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

(0) Obligation:

Clauses:

flatten(atom(X), Y) :- ','(!, eq(Y, .(X, []))).
flatten(L, Y) :- ','(head(L, atom(H)), ','(!, ','(eq(Y, .(H, Z)), ','(tail(L, T), flatten(T, Z))))).
flatten(L, X) :- ','(head(L, cons(U, V)), ','(tail(L, W), flatten(cons(U, cons(V, W)), X))).
head(nil, X1).
head(cons(H, X2), H).
tail(nil, nil).
tail(cons(X3, T), T).
eq(X, X).

Query: flatten(g,a)

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: flatten(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: flatten(T1, T2), SCOPE: 1, CLAUSE: 0 | flatten(T1, T2), SCOPE: 1, CLAUSE: 1 | flatten(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(!_1, eq(T7, .(T5, []))) | flatten(atom(T5), T2), SCOPE: 1, CLAUSE: 1 | flatten(atom(T5), T2), SCOPE: 1, CLAUSE: 2\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: flatten(T1, T2), SCOPE: 1, CLAUSE: 1 | flatten(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground\nX6 is free\nX7 is free\nflatten(T1, T2) !=? flatten(atom(X6), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: eq(T7, .(T5, []))\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: eq(T7, .(T5, [])), SCOPE: 2, CLAUSE: 7\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: ','(head(T16, atom(X15)), ','(!_1, ','(eq(T18, .(X15, X16)), ','(tail(T16, X17), flatten(X17, X16))))) | flatten(T16, T2), SCOPE: 1, CLAUSE: 2\n\nT16 is ground\nX6 is free\nX7 is free\nX15 is free\nX16 is free\nX17 is free\nflatten(T16, T2) !=? flatten(atom(X6), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(head(T16, atom(X15)), ','(!_1, ','(eq(T18, .(X15, X16)), ','(tail(T16, X17), flatten(X17, X16))))), SCOPE: 3, CLAUSE: 3 | ','(head(T16, atom(X15)), ','(!_1, ','(eq(T18, .(X15, X16)), ','(tail(T16, X17), flatten(X17, X16))))), SCOPE: 3, CLAUSE: 4 | ?_3 | flatten(T16, T2), SCOPE: 1, CLAUSE: 2\n\nT16 is ground\nX6 is free\nX7 is free\nX15 is free\nX16 is free\nX17 is free\nflatten(T16, T2) !=? flatten(atom(X6), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(!_1, ','(eq(T18, .(X23, X16)), ','(tail(nil, X17), flatten(X17, X16)))) | ','(head(nil, atom(X15)), ','(!_1, ','(eq(T18, .(X15, X16)), ','(tail(nil, X17), flatten(X17, X16))))), SCOPE: 3, CLAUSE: 4 | ?_3 | flatten(nil, T2), SCOPE: 1, CLAUSE: 2\n\nX15 is free\nX16 is free\nX17 is free\nX23 is free", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(head(T16, atom(X15)), ','(!_1, ','(eq(T18, .(X15, X16)), ','(tail(T16, X17), flatten(X17, X16))))), SCOPE: 3, CLAUSE: 4 | ?_3 | flatten(T16, T2), SCOPE: 1, CLAUSE: 2\n\nT16 is ground\nX6 is free\nX7 is free\nX15 is free\nX16 is free\nX17 is free\nX22 is free\nflatten(T16, T2) !=? flatten(atom(X6), X7)\nhead(T16, atom(X15)) !=? head(nil, X22)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ','(eq(T18, .(X23, X16)), ','(tail(nil, X17), flatten(X17, X16)))\n\nX16 is free\nX17 is free\nX23 is free", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(eq(T18, .