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

(0) Obligation:

Clauses:

thief(john).
thief(X) :- ','(thief(X), !).

Query: thief(g)

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: thief(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: thief(T1), SCOPE: 1, CLAUSE: 0 | thief(T1), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | thief(john), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: thief(T1), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nthief(T1) !=? thief(john)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: thief(john), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(thief(john), !_1)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(thief(john), !_1), SCOPE: 2, CLAUSE: 0 | ','(thief(john), !_1), SCOPE: 2, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: !_1 | ','(thief(john), !_1), SCOPE: 2, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(thief(T3), !_1)\n\nT3 is ground\nthief(T3) !=? thief(john)", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(thief(T3), !_1), SCOPE: 3, CLAUSE: 0 | ','(thief(T3), !_1), SCOPE: 3, CLAUSE: 1\n\nT3 is ground\nthief(T3) !=? thief(john)", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(thief(T3), !_1), SCOPE: 3, CLAUSE: 1\n\nT3 is ground\nthief(T3) !=? thief(john)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ','(','(thief(T7), !_3), !_1)\n\nT7 is ground\nthief(T7) !=? thief(john)", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: thief(T7)\n\nT7 is ground\nthief(T7) !=? thief(john)", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(!_3, !_1)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: !_1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 20 [arrowhead = none ];
20 -> 2;

21 [label="EVAL with clause\nthief(john).\nand substitutionT1 -> john", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 21 [arrowhead = none ];
21 -> 3;

22 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 22 [arrowhead = none ];
22 -> 4;

23 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 23 [arrowhead = none ];
23 -> 5;

24 [label="ONLY EVAL with clause\nthief(X4) :- ','(thief(X4), !_1).\nand substitutionT1 -> T3,\nX4 -> T3", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 24 [arrowhead = none ];
24 -> 11;

25 [label="ONLY EVAL with clause\nthief(X2) :- ','(thief(X2), !_1).\nand substitutionX2 -> john", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 25 [arrowhead = none ];
25 -> 6;

26 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
6 -> 26 [arrowhead = none ];
26 -> 7;

27 [label="ONLY EVAL with clause\nthief(john).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 27 [arrowhead = none ];
27 -> 8;

28 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 28 [arrowhead = none ];
28 -> 9;

29 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 29 [arrowhead = none ];
29 -> 10;

30 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
11 -> 30 [arrowhead = none ];
30 -> 12;

31 [label="BACKTRACK\nfor clause: thief(john)\nwith clash: (thief(T3), thief(john))", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 31 [arrowhead = none ];
31 -> 13;

32 [label="ONLY EVAL with clause\nthief(X8) :- ','(thief(X8), !_3).\nand substitutionT3 -> T7,\nX8 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 32 [arrowhead = none ];
32 -> 14;

33 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
14 -> 33 [arrowhead = none ];
33 -> 15;

34 [label="SPLIT 2\nnew knowledge:\nT7 is ground", fontsize=14, style = filled, fillcolor = violet];
14 -> 34 [arrowhead = none ];
34 -> 16;

35 [label="INSTANCE with matching:\nT1 -> T7", fontsize=14, style = filled, fillcolor = lightgrey];
15 -> 35 [arrowhead = none , style=dashed];
35 -> 1[style=dashed];

36 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 36 [arrowhead = none ];
36 -> 17;

37 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 37 [arrowhead = none ];
37 -> 18;

38 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 38 [arrowhead = none ];
38 -> 19;

}

(2) YES