))))))\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(failure(a), ','(pop(empty, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(empty, X37), countstack(push(X35, push(X36, X37)), T14))))))), SCOPE: 9, CLAUSE: 15\n\nX34 is free\nX35 is free\nX36 is free\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: countstack(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\ncountstack(T1, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: countstack(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground\ncountstack(T1, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(no(empty_stack(T25)), ','(pop(T25, nil), ','(popped(T25, X53), countstack(X53, T27))))\n\nT25 is ground\nX53 is free\ncountstack(T25, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(no(empty_stack(T25)), ','(pop(T25, nil), ','(popped(T25, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 13 | ','(no(empty_stack(T25)), ','(pop(T25, nil), ','(popped(T25, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT25 is ground\nX53 is free\ncountstack(T25, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(','(call(empty_stack(T30)), ','(!_10, failure(a))), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))) | ','(no(empty_stack(T30)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT30 is ground\nX53 is free\ncountstack(T30, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(empty_stack(T30), ','(','(!_10, failure(a)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27))))) | ?_11 | ','(no(empty_stack(T30)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT30 is ground\nX53 is free\ncountstack(T30, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(empty_stack(T30), ','(','(!_10, failure(a)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27))))), SCOPE: 12, CLAUSE: 11 | ?_12 | ?_11 | ','(no(empty_stack(T30)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT30 is ground\nX53 is free\ncountstack(T30, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(','(!_10, failure(a)), ','(pop(empty, nil), ','(popped(empty, X53), countstack(X53, T27)))) | ?_12 | ?_11 | ','(no(empty_stack(empty)), ','(pop(empty, nil), ','(popped(empty, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ?_12 | ?_11 | ','(no(empty_stack(T30)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT30 is ground\nX53 is free\ncountstack(T30, T2) !=? countstack(empty, 0)\nempty_stack(T30) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X53), countstack(X53, T27))))\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(failure(a), ','(pop(empty, nil), ','(popped(empty, X53), countstack(X53, T27)))), SCOPE: 13, CLAUSE: 15\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ?_11 | ','(no(empty_stack(T30)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT30 is ground\nX53 is free\ncountstack(T30, T2) !=? countstack(empty, 0)\nempty_stack(T30) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(no(empty_stack(T30)), ','(pop(T30, nil), ','(popped(T30, X53), countstack(X53, T27)))), SCOPE: 10, CLAUSE: 14\n\nT30 is ground\nX53 is free\ncountstack(T30, T2) !=? countstack(empty, 0)\nempty_stack(T30) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(pop(T33, nil), ','(popped(T33, X53), countstack(X53, T27)))\n\nT33 is ground\nX53 is free\ncountstack(T33, T2) !=? countstack(empty, 0)\nempty_stack(T33) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ','(pop(T33, nil), ','(popped(T33, X53), countstack(X53, T27))), SCOPE: 14, CLAUSE: 3 | ','(pop(T33, nil), ','(popped(T33, X53), countstack(X53, T27))), SCOPE: 14, CLAUSE: 4\n\nT33 is ground\nX53 is free\ncountstack(T33, T2) !=? countstack(empty, 0)\nempty_stack(T33) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(pop(T33, nil), ','(popped(T33, X53), countstack(X53, T27))), SCOPE: 14, CLAUSE: 4\n\nT33 is ground\nX53 is free\ncountstack(T33, T2) !=? countstack(empty, 0)\nempty_stack(T33) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(popped(push(nil, T39), X53), countstack(X53, T27))\n\nT39 is ground\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(popped(push(nil, T39), X53), countstack(X53, T27)), SCOPE: 15, CLAUSE: 5 | ','(popped(push(nil, T39), X53), countstack(X53, T27)), SCOPE: 15, CLAUSE: 6\n\nT39 is ground\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(popped(push(nil, T39), X53), countstack(X53, T27)), SCOPE: 15, CLAUSE: 6\n\nT39 is ground\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: countstack(T42, T27)\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(no(empty_stack(T47)), ','(pop(T47, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T47, X86), countstack(push(X84, push(X85, X86)), T49)))))))\n\nT47 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T47, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(no(empty_stack(T47)), ','(pop(T47, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T47, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 13 | ','(no(empty_stack(T47)), ','(pop(T47, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T47, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT47 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T47, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(','(call(empty_stack(T52)), ','(!