(X23, X16)), ','(tail(nil, X17), flatten(X17, X16))), SCOPE: 4, CLAUSE: 7\n\nX16 is free\nX17 is free\nX23 is free", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(tail(nil, X17), flatten(X17, T28))\n\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(tail(nil, X17), flatten(X17, T28)), SCOPE: 5, CLAUSE: 5 | ','(tail(nil, X17), flatten(X17, T28)), SCOPE: 5, CLAUSE: 6\n\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(tail(nil, X17), flatten(X17, T28)), SCOPE: 5, CLAUSE: 5\n\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(tail(nil, X17), flatten(X17, T28)), SCOPE: 5, CLAUSE: 6\n\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: flatten(nil, T28)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: flatten(nil, T28), SCOPE: 6, CLAUSE: 0 | flatten(nil, T28), SCOPE: 6, CLAUSE: 1 | flatten(nil, T28), SCOPE: 6, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: flatten(nil, T28), SCOPE: 6, CLAUSE: 1 | flatten(nil, T28), SCOPE: 6, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(head(nil, atom(X51)), ','(!_6, ','(eq(T34, .(X51, X52)), ','(tail(nil, X53), flatten(X53, X52))))) | flatten(nil, T28), SCOPE: 6, CLAUSE: 2\n\nX51 is free\nX52 is free\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(head(nil, atom(X51)), ','(!_6, ','(eq(T34, .(X51, X52)), ','(tail(nil, X53), flatten(X53, X52))))), SCOPE: 7, CLAUSE: 3 | ','(head(nil, atom(X51)), ','(!_6, ','(eq(T34, .(X51, X52)), ','(tail(nil, X53), flatten(X53, X52))))), SCOPE: 7, CLAUSE: 4 | ?_7 | flatten(nil, T28), SCOPE: 6, CLAUSE: 2\n\nX51 is free\nX52 is free\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(!_6, ','(eq(T34, .(X59, X52)), ','(tail(nil, X53), flatten(X53, X52)))) | ','(head(nil, atom(X51)), ','(!_6, ','(eq(T34, .(X51, X52)), ','(tail(nil, X53), flatten(X53, X52))))), SCOPE: 7, CLAUSE: 4 | ?_7 | flatten(nil, T28), SCOPE: 6, CLAUSE: 2\n\nX51 is free\nX52 is free\nX53 is free\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(eq(T34, .(X59, X52)), ','(tail(nil, X53), flatten(X53, X52)))\n\nX52 is free\nX53 is free\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(eq(T34, .(X59, X52)), ','(tail(nil, X53), flatten(X53, X52))), SCOPE: 8, CLAUSE: 7\n\nX52 is free\nX53 is free\nX59 is free", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(tail(nil, X53), flatten(X53, T44))\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(tail(nil, X53), flatten(X53, T44)), SCOPE: 9, CLAUSE: 5 | ','(tail(nil, X53), flatten(X53, T44)), SCOPE: 9, CLAUSE: 6\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(tail(nil, X53), flatten(X53, T44)), SCOPE: 9, CLAUSE: 5\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(tail(nil, X53), flatten(X53, T44)), SCOPE: 9, CLAUSE: 6\n\nX53 is free", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: flatten(nil, T44)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(!_1, ','(eq(T18, .(T54, X16)), ','(tail(cons(atom(T54), T53), X17), flatten(X17, X16)))) | ?_3 | flatten(cons(atom(T54), T53), T2), SCOPE: 1, CLAUSE: 2\n\nT54 is ground\nT53 is ground\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ?_3 | flatten(T16, T2), SCOPE: 1, CLAUSE: 2\n\nT16 is ground\nX6 is free\nX7 is free\nX15 is free\nX22 is free\nX84 is free\nX85 is free\nflatten(T16, T2) !=? flatten(atom(X6), X7)\nhead(T16, atom(X15)) !=? head(nil, X22)\nhead(T16, atom(X15)) !=? head(cons(X84, X85), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(eq(T18, .(T54, X16)), ','(tail(cons(atom(T54), T53), X17), flatten(X17, X16)))\n\nT54 is ground\nT53 is ground\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(eq(T18, .