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

(0) Obligation:

Clauses:

p(X) :- ','(q(f(Y)), p(Y)).
q(g(Y)).

Query: p(a)

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: p(T1)\n\n", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: p(T1), SCOPE: 1, CLAUSE: 0\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(q(f(X3)), p(X3))\n\nX3 is free", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(q(f(X3)), p(X3)), SCOPE: 2, CLAUSE: 1\n\nX3 is free", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 6 [arrowhead = none ];
6 -> 2;

7 [label="ONLY EVAL with clause\np(X2) :- ','(q(f(X3)), p(X3)).\nand substitutionT1 -> T3,\nX2 -> T3", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 7 [arrowhead = none ];
7 -> 3;

8 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 8 [arrowhead = none ];
8 -> 4;

9 [label="BACKTRACK\nfor clause: q(g(Y))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 9 [arrowhead = none ];
9 -> 5;

}

(2) YES