_16, failure(a))), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))) | ','(no(empty_stack(T52)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT52 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T52, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(empty_stack(T52), ','(','(!_16, failure(a)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49)))))))) | ?_17 | ','(no(empty_stack(T52)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT52 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T52, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: ','(empty_stack(T52), ','(','(!_16, failure(a)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49)))))))), SCOPE: 18, CLAUSE: 11 | ?_18 | ?_17 | ','(no(empty_stack(T52)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT52 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T52, T2) !=? countstack(empty, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(','(!_16, failure(a)), ','(pop(empty, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(empty, X86), countstack(push(X84, push(X85, X86)), T49))))))) | ?_18 | ?_17 | ','(no(empty_stack(empty)), ','(pop(empty, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(empty, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nX83 is free\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ?_18 | ?_17 | ','(no(empty_stack(T52)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT52 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T52, T2) !=? countstack(empty, 0)\nempty_stack(T52) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(failure(a), ','(pop(empty, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(empty, X86), countstack(push(X84, push(X85, X86)), T49)))))))\n\nX83 is free\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(failure(a), ','(pop(empty, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(empty, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 19, CLAUSE: 15\n\nX83 is free\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ?_17 | ','(no(empty_stack(T52)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT52 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T52, T2) !=? countstack(empty, 0)\nempty_stack(T52) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(no(empty_stack(T52)), ','(pop(T52, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T52, X86), countstack(push(X84, push(X85, X86)), T49))))))), SCOPE: 16, CLAUSE: 14\n\nT52 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T52, T2) !=? countstack(empty, 0)\nempty_stack(T52) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(pop(T55, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T55, X86), countstack(push(X84, push(X85, X86)), T49))))))\n\nT55 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T55, T2) !=? countstack(empty, 0)\nempty_stack(T55) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(pop(T55, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T55, X86), countstack(push(X84, push(X85, X86)), T49)))))), SCOPE: 20, CLAUSE: 3 | ','(pop(T55, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T55, X86), countstack(push(X84, push(X85, X86)), T49)))))), SCOPE: 20, CLAUSE: 4\n\nT55 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T55, T2) !=? countstack(empty, 0)\nempty_stack(T55) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(pop(T55, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(T55, X86), countstack(push(X84, push(X85, X86)), T49)))))), SCOPE: 20, CLAUSE: 4\n\nT55 is ground\nX83 is free\nX84 is free\nX85 is free\nX86 is free\ncountstack(T55, T2) !=? countstack(empty, 0)\nempty_stack(T55) !=? empty_stack(empty)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(no(empty_list(T60)), ','(head(T60, X84), ','(tail(T60, X85), ','(popped(push(T60, T61), X86), countstack(push(X84, push(X85, X86)), T49)))))\n\nT60 is ground\nT61 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(no(empty_list(T60)), ','(head(T60, X84), ','(tail(T60, X85), ','(popped(push(T60, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 13 | ','(no(empty_list(T60)), ','(head(T60, X84), ','(tail(T60, X85), ','(popped(push(T60, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT60 is ground\nT61 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(','(call(empty_list(T64)), ','(!_21, failure(a))), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))) | ','(no(empty_list(T64)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nT64 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(empty_list(T64), ','(','(!