(T54, X16)), ','(tail(cons(atom(T54), T53), X17), flatten(X17, X16))), SCOPE: 10, CLAUSE: 7\n\nT54 is ground\nT53 is ground\nX16 is free\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(tail(cons(atom(T62), T53), X17), flatten(X17, T64))\n\nT53 is ground\nT62 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(tail(cons(atom(T62), T53), X17), flatten(X17, T64)), SCOPE: 11, CLAUSE: 5 | ','(tail(cons(atom(T62), T53), X17), flatten(X17, T64)), SCOPE: 11, CLAUSE: 6\n\nT53 is ground\nT62 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(tail(cons(atom(T62), T53), X17), flatten(X17, T64)), SCOPE: 11, CLAUSE: 6\n\nT53 is ground\nT62 is ground\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: flatten(T73, T64)\n\nT73 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: flatten(T16, T2), SCOPE: 1, CLAUSE: 2\n\nT16 is ground\nX6 is free\nX7 is free\nX15 is free\nX22 is free\nX84 is free\nX85 is free\nflatten(T16, T2) !=? flatten(atom(X6), X7)\nhead(T16, atom(X15)) !=? head(nil, X22)\nhead(T16, atom(X15)) !=? head(cons(X84, X85), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(head(T81, cons(X117, X118)), ','(tail(T81, X119), flatten(cons(X117, cons(X118, X119)), T83)))\n\nT81 is ground\nX6 is free\nX7 is free\nX15 is free\nX22 is free\nX84 is free\nX85 is free\nX117 is free\nX118 is free\nX119 is free\nflatten(T81, T2) !=? flatten(atom(X6), X7)\nhead(T81, atom(X15)) !=? head(nil, X22)\nhead(T81, atom(X15)) !=? head(cons(X84, X85), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(head(T81, cons(X117, X118)), ','(tail(T81, X119), flatten(cons(X117, cons(X118, X119)), T83))), SCOPE: 12, CLAUSE: 3 | ','(head(T81, cons(X117, X118)), ','(tail(T81, X119), flatten(cons(X117, cons(X118, X119)), T83))), SCOPE: 12, CLAUSE: 4\n\nT81 is ground\nX6 is free\nX7 is free\nX15 is free\nX22 is free\nX84 is free\nX85 is free\nX117 is free\nX118 is free\nX119 is free\nflatten(T81, T2) !=? flatten(atom(X6), X7)\nhead(T81, atom(X15)) !=? head(nil, X22)\nhead(T81, atom(X15)) !=? head(cons(X84, X85), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(head(T81, cons(X117, X118)), ','(tail(T81, X119), flatten(cons(X117, cons(X118, X119)), T83))), SCOPE: 12, CLAUSE: 4\n\nT81 is ground\nX6 is free\nX7 is free\nX15 is free\nX22 is free\nX84 is free\nX85 is free\nX117 is free\nX118 is free\nX119 is free\nflatten(T81, T2) !=? flatten(atom(X6), X7)\nhead(T81, atom(X15)) !=? head(nil, X22)\nhead(T81, atom(X15)) !=? head(cons(X84, X85), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(tail(cons(cons(T94, T95), T93), X119), flatten(cons(T94, cons(T95, X119)), T83))\n\nT94 is ground\nT95 is ground\nT93 is ground\nX119 is free", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(tail(cons(cons(T94, T95), T93), X119), flatten(cons(T94, cons(T95, X119)), T83)), SCOPE: 13, CLAUSE: 5 | ','(tail(cons(cons(T94, T95), T93), X119), flatten(cons(T94, cons(T95, X119)), T83)), SCOPE: 13, CLAUSE: 6\n\nT94 is ground\nT95 is ground\nT93 is ground\nX119 is free", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(tail(cons(cons(T94, T95), T93), X119), flatten(cons(T94, cons(T95, X119)), T83)), SCOPE: 13, CLAUSE: 6\n\nT94 is ground\nT95 is ground\nT93 is ground\nX119 is free", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: flatten(cons(T102, cons(T103, T104)), T83)\n\nT102 is ground\nT103 is ground\nT104 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 55 [arrowhead = none ];
55 -> 2;

