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.
q :- q.
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, !_1))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(q, ','(r, !_1)), SCOPE: 2, CLAUSE: 1 | ','(q, ','(r, !_1)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(r, !_1) | ','(q, ','(r, !_1)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(r, !_1), SCOPE: 3, CLAUSE: 3 | ?_3 | ','(q, ','(r, !_1)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: !_1 | ?_3 | ','(q, ','(r, !_1)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 10 [arrowhead = none ];
10 -> 2;

11 [label="ONLY EVAL with clause\np :- ','(q, ','(r, !_1)).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 11 [arrowhead = none ];
11 -> 3;

12 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 12 [arrowhead = none ];
12 -> 4;

13 [label="ONLY EVAL with clause\nq.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 13 [arrowhead = none ];
13 -> 5;

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

15 [label="ONLY EVAL with clause\nr.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 15 [arrowhead = none ];
15 -> 7;

16 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 16 [arrowhead = none ];
16 -> 8;

17 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 17 [arrowhead = none ];
17 -> 9;

}

(2) Obligation:

Triples:


Clauses:


Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

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

(4) YES