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

(0) Obligation:

Clauses:

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

Query: p()

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="A: p\n\n", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: p, SCOPE: 1, CLAUSE: 0\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: r\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: r, SCOPE: 2, CLAUSE: 1 | r, SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(q, !_2) | r, SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(q, !_2), SCOPE: 3, CLAUSE: 3 | ','(q, !_2), SCOPE: 3, CLAUSE: 4 | ?_3 | r, SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: !_2 | ','(q, !_2), SCOPE: 3, CLAUSE: 4 | ?_3 | r, SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 22 [arrowhead = none ];
22 -> 4;

23 [label="ONLY EVAL with clause\np :- r.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 23 [arrowhead = none ];
23 -> 8;

24 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 24 [arrowhead = none ];
24 -> 10;

25 [label="ONLY EVAL with clause\nr :- ','(q, !_2).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 25 [arrowhead = none ];
25 -> 13;

26 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
13 -> 26 [arrowhead = none ];
26 -> 15;

27 [label="ONLY EVAL with clause\nq.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 27 [arrowhead = none ];
27 -> 17;

28 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 28 [arrowhead = none ];
28 -> 19;

29 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 29 [arrowhead = none ];
29 -> 21;

}

(2) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

pA_in_ → pA_out_

Pi is empty.

(3) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
P is empty.
The TRS R consists of the following rules:

pA_in_ → pA_out_

Pi is empty.
We have to consider all (P,R,Pi)-chains

(4) Obligation:

Pi DP problem:
P is empty.
The TRS R consists of the following rules:

pA_in_ → pA_out_

Pi is empty.
We have to consider all (P,R,Pi)-chains

(5) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,R,Pi) chain.

(6) YES