(ignored inputs)COMMENT submitted by: Hans Zantema
Rewrite Rules:
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)),
     p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
Apply Direct Methods...
Inner CPs:
   [ a(a(b(a(?x_1)))) = b(a(b(b(?x_1)))),
     a(b(c(a(c(?x_2))))) = b(a(b(c(a(?x_2))))),
     a(b(d(a(d(?x_4))))) = b(a(b(d(a(?x_4))))),
     b(b(a(b(?x)))) = a(b(a(a(?x)))),
     b(a(c(b(?x_6)))) = a(b(a(c(?x_6)))),
     b(a(d(b(?x_8)))) = a(b(a(d(?x_8)))),
     a(c(b(a(b(?x))))) = c(a(c(b(a(?x))))),
     a(a(c(a(?x_3)))) = c(a(c(c(?x_3)))),
     a(c(d(a(d(?x_4))))) = c(a(c(d(a(?x_4))))),
     c(c(a(c(?x_2)))) = a(c(a(a(?x_2)))),
     c(a(b(c(?x_7)))) = a(c(a(b(?x_7)))),
     c(a(d(c(?x_11)))) = a(c(a(d(?x_11)))),
     a(d(b(a(b(?x))))) = d(a(d(b(a(?x))))),
     a(d(c(a(c(?x_2))))) = d(a(d(c(a(?x_2))))),
     a(a(d(a(?x_5)))) = d(a(d(d(?x_5)))),
     d(d(a(d(?x_4)))) = a(d(a(a(?x_4)))),
     d(a(b(d(?x_9)))) = a(d(a(b(?x_9)))),
     d(a(c(d(?x_10)))) = a(d(a(c(?x_10)))),
     b(a(c(a(?x_3)))) = c(b(a(c(?x_3)))),
     b(b(c(?x_7))) = c(b(b(?x_7))),
     b(d(c(?x_11))) = c(b(d(?x_11))),
     c(a(b(a(?x_1)))) = b(c(a(b(?x_1)))),
     c(c(b(?x_6))) = b(c(c(?x_6))),
     c(d(b(?x_8))) = b(c(d(?x_8))),
     b(a(d(a(?x_5)))) = d(b(a(d(?x_5)))),
     b(b(d(?x_9))) = d(b(b(?x_9))),
     b(c(d(?x_10))) = d(b(c(?x_10))),
     d(a(b(a(?x_1)))) = b(d(a(b(?x_1)))),
     d(c(b(?x_6))) = b(d(c(?x_6))),
     d(d(b(?x_8))) = b(d(d(?x_8))),
     d(a(c(a(?x_3)))) = c(d(a(c(?x_3)))),
     d(b(c(?x_7))) = c(d(b(?x_7))),
     d(d(c(?x_11))) = c(d(d(?x_11))),
     c(a(d(a(?x_5)))) = d(c(a(d(?x_5)))),
     c(b(d(?x_9))) = d(c(b(?x_9))),
     c(c(d(?x_10))) = d(c(c(?x_10))),
     a(b(b(a(b(?x))))) = b(a(b(b(a(?x))))),
     b(a(a(b(a(?x))))) = a(b(a(a(b(?x))))),
     a(c(c(a(c(?x))))) = c(a(c(c(a(?x))))),
     c(a(a(c(a(?x))))) = a(c(a(a(c(?x))))),
     a(d(d(a(d(?x))))) = d(a(d(d(a(?x))))),
     d(a(a(d(a(?x))))) = a(d(a(a(d(?x))))) ]
Outer CPs:
   [ a(p) = b(p),
     a(p) = c(p),
     a(p) = d(p),
     b(p) = c(p),
     b(p) = d(p),
     c(p) = d(p) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ a(a(b(a(?x_2)))) = b(a(b(b(?x_2)))),
     a(b(b(a(b(?x_1))))) = b(a(b(b(a(?x_1))))),
     a(b(c(a(c(?x_3))))) = b(a(b(c(a(?x_3))))),