_21, failure(a)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49)))))) | ?_22 | ','(no(empty_list(T64)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nT64 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(empty_list(T64), ','(','(!_21, failure(a)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49)))))), SCOPE: 23, CLAUSE: 12 | ?_23 | ?_22 | ','(no(empty_list(T64)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nT64 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(','(!_21, failure(a)), ','(head(nil, X84), ','(tail(nil, X85), ','(popped(push(nil, T61), X86), countstack(push(X84, push(X85, X86)), T49))))) | ?_23 | ?_22 | ','(no(empty_list(nil)), ','(head(nil, X84), ','(tail(nil, X85), ','(popped(push(nil, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ?_23 | ?_22 | ','(no(empty_list(T64)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nT64 is ground\nX84 is free\nX85 is free\nX86 is free\nempty_list(T64) !=? empty_list(nil)", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(failure(a), ','(head(nil, X84), ','(tail(nil, X85), ','(popped(push(nil, T61), X86), countstack(push(X84, push(X85, X86)), T49)))))\n\nT61 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(failure(a), ','(head(nil, X84), ','(tail(nil, X85), ','(popped(push(nil, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 24, CLAUSE: 15\n\nT61 is ground\nX84 is free\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ?_22 | ','(no(empty_list(T64)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nT64 is ground\nX84 is free\nX85 is free\nX86 is free\nempty_list(T64) !=? empty_list(nil)", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(no(empty_list(T64)), ','(head(T64, X84), ','(tail(T64, X85), ','(popped(push(T64, T61), X86), countstack(push(X84, push(X85, X86)), T49))))), SCOPE: 21, CLAUSE: 14\n\nT61 is ground\nT64 is ground\nX84 is free\nX85 is free\nX86 is free\nempty_list(T64) !=? empty_list(nil)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(head(T67, X84), ','(tail(T67, X85), ','(popped(push(T67, T61), X86), countstack(push(X84, push(X85, X86)), T49))))\n\nT61 is ground\nT67 is ground\nX84 is free\nX85 is free\nX86 is free\nempty_list(T67) !=? empty_list(nil)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: ','(head(T67, X84), ','(tail(T67, X85), ','(popped(push(T67, T61), X86), countstack(push(X84, push(X85, X86)), T49)))), SCOPE: 25, CLAUSE: 7 | ','(head(T67, X84), ','(tail(T67, X85), ','(popped(push(T67, T61), X86), countstack(push(X84, push(X85, X86)), T49)))), SCOPE: 25, CLAUSE: 8\n\nT61 is ground\nT67 is ground\nX84 is free\nX85 is free\nX86 is free\nempty_list(T67) !=? empty_list(nil)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(head(T67, X84), ','(tail(T67, X85), ','(popped(push(T67, T61), X86), countstack(push(X84, push(X85, X86)), T49)))), SCOPE: 25, CLAUSE: 8\n\nT61 is ground\nT67 is ground\nX84 is free\nX85 is free\nX86 is free\nempty_list(T67) !=? empty_list(nil)", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ','(tail(cons(T72, T73), X85), ','(popped(push(cons(T72, T73), T61), X86), countstack(push(T72, push(X85, X86)), T49)))\n\nT61 is ground\nT72 is ground\nT73 is ground\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(tail(cons(T72, T73), X85), ','(popped(push(cons(T72, T73), T61), X86), countstack(push(T72, push(X85, X86)), T49))), SCOPE: 26, CLAUSE: 9 | ','(tail(cons(T72, T73), X85), ','(popped(push(cons(T72, T73), T61), X86), countstack(push(T72, push(X85, X86)), T49))), SCOPE: 26, CLAUSE: 10\n\nT61 is ground\nT72 is ground\nT73 is ground\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: ','(tail(cons(T72, T73), X85), ','(popped(push(cons(T72, T73), T61), X86), countstack(push(T72, push(X85, X86)), T49))), SCOPE: 26, CLAUSE: 10\n\nT61 is ground\nT72 is ground\nT73 is ground\nX85 is free\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ','(popped(push(cons(T78, T79), T61), X86), countstack(push(T78, push(T79, X86)), T49))\n\nT61 is ground\nT78 is ground\nT79 is ground\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(popped(push(cons(T78, T79), T61), X86), countstack(push(T78, push(T79, X86)), T49)), SCOPE: 27, CLAUSE: 5 | ','(popped(push(cons(T78, T79), T61), X86), countstack(push(T78, push(T79, X86)), T49)), SCOPE: 27, CLAUSE: 6\n\nT61 is ground\nT78 is ground\nT79 is ground\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: ','(popped(push(cons(T78, T79), T61), X86), countstack(push(T78, push(T79, X86)), T49)), SCOPE: 27, CLAUSE: 6\n\nT61 is ground\nT78 is ground\nT79 is ground\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: countstack(push(T86, push(T87, T88)), T49)\n\nT86 is ground\nT87 is ground\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 185 [arrowhead = none ];
185 -> 4;

