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

(0) Obligation:

Clauses:

p :- q(','(r, !)).
q(X) :- X.
r.
r :- r.

Query: p()

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

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

12 [label="ONLY EVAL with clause\np :- q(','(r, !)).\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(X3) :- call(X3).\nand substitutionX3 -> ','(r, !)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 14 [arrowhead = none ];
14 -> 5;

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

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

17 [label="ONLY EVAL with clause\nr.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 17 [arrowhead = none ];
17 -> 8;

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

19 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 19 [arrowhead = none ];
19 -> 10;

}

(2) Obligation:

Triples:


Clauses:


Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

There are no more dependency triples. Hence, the dependency triple problem trivially terminates.

(4) YES