     a(b(d(a(d(?x_5))))) = b(a(b(d(a(?x_5))))),
     b(a(b(a(b(a(?x_2)))))) = a(b(b(a(b(b(?x_2)))))),
     b(a(b(b(b(a(b(?x_1))))))) = a(b(b(a(b(b(a(?x_1))))))),
     b(a(b(b(c(a(c(?x_3))))))) = a(b(b(a(b(c(a(?x_3))))))),
     b(a(b(b(d(a(d(?x_5))))))) = a(b(b(a(b(d(a(?x_5))))))),
     a(b(a(b(a(b(?x_1)))))) = b(b(a(b(b(a(?x_1)))))),
     a(b(a(c(a(c(?x_3)))))) = b(b(a(b(c(a(?x_3)))))),
     a(b(a(d(a(d(?x_5)))))) = b(b(a(b(d(a(?x_5)))))),
     c(a(c(a(b(a(?x_2)))))) = a(c(b(a(b(b(?x_2)))))),
     c(a(c(b(b(a(b(?x_1))))))) = a(c(b(a(b(b(a(?x_1))))))),
     c(a(c(b(c(a(c(?x_3))))))) = a(c(b(a(b(c(a(?x_3))))))),
     c(a(c(b(d(a(d(?x_5))))))) = a(c(b(a(b(d(a(?x_5))))))),
     d(a(d(a(b(a(?x_2)))))) = a(d(b(a(b(b(?x_2)))))),
     d(a(d(b(b(a(b(?x_1))))))) = a(d(b(a(b(b(a(?x_1))))))),
     d(a(d(b(c(a(c(?x_3))))))) = a(d(b(a(b(c(a(?x_3))))))),
     d(a(d(b(d(a(d(?x_5))))))) = a(d(b(a(b(d(a(?x_5))))))),
     b(a(b(b(a(?x))))) = a(b(b(a(b(?x))))),
     a(b(a(a(?x)))) = b(b(a(b(?x)))),
     c(a(c(b(a(?x))))) = a(c(b(a(b(?x))))),
     d(a(d(b(a(?x))))) = a(d(b(a(b(?x))))),
     b(b(a(b(?x_2)))) = a(b(a(a(?x_2)))),
     b(a(a(b(a(?x_1))))) = a(b(a(a(b(?x_1))))),
     b(a(c(b(?x_7)))) = a(b(a(c(?x_7)))),
     b(a(d(b(?x_9)))) = a(b(a(d(?x_9)))),
     a(b(a(b(a(b(?x_2)))))) = b(a(a(b(a(a(?x_2)))))),
     a(b(a(a(a(b(a(?x_1))))))) = b(a(a(b(a(a(b(?x_1))))))),
     a(b(a(a(c(b(?x_7)))))) = b(a(a(b(a(c(?x_7)))))),
     a(b(a(a(d(b(?x_9)))))) = b(a(a(b(a(d(?x_9)))))),
     b(a(b(a(b(a(?x_1)))))) = a(a(b(a(a(b(?x_1)))))),
     b(a(b(c(b(?x_7))))) = a(a(b(a(c(?x_7))))),
     b(a(b(d(b(?x_9))))) = a(a(b(a(d(?x_9))))),
     b(c(b(a(b(?x_2))))) = c(a(b(a(a(?x_2))))),
     b(c(a(a(b(a(?x_1)))))) = c(a(b(a(a(b(?x_1)))))),
     b(c(a(c(b(?x_7))))) = c(a(b(a(c(?x_7))))),
     b(c(a(d(b(?x_9))))) = c(a(b(a(d(?x_9))))),
     b(d(b(a(b(?x_2))))) = d(a(b(a(a(?x_2))))),
     b(d(a(a(b(a(?x_1)))))) = d(a(b(a(a(b(?x_1)))))),
     b(d(a(c(b(?x_7))))) = d(a(b(a(c(?x_7))))),
     b(d(a(d(b(?x_9))))) = d(a(b(a(d(?x_9))))),
     a(b(a(a(b(?x))))) = b(a(a(b(a(?x))))),
     b(a(b(b(?x)))) = a(a(b(a(?x)))),
     b(c(a(b(?x)))) = c(a(b(a(?x)))),
     b(d(a(b(?x)))) = d(a(b(a(?x)))),
     a(a(c(a(?x_4)))) = c(a(c(c(?x_4)))),
     a(c(c(a(c(?x_1))))) = c(a(c(c(a(?x_1))))),
     a(c(b(a(b(?x_2))))) = c(a(c(b(a(?x_2))))),