186 [label="EVAL with clause\ncountstack(empty, 0).\nand substitutionT1 -> empty,\nT2 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 186 [arrowhead = none ];
186 -> 6;

187 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 187 [arrowhead = none ];
187 -> 8;

188 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 188 [arrowhead = none ];
188 -> 10;

189 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 189 [arrowhead = none ];
189 -> 55;

190 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 190 [arrowhead = none ];
190 -> 56;

191 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 191 [arrowhead = none ];
191 -> 12;

192 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 192 [arrowhead = none ];
192 -> 14;

193 [label="ONLY EVAL with clause\ncountstack(X18, X19) :- ','(no(empty_stack(X18)), ','(pop(X18, nil), ','(popped(X18, X20), countstack(X20, X19)))).\nand substitutionX18 -> empty,\nT2 -> T10,\nX19 -> T10,\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 193 [arrowhead = none ];
193 -> 18;

194 [label="EVAL with clause\ncountstack(X32, s(X33)) :- ','(no(empty_stack(X32)), ','(pop(X32, X34), ','(no(empty_list(X34)), ','(head(X34, X35), ','(tail(X34, X36), ','(popped(X32, X37), countstack(push(X35, push(X36, X37)), X33))))))).\nand substitutionX32 -> empty,\nX33 -> T14,\nT2 -> s(T14),\nT13 -> T14", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 194 [arrowhead = none ];
194 -> 35;

195 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 195 [arrowhead = none ];
195 -> 36;

196 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
18 -> 196 [arrowhead = none ];
196 -> 20;

197 [label="ONLY EVAL with clause\nno(X23) :- ','(call(X23), ','(!_2, failure(a))).\nand substitutionX23 -> empty_stack(empty)", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 197 [arrowhead = none ];
197 -> 22;

198 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 198 [arrowhead = none ];
198 -> 25;

199 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 199 [arrowhead = none ];
199 -> 26;

200 [label="ONLY EVAL with clause\nempty_stack(empty).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 200 [arrowhead = none ];
200 -> 28;

201 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 201 [arrowhead = none ];
201 -> 29;

202 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 202 [arrowhead = none ];
202 -> 30;

203 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 203 [arrowhead = none ];
203 -> 31;

204 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 204 [arrowhead = none ];
204 -> 38;

205 [label="ONLY EVAL with clause\nno(X40) :- ','(call(X40), ','(!_6, failure(a))).\nand substitutionX40 -> empty_stack(empty)", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 205 [arrowhead = none ];
205 -> 41;

206 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
41 -> 206 [arrowhead = none ];
206 -> 44;

207 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
44 -> 207 [arrowhead = none ];
207 -> 46;

208 [label="ONLY EVAL with clause\nempty_stack(empty).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 208 [arrowhead = none ];
208 -> 48;

209 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 209 [arrowhead = none ];
209 -> 49;

210 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 210 [arrowhead = none ];
210 -> 50;

211 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
50 -> 211 [arrowhead = none ];
211 -> 52;

212 [label="ONLY EVAL with clause\ncountstack(X51, X52) :- ','(no(empty_stack(X51)), ','(pop(X51, nil), ','(popped(X51, X53), countstack(X53, X52)))).\nand substitutionT1 -> T25,\nX51 -> T25,\nT2 -> T27,\nX52 -> T27,\nT26 -> T27", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 212 [arrowhead = none ];
212 -> 65;

