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) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [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];
9 [label="9: q(','(r, !))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: q(','(r, !)), SCOPE: 2, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: call(','(r, !))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(r, !_3)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(r, !_3), SCOPE: 4, CLAUSE: 2 | ','(r, !_3), SCOPE: 4, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: !_3 | ','(r, !_3), SCOPE: 4, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 30 [arrowhead = none ];
30 -> 4;

31 [label="ONLY EVAL with clause\np :- q(','(r, !)).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 31 [arrowhead = none ];
31 -> 9;

32 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 32 [arrowhead = none ];
32 -> 12;

33 [label="ONLY EVAL with clause\nq(X3) :- call(X3).\nand substitutionX3 -> ','(r, !)", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 33 [arrowhead = none ];
33 -> 14;

34 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 34 [arrowhead = none ];
34 -> 16;

35 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 35 [arrowhead = none ];
35 -> 19;

36 [label="ONLY EVAL with clause\nr.\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 36 [arrowhead = none ];
36 -> 22;

37 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 37 [arrowhead = none ];
37 -> 25;

38 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 38 [arrowhead = none ];
38 -> 29;

}

(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