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

(0) Obligation:

Clauses:

list([]).
list(X) :- ','(no(empty(X)), ','(tail(X, T), list(T))).
tail([], []).
tail(.(X, Xs), Xs).
empty(X).
no(X) :- ','(X, ','(!, failure(a))).
no(X1).
failure(b).

Query: list(g)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="A: list(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
5 [label="5: list(T1), SCOPE: 1, CLAUSE: 0 | list(T1), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: true | list([]), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: list(T1), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nlist(T1) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: list([]), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(no(empty([])), ','(tail([], X4), list(X4)))\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(no(empty([])), ','(tail([], X4), list(X4))), SCOPE: 2, CLAUSE: 5 | ','(no(empty([])), ','(tail([], X4), list(X4))), SCOPE: 2, CLAUSE: 6\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(','(call(empty([])), ','(!_2, failure(a))), ','(tail([], X4), list(X4))) | ','(no(empty([])), ','(tail([], X4), list(X4))), SCOPE: 2, CLAUSE: 6\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(empty([]), ','(','(!_2, failure(a)), ','(tail([], X4), list(X4)))) | ?_3 | ','(no(empty([])), ','(tail([], X4), list(X4))), SCOPE: 2, CLAUSE: 6\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(empty([]), ','(','(!_2, failure(a)), ','(tail([], X4), list(X4)))), SCOPE: 4, CLAUSE: 4 | ?_4 | ?_3 | ','(no(empty([])), ','(tail([], X4), list(X4))), SCOPE: 2, CLAUSE: 6\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(','(!_2, failure(a)), ','(tail([], X4), list(X4))) | ?_4 | ?_3 | ','(no(empty([])), ','(tail([], X4), list(X4))), SCOPE: 2, CLAUSE: 6\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: ','(failure(a), ','(tail([], X4), list(X4)))\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(failure(a), ','(tail([], X4), list(X4))), SCOPE: 5, CLAUSE: 7\n\nX4 is free", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(no(empty(T3)), ','(tail(T3, X13), list(X13)))\n\nT3 is ground\nX13 is free\nlist(T3) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(no(empty(T3)), ','(tail(T3, X13), list(X13))), SCOPE: 6, CLAUSE: 5 | ','(no(empty(T3)), ','(tail(T3, X13), list(X13))), SCOPE: 6, CLAUSE: 6\n\nT3 is ground\nX13 is free\nlist(T3) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(','(call(empty(T6)), ','(!_6, failure(a))), ','(tail(T6, X13), list(X13))) | ','(no(empty(T6)), ','(tail(T6, X13), list(X13))), SCOPE: 6, CLAUSE: 6\n\nT6 is ground\nX13 is free\nlist(T6) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(empty(T6), ','(','(!_6, failure(a)), ','(tail(T6, X13), list(X13)))) | ?_7 | ','(no(empty(T6)), ','(tail(T6, X13), list(X13))), SCOPE: 6, CLAUSE: 6\n\nT6 is ground\nX13 is free\nlist(T6) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(empty(T6), ','(','(!_6, failure(a)), ','(tail(T6, X13), list(X13)))), SCOPE: 8, CLAUSE: 4 | ?_8 | ?_7 | ','(no(empty(T6)), ','(tail(T6, X13), list(X13))), SCOPE: 6, CLAUSE: 6\n\nT6 is ground\nX13 is free\nlist(T6) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(','(!_6, failure(a)), ','(tail(T9, X13), list(X13))) | ?_8 | ?_7 | ','(no(empty(T9)), ','(tail(T9, X13), list(X13))), SCOPE: 6, CLAUSE: 6\n\nT9 is ground\nX13 is free\nlist(T9) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(failure(a), ','(tail(T9, X13), list(X13)))\n\nT9 is ground\nX13 is free\nlist(T9) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(failure(a), ','(tail(T9, X13), list(X13))), SCOPE: 9, CLAUSE: 7\n\nT9 is ground\nX13 is free\nlist(T9) !=? list([])", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 59 [arrowhead = none ];
59 -> 5;

60 [label="EVAL with clause\nlist([]).\nand substitutionT1 -> []", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 60 [arrowhead = none ];
60 -> 9;

61 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 61 [arrowhead = none ];
61 -> 10;

62 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 62 [arrowhead = none ];
62 -> 16;

63 [label="ONLY EVAL with clause\nlist(X12) :- ','(no(empty(X12)), ','(tail(X12, X13), list(X13))).\nand substitutionT1 -> T3,\nX12 -> T3", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 63 [arrowhead = none ];
63 -> 45;

64 [label="ONLY EVAL with clause\nlist(X3) :- ','(no(empty(X3)), ','(tail(X3, X4), list(X4))).\nand substitutionX3 -> []", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 64 [arrowhead = none ];
64 -> 19;

65 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 65 [arrowhead = none ];
65 -> 21;

66 [label="ONLY EVAL with clause\nno(X7) :- ','(call(X7), ','(!_2, failure(a))).\nand substitutionX7 -> empty([])", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 66 [arrowhead = none ];
66 -> 24;

67 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
24 -> 67 [arrowhead = none ];
67 -> 27;

68 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
27 -> 68 [arrowhead = none ];
68 -> 31;

69 [label="ONLY EVAL with clause\nempty(X10).\nand substitutionX10 -> []", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 69 [arrowhead = none ];
69 -> 33;

70 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 70 [arrowhead = none ];
70 -> 35;

71 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 71 [arrowhead = none ];
71 -> 41;

72 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 72 [arrowhead = none ];
72 -> 44;

73 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
45 -> 73 [arrowhead = none ];
73 -> 47;

74 [label="ONLY EVAL with clause\nno(X16) :- ','(call(X16), ','(!_6, failure(a))).\nand substitutionT3 -> T6,\nX16 -> empty(T6)", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 74 [arrowhead = none ];
74 -> 49;

75 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 75 [arrowhead = none ];
75 -> 51;

76 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
51 -> 76 [arrowhead = none ];
76 -> 53;

77 [label="ONLY EVAL with clause\nempty(X19).\nand substitutionT6 -> T9,\nX19 -> T9", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 77 [arrowhead = none ];
77 -> 55;

78 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 78 [arrowhead = none ];
78 -> 56;

79 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 79 [arrowhead = none ];
79 -> 57;

80 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
57 -> 80 [arrowhead = none ];
80 -> 58;

}

(2) Obligation:

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

listA_in_g([]) → listA_out_g([])

Pi is empty.

(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:

listA_in_g([]) → listA_out_g([])

Pi is empty.
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:

listA_in_g([]) → listA_out_g([])

Pi is empty.
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