56 [label="EVAL with clause\nflatten(atom(X6), X7) :- ','(!_1, eq(X7, .(X6, []))).\nand substitutionX6 -> T5,\nT1 -> atom(T5),\nT2 -> T7,\nX7 -> T7,\nT6 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 56 [arrowhead = none ];
56 -> 3;

57 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 57 [arrowhead = none ];
57 -> 4;

58 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 58 [arrowhead = none ];
58 -> 5;

59 [label="ONLY EVAL with clause\nflatten(X13, X14) :- ','(head(X13, atom(X15)), ','(!_1, ','(eq(X14, .(X15, X16)), ','(tail(X13, X17), flatten(X17, X16))))).\nand substitutionT1 -> T16,\nX13 -> T16,\nT2 -> T18,\nX14 -> T18,\nT17 -> T18", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 59 [arrowhead = none ];
59 -> 10;

60 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5 -> 60 [arrowhead = none ];
60 -> 6;

61 [label="EVAL with clause\neq(X10, X10).\nand substitutionT7 -> .(T13, []),\nX10 -> .(T13, []),\nT5 -> T13,\nT12 -> .(T13, [])", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 61 [arrowhead = none ];
61 -> 7;

62 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 62 [arrowhead = none ];
62 -> 8;

63 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 63 [arrowhead = none ];
63 -> 9;

64 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
10 -> 64 [arrowhead = none ];
64 -> 11;

65 [label="EVAL with clause\nhead(nil, X22).\nand substitutionT16 -> nil,\nX15 -> X23,\nX22 -> atom(X23)", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 65 [arrowhead = none ];
65 -> 12;

66 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 66 [arrowhead = none ];
66 -> 13;

67 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 67 [arrowhead = none ];
67 -> 14;

68 [label="EVAL with clause\nhead(cons(X84, X85), X84).\nand substitutionX84 -> atom(T54),\nX85 -> T53,\nT16 -> cons(atom(T54), T53),\nX15 -> T54,\nT52 -> atom(T54)", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 68 [arrowhead = none ];
68 -> 37;

69 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 69 [arrowhead = none ];
69 -> 38;

70 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 70 [arrowhead = none ];
70 -> 15;

71 [label="EVAL with clause\neq(X30, X30).\nand substitutionT18 -> .(T26, T28),\nX30 -> .(T26, T28),\nX23 -> T26,\nX16 -> T28,\nT25 -> .(T26, T28),\nT27 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 71 [arrowhead = none ];
71 -> 16;

72 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 72 [arrowhead = none ];
72 -> 17;

73 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 73 [arrowhead = none ];
73 -> 18;

74 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 74 [arrowhead = none ];
74 -> 19;

75 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 75 [arrowhead = none ];
75 -> 20;

76 [label="ONLY EVAL with clause\ntail(nil, nil).\nand substitutionX17 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 76 [arrowhead = none ];
76 -> 21;

77 [label="BACKTRACK\nfor clause: tail(cons(X3, T), T)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 77 [arrowhead = none ];
77 -> 36;

78 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
21 -> 78 [arrowhead = none ];
78 -> 22;

79 [label="BACKTRACK\nfor clause: flatten(atom(X), Y) :- ','(!, eq(Y, .(X, [])))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 79 [arrowhead = none ];
79 -> 23;

80 [label="ONLY EVAL with clause\nflatten(X49, X50) :- ','(head(X49, atom(X51)), ','(!_6, ','(eq(X50, .(X51, X52)), ','(tail(X49, X53), flatten(X53, X52))))).\nand substitutionX49 -> nil,\nT28 -> T34,\nX50 -> T34,\nT33 -> T34", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 80 [arrowhead = none ];
80 -> 24;

81 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
24 -> 81 [arrowhead = none ];
81 -> 25;

82 [label="ONLY EVAL with clause\nhead(nil, X58).\nand substitutionX51 -> X59,\nX58 -> atom(X59)", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 82 [arrowhead = none ];
82 -> 26;

83 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
26 -> 83 [arrowhead = none ];
83 -> 27;

84 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
27 -> 84 [arrowhead = none ];
84 -> 28;

85 [label="EVAL with clause\neq(X66, X66).\nand substitutionT34 -> .(T42, T44),\nX66 -> .(T42, T44),\nX59 -> T42,\nX52 -> T44,\nT41 -> .(T42, T44),\nT43 -> T44", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 85 [arrowhead = none ];
85 -> 29;

