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

(0) Obligation:

Clauses:

a :- b.
a :- e.
b :- c.
c :- d.
d :- b.
e :- f.
f :- g.
g :- e.

Query: a()

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: a\n\n", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: a, SCOPE: 1, CLAUSE: 0 | a, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: b | a, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: b, SCOPE: 2, CLAUSE: 2 | ?_2 | a, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: b, SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ?_2 | a, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: c\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: c, SCOPE: 3, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: d\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: d, SCOPE: 4, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: b\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: b, SCOPE: 5, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: c\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: a, SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: e\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: e, SCOPE: 6, CLAUSE: 5\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: f\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: f, SCOPE: 7, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: g\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: g, SCOPE: 8, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: e\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 22 [arrowhead = none ];
22 -> 2;

23 [label="ONLY EVAL with clause\na :- b.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 23 [arrowhead = none ];
23 -> 3;

24 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 24 [arrowhead = none ];
24 -> 4;

25 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 25 [arrowhead = none ];
25 -> 5;

26 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 26 [arrowhead = none ];
26 -> 6;

27 [label="ONLY EVAL with clause\nb :- c.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 27 [arrowhead = none ];
27 -> 7;

28 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 28 [arrowhead = none ];
28 -> 14;

29 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 29 [arrowhead = none ];
29 -> 8;

30 [label="ONLY EVAL with clause\nc :- d.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 30 [arrowhead = none ];
30 -> 9;

31 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 31 [arrowhead = none ];
31 -> 10;

32 [label="ONLY EVAL with clause\nd :- b.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 32 [arrowhead = none ];
32 -> 11;

33 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
11 -> 33 [arrowhead = none ];
33 -> 12;

34 [label="ONLY EVAL with clause\nb :- c.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 34 [arrowhead = none ];
34 -> 13;

35 [label="INSTANCE", fontsize=14, style = filled, fillcolor = lightgrey];
13 -> 35 [arrowhead = none , style=dashed];
35 -> 7[style=dashed];

36 [label="ONLY EVAL with clause\na :- e.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 36 [arrowhead = none ];
36 -> 15;

37 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 37 [arrowhead = none ];
37 -> 16;

38 [label="ONLY EVAL with clause\ne :- f.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 38 [arrowhead = none ];
38 -> 17;

39 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 39 [arrowhead = none ];
39 -> 18;

40 [label="ONLY EVAL with clause\nf :- g.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 40 [arrowhead = none ];
40 -> 19;

41 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 41 [arrowhead = none ];
41 -> 20;

42 [label="ONLY EVAL with clause\ng :- e.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 42 [arrowhead = none ];
42 -> 21;

43 [label="INSTANCE", fontsize=14, style = filled, fillcolor = lightgrey];
21 -> 43 [arrowhead = none , style=dashed];
43 -> 15[style=dashed];

}

(2) YES