213 [label="EVAL with clause\ncountstack(X81, s(X82)) :- ','(no(empty_stack(X81)), ','(pop(X81, X83), ','(no(empty_list(X83)), ','(head(X83, X84), ','(tail(X83, X85), ','(popped(X81, X86), countstack(push(X84, push(X85, X86)), X82))))))).\nand substitutionT1 -> T47,\nX81 -> T47,\nX82 -> T49,\nT2 -> s(T49),\nT48 -> T49", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 213 [arrowhead = none ];
213 -> 112;

214 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 214 [arrowhead = none ];
214 -> 113;

215 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
65 -> 215 [arrowhead = none ];
215 -> 66;

216 [label="ONLY EVAL with clause\nno(X56) :- ','(call(X56), ','(!_10, failure(a))).\nand substitutionT25 -> T30,\nX56 -> empty_stack(T30)", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 216 [arrowhead = none ];
216 -> 67;

217 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
67 -> 217 [arrowhead = none ];
217 -> 69;

218 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
69 -> 218 [arrowhead = none ];
218 -> 71;

219 [label="EVAL with clause\nempty_stack(empty).\nand substitutionT30 -> empty", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 219 [arrowhead = none ];
219 -> 73;

220 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 220 [arrowhead = none ];
220 -> 74;

221 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 221 [arrowhead = none ];
221 -> 75;

222 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
74 -> 222 [arrowhead = none ];
222 -> 79;

223 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
75 -> 223 [arrowhead = none ];
223 -> 76;

224 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 224 [arrowhead = none ];
224 -> 77;

225 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 225 [arrowhead = none ];
225 -> 80;

226 [label="ONLY EVAL with clause\nno(X59).\nand substitutionT30 -> T33,\nX59 -> empty_stack(T33)", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 226 [arrowhead = none ];
226 -> 85;

227 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
85 -> 227 [arrowhead = none ];
227 -> 88;

228 [label="BACKTRACK\nfor clause: pop(empty, X1)\nwith clash: (empty_stack(T33), empty_stack(empty))", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 228 [arrowhead = none ];
228 -> 90;

229 [label="EVAL with clause\npop(push(X65, X66), X65).\nand substitutionX65 -> nil,\nX66 -> T39,\nT33 -> push(nil, T39),\nT38 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 229 [arrowhead = none ];
229 -> 93;

230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 230 [arrowhead = none ];
230 -> 95;

231 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
93 -> 231 [arrowhead = none ];
231 -> 97;

232 [label="BACKTRACK\nfor clause: popped(empty, empty)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 232 [arrowhead = none ];
232 -> 98;

233 [label="ONLY EVAL with clause\npopped(push(X71, X72), X72).\nand substitutionX71 -> nil,\nT39 -> T42,\nX72 -> T42,\nX53 -> T42", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 233 [arrowhead = none ];
233 -> 100;

234 [label="INSTANCE with matching:\nT1 -> T42\nT2 -> T27", fontsize=14, style = filled, fillcolor = lightgrey];
100 -> 234 [arrowhead = none , style=dashed];
234 -> 1[style=dashed];

235 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
112 -> 235 [arrowhead = none ];
235 -> 115;

236 [label="ONLY EVAL with clause\nno(X89) :- ','(call(X89), ','(!_16, failure(a))).\nand substitutionT47 -> T52,\nX89 -> empty_stack(T52)", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 236 [arrowhead = none ];
236 -> 118;

237 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 237 [arrowhead = none ];
237 -> 120;

238 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
120 -> 238 [arrowhead = none ];
238 -> 124;

239 [label="EVAL with clause\nempty_stack(empty).\nand substitutionT52 -> empty", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 239 [arrowhead = none ];
239 -> 125;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 240 [arrowhead = none ];
240 -> 126;

241 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 241 [arrowhead = none ];
241 -> 127;

242 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 242 [arrowhead = none ];
242 -> 132;

243 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 243 [arrowhead = none ];
243 -> 129;

