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

(0) Obligation:

Clauses:

num(0) :- !.
num(X) :- ','(p(X, Y), num(Y)).
p(0, 0).
p(s(X), X).

Query: num(g)

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: num(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: num(T1), SCOPE: 1, CLAUSE: 0 | num(T1), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: !_1 | num(0), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: num(T1), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nnum(T1) !=? num(0)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(p(T3, X3), num(X3))\n\nT3 is ground\nX3 is free\nnum(T3) !=? num(0)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: ','(p(T3, X3), num(X3)), SCOPE: 2, CLAUSE: 2 | ','(p(T3, X3), num(X3)), SCOPE: 2, CLAUSE: 3\n\nT3 is ground\nX3 is free\nnum(T3) !=? num(0)", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(p(T3, X3), num(X3)), SCOPE: 2, CLAUSE: 3\n\nT3 is ground\nX3 is free\nnum(T3) !=? num(0)", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: num(T6)\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 12 [arrowhead = none ];
12 -> 2;

13 [label="EVAL with clause\nnum(0) :- !_1.\nand substitutionT1 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 13 [arrowhead = none ];
13 -> 3;

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

15 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 15 [arrowhead = none ];
15 -> 5;

16 [label="ONLY EVAL with clause\nnum(X2) :- ','(p(X2, X3), num(X3)).\nand substitutionT1 -> T3,\nX2 -> T3", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 16 [arrowhead = none ];
16 -> 7;

17 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 17 [arrowhead = none ];
17 -> 6;

18 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 18 [arrowhead = none ];
18 -> 8;

19 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (num(T3), num(0))", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 19 [arrowhead = none ];
19 -> 9;

20 [label="EVAL with clause\np(s(X6), X6).\nand substitutionX6 -> T6,\nT3 -> s(T6),\nX3 -> T6", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 20 [arrowhead = none ];
20 -> 10;

21 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 21 [arrowhead = none ];
21 -> 11;

22 [label="INSTANCE with matching:\nT1 -> T6", fontsize=14, style = filled, fillcolor = lightgrey];
10 -> 22 [arrowhead = none , style=dashed];
22 -> 1[style=dashed];

}

(2) YES