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

(0) Obligation:

Clauses:

p :- ','(q, !).
p :- p.
q :- ','(!, failure(a)).
q.
failure(b).

Query: p()

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: p\n\n", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: p, SCOPE: 1, CLAUSE: 0 | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(q, !_1) | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(q, !_1), SCOPE: 2, CLAUSE: 2 | ','(q, !_1), SCOPE: 2, CLAUSE: 3 | ?_2 | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(','(!_2, failure(a)), !_1) | ','(q, !_1), SCOPE: 2, CLAUSE: 3 | ?_2 | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(failure(a), !_1) | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(failure(a), !_1), SCOPE: 3, CLAUSE: 4 | ?_3 | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: ?_3 | p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: p, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: p\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 11 [arrowhead = none ];
11 -> 2;

12 [label="ONLY EVAL with clause\np :- ','(q, !_1).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 12 [arrowhead = none ];
12 -> 3;

13 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 13 [arrowhead = none ];
13 -> 4;

14 [label="ONLY EVAL with clause\nq :- ','(!_2, failure(a)).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 14 [arrowhead = none ];
14 -> 5;

15 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 15 [arrowhead = none ];
15 -> 6;

16 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
6 -> 16 [arrowhead = none ];
16 -> 7;

17 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 17 [arrowhead = none ];
17 -> 8;

18 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 18 [arrowhead = none ];
18 -> 9;

19 [label="ONLY EVAL with clause\np :- p.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 19 [arrowhead = none ];
19 -> 10;

20 [label="INSTANCE", fontsize=14, style = filled, fillcolor = lightgrey];
10 -> 20 [arrowhead = none , style=dashed];
20 -> 1[style=dashed];

}

(2) YES