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

(0) Obligation:

Clauses:

fold(X, .(Y, Ys), Z) :- ','(myop(X, Y, V), fold(V, Ys, Z)).
fold(X, [], X).
myop(a, b, c).

Query: fold(g,g,a)

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: fold(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: fold(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | fold(T1, T2, T3), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(myop(T8, T9, X9), fold(X9, T10, T12)) | fold(T8, .(T9, T10), T3), SCOPE: 1, CLAUSE: 1\n\nT8 is ground\nT9 is ground\nT10 is ground\nX9 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: fold(T1, T2, T3), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nT2 is ground\nX5 is free\nX6 is free\nX7 is free\nX8 is free\nfold(T1, T2, T3) !=? fold(X5, .(X6, X7), X8)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(myop(T8, T9, X9), fold(X9, T10, T12)), SCOPE: 2, CLAUSE: 2 | ?_2 | fold(T8, .(T9, T10), T3), SCOPE: 1, CLAUSE: 1\n\nT8 is ground\nT9 is ground\nT10 is ground\nX9 is free", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(myop(T8, T9, X9), fold(X9, T10, T12)), SCOPE: 2, CLAUSE: 2\n\nT8 is ground\nT9 is ground\nT10 is ground\nX9 is free", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ?_2 | fold(T8, .(T9, T10), T3), SCOPE: 1, CLAUSE: 1\n\nT8 is ground\nT9 is ground\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: fold(c, T10, T12)\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: fold(c, T10, T12), SCOPE: 3, CLAUSE: 0 | fold(c, T10, T12), SCOPE: 3, CLAUSE: 1\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: fold(c, T10, T12), SCOPE: 3, CLAUSE: 0\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: fold(c, T10, T12), SCOPE: 3, CLAUSE: 1\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(myop(c, T28, X37), fold(X37, T29, T31))\n\nT28 is ground\nT29 is ground\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(myop(c, T28, X37), fold(X37, T29, T31)), SCOPE: 4, CLAUSE: 2\n\nT28 is ground\nT29 is ground\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: fold(T8, .(T9, T10), T3), SCOPE: 1, CLAUSE: 1\n\nT8 is ground\nT9 is ground\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 25 [arrowhead = none ];
25 -> 2;

26 [label="EVAL with clause\nfold(X5, .(X6, X7), X8) :- ','(myop(X5, X6, X9), fold(X9, X7, X8)).\nand substitutionT1 -> T8,\nX5 -> T8,\nX6 -> T9,\nX7 -> T10,\nT2 -> .(T9, T10),\nT3 -> T12,\nX8 -> T12,\nT11 -> T12", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 26 [arrowhead = none ];
26 -> 3;

27 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 27 [arrowhead = none ];
27 -> 4;

28 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 28 [arrowhead = none ];
28 -> 5;

29 [label="EVAL with clause\nfold(X49, [], X49).\nand substitutionT1 -> T37,\nX49 -> T37,\nT2 -> [],\nT3 -> T37", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 29 [arrowhead = none ];
29 -> 22;

30 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 30 [arrowhead = none ];
30 -> 23;

31 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5 -> 31 [arrowhead = none ];
31 -> 6;

32 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5 -> 32 [arrowhead = none ];
32 -> 7;

33 [label="EVAL with clause\nmyop(a, b, c).\nand substitutionT8 -> a,\nT9 -> b,\nX9 -> c", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 33 [arrowhead = none ];
33 -> 8;

34 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 34 [arrowhead = none ];
34 -> 9;

35 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 35 [arrowhead = none ];
35 -> 20;

36 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 36 [arrowhead = none ];
36 -> 10;

37 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 37 [arrowhead = none ];
37 -> 11;

38 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 38 [arrowhead = none ];
38 -> 12;

39 [label="EVAL with clause\nfold(X33, .(X34, X35), X36) :- ','(myop(X33, X34, X37), fold(X37, X35, X36)).\nand substitutionX33 -> c,\nX34 -> T28,\nX35 -> T29,\nT10 -> .(T28, T29),\nT12 -> T31,\nX36 -> T31,\nT30 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 39 [arrowhead = none ];
39 -> 13;

40 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 40 [arrowhead = none ];
40 -> 14;

41 [label="EVAL with clause\nfold(X46, [], X46).\nand substitutionX46 -> c,\nT10 -> [],\nT12 -> c", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 41 [arrowhead = none ];
41 -> 17;

42 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 42 [arrowhead = none ];
42 -> 18;

43 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
13 -> 43 [arrowhead = none ];
43 -> 15;

44 [label="BACKTRACK\nfor clause: myop(a, b, c)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 44 [arrowhead = none ];
44 -> 16;

45 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 45 [arrowhead = none ];
45 -> 19;

46 [label="BACKTRACK\nfor clause: fold(X, [], X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 46 [arrowhead = none ];
46 -> 21;

47 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 47 [arrowhead = none ];
47 -> 24;

}

(2) YES