Left Termination 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) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="A: fold(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
6 [label="6: 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];
10 [label="10: ','(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];
12 [label="12: 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];
14 [label="14: ','(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];
16 [label="16: ','(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];
18 [label="18: ?_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];
20 [label="20: fold(c, T10, T12)\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: 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];
33 [label="33: fold(c, T10, T12), SCOPE: 3, CLAUSE: 0\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: fold(c, T10, T12), SCOPE: 3, CLAUSE: 1\n\nT10 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(myop(c, T28, X37), fold(X37, T29, T31))\n\nT28 is ground\nT29 is ground\nX37 is free", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(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];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: 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];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 71 [arrowhead = none ];
71 -> 6;

72 [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];
6 -> 72 [arrowhead = none ];
72 -> 10;

73 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 73 [arrowhead = none ];
73 -> 12;

74 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
10 -> 74 [arrowhead = none ];
74 -> 14;

75 [label="EVAL with clause\nfold(X49, [], X49).\nand substitutionT1 -> T37,\nX49 -> T37,\nT2 -> [],\nT3 -> T37", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 75 [arrowhead = none ];
75 -> 66;

76 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 76 [arrowhead = none ];
76 -> 68;

77 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 77 [arrowhead = none ];
77 -> 16;

78 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 78 [arrowhead = none ];
78 -> 18;

79 [label="EVAL with clause\nmyop(a, b, c).\nand substitutionT8 -> a,\nT9 -> b,\nX9 -> c", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 79 [arrowhead = none ];
79 -> 20;

80 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 80 [arrowhead = none ];
80 -> 23;

81 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 81 [arrowhead = none ];
81 -> 56;

82 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
20 -> 82 [arrowhead = none ];
82 -> 30;

83 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
30 -> 83 [arrowhead = none ];
83 -> 33;

84 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
30 -> 84 [arrowhead = none ];
84 -> 34;

85 [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];
33 -> 85 [arrowhead = none ];
85 -> 39;

86 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 86 [arrowhead = none ];
86 -> 40;

87 [label="EVAL with clause\nfold(X46, [], X46).\nand substitutionX46 -> c,\nT10 -> [],\nT12 -> c", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 87 [arrowhead = none ];
87 -> 47;

88 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 88 [arrowhead = none ];
88 -> 49;

89 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 89 [arrowhead = none ];
89 -> 45;

90 [label="BACKTRACK\nfor clause: myop(a, b, c)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
45 -> 90 [arrowhead = none ];
90 -> 46;

91 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 91 [arrowhead = none ];
91 -> 52;

92 [label="BACKTRACK\nfor clause: fold(X, [], X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 92 [arrowhead = none ];
92 -> 61;

93 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
66 -> 93 [arrowhead = none ];
93 -> 70;

}

(2) Obligation:

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

foldA_in_gga(a, .(b, []), c) → foldA_out_gga(a, .(b, []), c)
foldA_in_gga(T37, [], T37) → foldA_out_gga(T37, [], T37)

The argument filtering Pi contains the following mapping:
foldA_in_gga(x1, x2, x3)  =  foldA_in_gga(x1, x2)
a  =  a
.(x1, x2)  =  .(x1, x2)
b  =  b
[]  =  []
foldA_out_gga(x1, x2, x3)  =  foldA_out_gga(x1, x2, x3)

(3) DependencyPairsProof (EQUIVALENT transformation)

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

foldA_in_gga(a, .(b, []), c) → foldA_out_gga(a, .(b, []), c)
foldA_in_gga(T37, [], T37) → foldA_out_gga(T37, [], T37)

The argument filtering Pi contains the following mapping:
foldA_in_gga(x1, x2, x3)  =  foldA_in_gga(x1, x2)
a  =  a
.(x1, x2)  =  .(x1, x2)
b  =  b
[]  =  []
foldA_out_gga(x1, x2, x3)  =  foldA_out_gga(x1, x2, x3)

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

(4) Obligation:

Pi DP problem:
P is empty.
The TRS R consists of the following rules:

foldA_in_gga(a, .(b, []), c) → foldA_out_gga(a, .(b, []), c)
foldA_in_gga(T37, [], T37) → foldA_out_gga(T37, [], T37)

The argument filtering Pi contains the following mapping:
foldA_in_gga(x1, x2, x3)  =  foldA_in_gga(x1, x2)
a  =  a
.(x1, x2)  =  .(x1, x2)
b  =  b
[]  =  []
foldA_out_gga(x1, x2, x3)  =  foldA_out_gga(x1, x2, x3)

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

(5) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,R,Pi) chain.

(6) YES