     a(c(d(a(d(?x_5))))) = c(a(c(d(a(?x_5))))),
     c(a(c(a(c(a(?x_4)))))) = a(c(c(a(c(c(?x_4)))))),
     c(a(c(c(c(a(c(?x_1))))))) = a(c(c(a(c(c(a(?x_1))))))),
     c(a(c(c(b(a(b(?x_2))))))) = a(c(c(a(c(b(a(?x_2))))))),
     c(a(c(c(d(a(d(?x_5))))))) = a(c(c(a(c(d(a(?x_5))))))),
     b(a(b(a(c(a(?x_4)))))) = a(b(c(a(c(c(?x_4)))))),
     b(a(b(c(c(a(c(?x_1))))))) = a(b(c(a(c(c(a(?x_1))))))),
     b(a(b(c(b(a(b(?x_2))))))) = a(b(c(a(c(b(a(?x_2))))))),
     b(a(b(c(d(a(d(?x_5))))))) = a(b(c(a(c(d(a(?x_5))))))),
     a(c(a(c(a(c(?x_1)))))) = c(c(a(c(c(a(?x_1)))))),
     a(c(a(b(a(b(?x_2)))))) = c(c(a(c(b(a(?x_2)))))),
     a(c(a(d(a(d(?x_5)))))) = c(c(a(c(d(a(?x_5)))))),
     d(a(d(a(c(a(?x_4)))))) = a(d(c(a(c(c(?x_4)))))),
     d(a(d(c(c(a(c(?x_1))))))) = a(d(c(a(c(c(a(?x_1))))))),
     d(a(d(c(b(a(b(?x_2))))))) = a(d(c(a(c(b(a(?x_2))))))),
     d(a(d(c(d(a(d(?x_5))))))) = a(d(c(a(c(d(a(?x_5))))))),
     c(a(c(c(a(?x))))) = a(c(c(a(c(?x))))),
     b(a(b(c(a(?x))))) = a(b(c(a(c(?x))))),
     a(c(a(a(?x)))) = c(c(a(c(?x)))),
     d(a(d(c(a(?x))))) = a(d(c(a(c(?x))))),
     c(c(a(c(?x_4)))) = a(c(a(a(?x_4)))),
     c(a(a(c(a(?x_1))))) = a(c(a(a(c(?x_1))))),
     c(a(b(c(?x_8)))) = a(c(a(b(?x_8)))),
     c(a(d(c(?x_12)))) = a(c(a(d(?x_12)))),
     a(c(a(c(a(c(?x_4)))))) = c(a(a(c(a(a(?x_4)))))),
     a(c(a(a(a(c(a(?x_1))))))) = c(a(a(c(a(a(c(?x_1))))))),
     a(c(a(a(b(c(?x_8)))))) = c(a(a(c(a(b(?x_8)))))),
     a(c(a(a(d(c(?x_12)))))) = c(a(a(c(a(d(?x_12)))))),
     c(a(c(a(c(a(?x_1)))))) = a(a(c(a(a(c(?x_1)))))),
     c(a(c(b(c(?x_8))))) = a(a(c(a(b(?x_8))))),
     c(a(c(d(c(?x_12))))) = a(a(c(a(d(?x_12))))),
     c(b(c(a(c(?x_4))))) = b(a(c(a(a(?x_4))))),
     c(b(a(a(c(a(?x_1)))))) = b(a(c(a(a(c(?x_1)))))),
     c(b(a(b(c(?x_8))))) = b(a(c(a(b(?x_8))))),
     c(b(a(d(c(?x_12))))) = b(a(c(a(d(?x_12))))),
     c(d(c(a(c(?x_4))))) = d(a(c(a(a(?x_4))))),
     c(d(a(a(c(a(?x_1)))))) = d(a(c(a(a(c(?x_1)))))),
     c(d(a(b(c(?x_8))))) = d(a(c(a(b(?x_8))))),
     c(d(a(d(c(?x_12))))) = d(a(c(a(d(?x_12))))),
     a(c(a(a(c(?x))))) = c(a(a(c(a(?x))))),
     c(a(c(c(?x)))) = a(a(c(a(?x)))),
     c(b(a(c(?x)))) = b(a(c(a(?x)))),
     c(d(a(c(?x)))) = d(a(c(a(?x)))),
     a(a(d(a(?x_6)))) = d(a(d(d(?x_6)))),
     a(d(d(a(d(?x_1))))) = d(a(d(d(a(?x_1))))),
