MAYBE
(ignored inputs)COMMENT submitted by: Raul Gutierrez secret problem 2021 category: SRS
Rewrite Rules:
   [ a(b(?x)) -> b(c(?x)),
     a(c(?x)) -> c(a(?x)),
     b(b(?x)) -> a(c(?x)),
     c(b(?x)) -> b(c(?x)),
     c(b(?x)) -> c(c(?x)),
     c(c(?x)) -> c(b(?x)),
     P(?x) -> Q(Q(p(?x))),
     p(p(?x)) -> q(q(?x)),
     p(Q(Q(?x))) -> Q(Q(p(?x))),
     Q(p(q(?x))) -> q(p(Q(?x))),
     q(q(p(?x))) -> p(q(q(?x))),
     q(Q(?x)) -> ?x,
     Q(q(?x)) -> ?x,
     p(P(?x)) -> ?x,
     P(p(?x)) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [ a(a(c(?x_2))) = b(c(b(?x_2))),
     a(b(c(?x_3))) = c(a(b(?x_3))),
     a(c(c(?x_4))) = c(a(b(?x_4))),
     a(c(b(?x_5))) = c(a(c(?x_5))),
     c(a(c(?x_2))) = b(c(b(?x_2))),
     c(a(c(?x_2))) = c(c(b(?x_2))),
     c(b(c(?x_3))) = c(b(b(?x_3))),
     c(c(c(?x_4))) = c(b(b(?x_4))),
     p(Q(Q(p(?x_8)))) = q(q(Q(Q(?x_8)))),
     p(?x_13) = q(q(P(?x_13))),
     p(Q(q(p(Q(?x_9))))) = Q(Q(p(p(q(?x_9))))),
     p(Q(?x_12)) = Q(Q(p(q(?x_12)))),
     Q(p(p(q(q(?x_10))))) = q(p(Q(q(p(?x_10))))),
     Q(p(?x_11)) = q(p(Q(Q(?x_11)))),
     q(q(q(q(?x_7)))) = p(q(q(p(?x_7)))),
     q(q(Q(Q(p(?x_8))))) = p(q(q(Q(Q(?x_8))))),
     q(q(?x_13)) = p(q(q(P(?x_13)))),
     q(q(p(Q(?x_9)))) = p(q(?x_9)),
     q(?x_12) = q(?x_12),
     Q(p(q(q(?x_10)))) = q(p(?x_10)),
     Q(?x_11) = Q(?x_11),
     p(Q(Q(p(?x_6)))) = ?x_6,
     p(?x_14) = p(?x_14),
     P(q(q(?x_7))) = p(?x_7),
     P(Q(Q(p(?x_8)))) = Q(Q(?x_8)),
     P(?x_13) = P(?x_13),
     b(a(c(?x))) = a(c(b(?x))),
     c(c(b(?x))) = c(b(c(?x))),
     p(q(q(?x))) = q(q(p(?x))) ]
Outer CPs:
   [ b(c(?x_3)) = c(c(?x_3)),
     Q(Q(p(p(?x_14)))) = ?x_14 ]
Linear
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Direct Methods: Can't judge

Combined result: Can't judge
1157.trs: Failure(unknown CR)
(1 msec.)