86 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 86 [arrowhead = none ];
86 -> 30;

87 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 87 [arrowhead = none ];
87 -> 31;

88 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
31 -> 88 [arrowhead = none ];
88 -> 32;

89 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
31 -> 89 [arrowhead = none ];
89 -> 33;

90 [label="ONLY EVAL with clause\ntail(nil, nil).\nand substitutionX53 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 90 [arrowhead = none ];
90 -> 34;

91 [label="BACKTRACK\nfor clause: tail(cons(X3, T), T)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 91 [arrowhead = none ];
91 -> 35;

92 [label="INSTANCE with matching:\nT28 -> T44", fontsize=14, style = filled, fillcolor = lightgrey];
34 -> 92 [arrowhead = none , style=dashed];
92 -> 21[style=dashed];

93 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 93 [arrowhead = none ];
93 -> 39;

94 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 94 [arrowhead = none ];
94 -> 46;

95 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 95 [arrowhead = none ];
95 -> 40;

96 [label="EVAL with clause\neq(X92, X92).\nand substitutionT18 -> .(T62, T64),\nX92 -> .(T62, T64),\nT54 -> T62,\nX16 -> T64,\nT61 -> .(T62, T64),\nT63 -> T64", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 96 [arrowhead = none ];
96 -> 41;

97 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
40 -> 97 [arrowhead = none ];
97 -> 42;

98 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
41 -> 98 [arrowhead = none ];
98 -> 43;

99 [label="BACKTRACK\nfor clause: tail(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
43 -> 99 [arrowhead = none ];
99 -> 44;

100 [label="ONLY EVAL with clause\ntail(cons(X102, X103), X103).\nand substitutionT62 -> T72,\nX102 -> atom(T72),\nT53 -> T73,\nX103 -> T73,\nX17 -> T73", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 100 [arrowhead = none ];
100 -> 45;

101 [label="INSTANCE with matching:\nT1 -> T73\nT2 -> T64", fontsize=14, style = filled, fillcolor = lightgrey];
45 -> 101 [arrowhead = none , style=dashed];
101 -> 1[style=dashed];

102 [label="ONLY EVAL with clause\nflatten(X115, X116) :- ','(head(X115, cons(X117, X118)), ','(tail(X115, X119), flatten(cons(X117, cons(X118, X119)), X116))).\nand substitutionT16 -> T81,\nX115 -> T81,\nT2 -> T83,\nX116 -> T83,\nT82 -> T83", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 102 [arrowhead = none ];
102 -> 47;

103 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 103 [arrowhead = none ];
103 -> 48;

104 [label="BACKTRACK\nfor clause: head(nil, X1)\nwith clash: (head(T81, atom(X15)), head(nil, X22))", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 104 [arrowhead = none ];
104 -> 49;

105 [label="EVAL with clause\nhead(cons(X129, X130), X129).\nand substitutionX129 -> cons(T94, T95),\nX130 -> T93,\nT81 -> cons(cons(T94, T95), T93),\nX117 -> T94,\nX118 -> T95,\nT92 -> cons(T94, T95)", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 105 [arrowhead = none ];
105 -> 50;

106 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
49 -> 106 [arrowhead = none ];
106 -> 51;

107 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
50 -> 107 [arrowhead = none ];
107 -> 52;

108 [label="BACKTRACK\nfor clause: tail(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 108 [arrowhead = none ];
108 -> 53;

109 [label="ONLY EVAL with clause\ntail(cons(X139, X140), X140).\nand substitutionT94 -> T102,\nT95 -> T103,\nX139 -> cons(T102, T103),\nT93 -> T104,\nX140 -> T104,\nX119 -> T104", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 109 [arrowhead = none ];
109 -> 54;

110 [label="INSTANCE with matching:\nT1 -> cons(T102, cons(T103, T104))\nT2 -> T83", fontsize=14, style = filled, fillcolor = lightgrey];
54 -> 110 [arrowhead = none , style=dashed];
110 -> 1[style=dashed];

}

(2) YES