244 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 244 [arrowhead = none ];
244 -> 130;

245 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
132 -> 245 [arrowhead = none ];
245 -> 134;

246 [label="ONLY EVAL with clause\nno(X92).\nand substitutionT52 -> T55,\nX92 -> empty_stack(T55)", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 246 [arrowhead = none ];
246 -> 135;

247 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
135 -> 247 [arrowhead = none ];
247 -> 137;

248 [label="BACKTRACK\nfor clause: pop(empty, X1)\nwith clash: (empty_stack(T55), empty_stack(empty))", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 248 [arrowhead = none ];
248 -> 139;

249 [label="EVAL with clause\npop(push(X99, X100), X99).\nand substitutionX99 -> T60,\nX100 -> T61,\nT55 -> push(T60, T61),\nX83 -> T60", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 249 [arrowhead = none ];
249 -> 145;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 250 [arrowhead = none ];
250 -> 148;

251 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
145 -> 251 [arrowhead = none ];
251 -> 150;

252 [label="ONLY EVAL with clause\nno(X103) :- ','(call(X103), ','(!_21, failure(a))).\nand substitutionT60 -> T64,\nX103 -> empty_list(T64)", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 252 [arrowhead = none ];
252 -> 152;

253 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
152 -> 253 [arrowhead = none ];
253 -> 153;

254 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
153 -> 254 [arrowhead = none ];
254 -> 154;

255 [label="EVAL with clause\nempty_list(nil).\nand substitutionT64 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 255 [arrowhead = none ];
255 -> 155;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
154 -> 256 [arrowhead = none ];
256 -> 156;

257 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 257 [arrowhead = none ];
257 -> 157;

258 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 258 [arrowhead = none ];
258 -> 160;

259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
157 -> 259 [arrowhead = none ];
259 -> 158;

260 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 260 [arrowhead = none ];
260 -> 159;

261 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
160 -> 261 [arrowhead = none ];
261 -> 162;

262 [label="ONLY EVAL with clause\nno(X106).\nand substitutionT64 -> T67,\nX106 -> empty_list(T67)", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 262 [arrowhead = none ];
262 -> 165;

263 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
165 -> 263 [arrowhead = none ];
263 -> 166;

264 [label="BACKTRACK\nfor clause: head(nil, X4)\nwith clash: (empty_list(T67), empty_list(nil))", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 264 [arrowhead = none ];
264 -> 167;

265 [label="EVAL with clause\nhead(cons(X113, X114), X113).\nand substitutionX113 -> T72,\nX114 -> T73,\nT67 -> cons(T72, T73),\nX84 -> T72", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 265 [arrowhead = none ];
265 -> 170;

266 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 266 [arrowhead = none ];
266 -> 171;

267 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
170 -> 267 [arrowhead = none ];
267 -> 173;

268 [label="BACKTRACK\nfor clause: tail(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 268 [arrowhead = none ];
268 -> 174;

269 [label="ONLY EVAL with clause\ntail(cons(X119, X120), X120).\nand substitutionT72 -> T78,\nX119 -> T78,\nT73 -> T79,\nX120 -> T79,\nX85 -> T79", fontsize=14, style = filled, fillcolor = lightblue];
174 -> 269 [arrowhead = none ];
269 -> 178;

270 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 270 [arrowhead = none ];
270 -> 179;

271 [label="BACKTRACK\nfor clause: popped(empty, empty)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 271 [arrowhead = none ];
271 -> 180;

272 [label="ONLY EVAL with clause\npopped(push(X125, X126), X126).\nand substitutionT78 -> T86,\nT79 -> T87,\nX125 -> cons(T86, T87),\nT61 -> T88,\nX126 -> T88,\nX86 -> T88", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 272 [arrowhead = none ];
272 -> 184;

273 [label="INSTANCE with matching:\nT1 -> push(T86, push(T87, T88))\nT2 -> T49", fontsize=14, style = filled, fillcolor = lightgrey];
184 -> 273 [arrowhead = none , style=dashed];
273 -> 1[style=dashed];

}

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(empty) → f1_out1(0)
f1_in(empty) → U1(f10_in, empty)
f1_in(z0) → U2(f8_in(z0), z0)
U1(f10_out1(z0), empty) → f1_out1(z0)
U1(f10_out2(z0), empty) → f1_out1(z0)
U2(f8_out1(z0), z1) → f1_out1(z0)
U2(f8_out2(z0), z1) → f1_out1(z0)
f55_in(push(nil, z0)) → U3(f1_in(z0), push(nil, z0))
U3(f1_out1(z0), push(nil, z1)) → f55_out1(z0)
f56_in(push(cons(z0, z1), z2)) → U4(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2))
U4(f1_out1(z0), push(cons(z1, z2), z3)) → f56_out1(s(z0))
f8_in(z0) → U5(f55_in(z0), f56_in(z0), z0)
U5(f55_out1(z0), z1, z2) → f8_out1(z0)
U5(z0, f56_out1(z1), z2) → f8_out2(z1)
f10_in → U6(f12_in, f14_in)
U6(f12_out1(z0), z1) → f10_out1(z0)
U6(z0, f14_out1(z1)) → f10_out2(z1)

Tuples:

F1_IN(empty) → c1(U1'(f10_in, empty), F10_IN)
F1_IN(z0) → c2(U2'(f8_in(z0), z0), F8_IN(z0))
F55_IN(push(nil, z0)) → c7(U3'(f1_in(z0), push(nil, z0)), F1_IN(z0))
F56_IN(push(cons(z0, z1), z2)) → c9(U4'(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2)), F1_IN(push(z0, push(z1, z2))))
F8_IN(z0) → c11(U5'(f55_in(z0), f56_in(z0), z0), F55_IN(z0), F56_IN(z0))
F10_IN → c14(U6'(f12_in, f14_in))

S tuples:

F1_IN(empty) → c1(U1'(f10_in, empty), F10_IN)
F1_IN(z0) → c2(U2'(f8_in(z0), z0), F8_IN(z0))
F55_IN(push(nil, z0)) → c7(U3'(f1_in(z0), push(nil, z0)), F1_IN(z0))
F56_IN(push(cons(z0, z1), z2)) → c9(U4'(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2)), F1_IN(push(z0, push(z1, z2))))
F8_IN(z0) → c11(U5'(f55_in(z0), f56_in(z0), z0), F55_IN(z0), F56_IN(z0))
F10_IN → c14(U6'(f12_in, f14_in))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f55_in, U3, f56_in, U4, f8_in, U5, f10_in, U6

Defined Pair Symbols:

F1_IN, F55_IN, F56_IN, F8_IN, F10_IN

Compound Symbols:

c1, c2, c7, c9, c11, c14

(11) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(empty) → f1_out1(0)
f1_in(empty) → U1(f10_in, empty)
f1_in(z0) → U2(f8_in(z0), z0)
U1(f10_out1(z0), empty) → f1_out1(z0)
U1(f10_out2(z0), empty) → f1_out1(z0)
U2(f8_out1(z0), z1) → f1_out1(z0)
U2(f8_out2(z0), z1) → f1_out1(z0)
f55_in(push(nil, z0)) → U3(f1_in(z0), push(nil, z0))
U3(f1_out1(z0), push(nil, z1)) → f55_out1(z0)
f56_in(push(cons(z0, z1), z2)) → U4(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2))
U4(f1_out1(z0), push(cons(z1, z2), z3)) → f56_out1(s(z0))
f8_in(z0) → U5(f55_in(z0), f56_in(z0), z0)
U5(f55_out1(z0), z1, z2) → f8_out1(z0)
U5(z0, f56_out1(z1), z2) → f8_out2(z1)
f10_in → U6(f12_in, f14_in)
U6(f12_out1(z0), z1) → f10_out1(z0)
U6(z0, f14_out1(z1)) → f10_out2(z1)

Tuples:

F1_IN(z0) → c2(U2'(f8_in(z0), z0), F8_IN(z0))
F55_IN(push(nil, z0)) → c7(U3'(f1_in(z0), push(nil, z0)), F1_IN(z0))
F56_IN(push(cons(z0, z1), z2)) → c9(U4'(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2)), F1_IN(push(z0, push(z1, z2))))
F8_IN(z0) → c11(U5'(f55_in(z0), f56_in(z0), z0), F55_IN(z0), F56_IN(z0))
F10_IN → c14(U6'(f12_in, f14_in))
F1_IN(empty) → c(U1'(f10_in, empty))
F1_IN(empty) → c(F10_IN)

S tuples:

F1_IN(z0) → c2(U2'(f8_in(z0), z0), F8_IN(z0))
F55_IN(push(nil, z0)) → c7(U3'(f1_in(z0), push(nil, z0)), F1_IN(z0))
F56_IN(push(cons(z0, z1), z2)) → c9(U4'(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2)), F1_IN(push(z0, push(z1, z2))))
F8_IN(z0) → c11(U5'(f55_in(z0), f56_in(z0), z0), F55_IN(z0), F56_IN(z0))
F10_IN → c14(U6'(f12_in, f14_in))
F1_IN(empty) → c(U1'(f10_in, empty))
F1_IN(empty) → c(F10_IN)

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f55_in, U3, f56_in, U4, f8_in, U5, f10_in, U6

Defined Pair Symbols:

F1_IN, F55_IN, F56_IN, F8_IN, F10_IN

Compound Symbols:

c2, c7, c9, c11, c14, c

(13) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(empty) → f1_out1(0)
f1_in(empty) → U1(f10_in, empty)
f1_in(z0) → U2(f8_in(z0), z0)
U1(f10_out1(z0), empty) → f1_out1(z0)
U1(f10_out2(z0), empty) → f1_out1(z0)
U2(f8_out1(z0), z1) → f1_out1(z0)
U2(f8_out2(z0), z1) → f1_out1(z0)
f55_in(push(nil, z0)) → U3(f1_in(z0), push(nil, z0))
U3(f1_out1(z0), push(nil, z1)) → f55_out1(z0)
f56_in(push(cons(z0, z1), z2)) → U4(f1_in(push(z0, push(z1, z2))), push(cons(z0, z1), z2))
U4(f1_out1(z0), push(cons(z1, z2), z3)) → f56_out1(s(z0))
f8_in(z0) → U5(f55_in(z0), f56_in(z0), z0)
U5(f55_out1(z0), z1, z2) → f8_out1(z0)
U5(z0, f56_out1(z1), z2) → f8_out2(z1)
f10_in → U6(f12_in, f14_in)
U6(f12_out1(z0), z1) → f10_out1(z0)
U6(z0, f14_out1(z1)) → f10_out2(z1)

Tuples:

F1_IN(empty) → c(F10_IN)
F1_IN(z0) → c2(F8_IN(z0))
F55_IN(push(nil, z0)) → c7(F1_IN(z0))
F56_IN(push(cons(z0, z1), z2)) → c9(F1_IN(push(z0, push(z1, z2))))
F8_IN(z0) → c11(F55_IN(z0), F56_IN(z0))
F10_IN → c14
F1_IN(empty) → c

S tuples:

F1_IN(empty) → c(F10_IN)
F1_IN(z0) → c2(F8_IN(z0))
F55_IN(push(nil, z0)) → c7(F1_IN(z0))
F56_IN(push(cons(z0, z1), z2)) → c9(F1_IN(push(z0, push(z1, z2))))
F8_IN(z0) → c11(F55_IN(z0), F56_IN(z0))
F10_IN → c14
F1_IN(empty) → c

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f55_in, U3, f56_in, U4, f8_in, U5, f10_in, U6

Defined Pair Symbols:

F1_IN, F55_IN, F56_IN, F8_IN, F10_IN

Compound Symbols:

c, c2, c7, c9, c11, c14, c