     a(d(b(a(b(?x_2))))) = d(a(d(b(a(?x_2))))),
     a(d(c(a(c(?x_4))))) = d(a(d(c(a(?x_4))))),
     d(a(d(a(d(a(?x_6)))))) = a(d(d(a(d(d(?x_6)))))),
     d(a(d(d(d(a(d(?x_1))))))) = a(d(d(a(d(d(a(?x_1))))))),
     d(a(d(d(b(a(b(?x_2))))))) = a(d(d(a(d(b(a(?x_2))))))),
     d(a(d(d(c(a(c(?x_4))))))) = a(d(d(a(d(c(a(?x_4))))))),
     b(a(b(a(d(a(?x_6)))))) = a(b(d(a(d(d(?x_6)))))),
     b(a(b(d(d(a(d(?x_1))))))) = a(b(d(a(d(d(a(?x_1))))))),
     b(a(b(d(b(a(b(?x_2))))))) = a(b(d(a(d(b(a(?x_2))))))),
     b(a(b(d(c(a(c(?x_4))))))) = a(b(d(a(d(c(a(?x_4))))))),
     c(a(c(a(d(a(?x_6)))))) = a(c(d(a(d(d(?x_6)))))),
     c(a(c(d(d(a(d(?x_1))))))) = a(c(d(a(d(d(a(?x_1))))))),
     c(a(c(d(b(a(b(?x_2))))))) = a(c(d(a(d(b(a(?x_2))))))),
     c(a(c(d(c(a(c(?x_4))))))) = a(c(d(a(d(c(a(?x_4))))))),
     a(d(a(d(a(d(?x_1)))))) = d(d(a(d(d(a(?x_1)))))),
     a(d(a(b(a(b(?x_2)))))) = d(d(a(d(b(a(?x_2)))))),
     a(d(a(c(a(c(?x_4)))))) = d(d(a(d(c(a(?x_4)))))),
     d(a(d(d(a(?x))))) = a(d(d(a(d(?x))))),
     b(a(b(d(a(?x))))) = a(b(d(a(d(?x))))),
     c(a(c(d(a(?x))))) = a(c(d(a(d(?x))))),
     a(d(a(a(?x)))) = d(d(a(d(?x)))),
     d(d(a(d(?x_6)))) = a(d(a(a(?x_6)))),
     d(a(a(d(a(?x_1))))) = a(d(a(a(d(?x_1))))),
     d(a(b(d(?x_10)))) = a(d(a(b(?x_10)))),
     d(a(c(d(?x_11)))) = a(d(a(c(?x_11)))),
     a(d(a(d(a(d(?x_6)))))) = d(a(a(d(a(a(?x_6)))))),
     a(d(a(a(a(d(a(?x_1))))))) = d(a(a(d(a(a(d(?x_1))))))),
     a(d(a(a(b(d(?x_10)))))) = d(a(a(d(a(b(?x_10)))))),
     a(d(a(a(c(d(?x_11)))))) = d(a(a(d(a(c(?x_11)))))),
     d(a(d(a(d(a(?x_1)))))) = a(a(d(a(a(d(?x_1)))))),
     d(a(d(b(d(?x_10))))) = a(a(d(a(b(?x_10))))),
     d(a(d(c(d(?x_11))))) = a(a(d(a(c(?x_11))))),
     d(b(d(a(d(?x_6))))) = b(a(d(a(a(?x_6))))),
     d(b(a(a(d(a(?x_1)))))) = b(a(d(a(a(d(?x_1)))))),
     d(b(a(b(d(?x_10))))) = b(a(d(a(b(?x_10))))),
     d(b(a(c(d(?x_11))))) = b(a(d(a(c(?x_11))))),
     d(c(d(a(d(?x_6))))) = c(a(d(a(a(?x_6))))),
     d(c(a(a(d(a(?x_1)))))) = c(a(d(a(a(d(?x_1)))))),
     d(c(a(b(d(?x_10))))) = c(a(d(a(b(?x_10))))),
     d(c(a(c(d(?x_11))))) = c(a(d(a(c(?x_11))))),
     a(d(a(a(d(?x))))) = d(a(a(d(a(?x))))),
     d(a(d(d(?x)))) = a(a(d(a(?x)))),
     d(b(a(d(?x)))) = b(a(d(a(?x)))),
     d(c(a(d(?x)))) = c(a(d(a(?x)))),
     b(a(c(a(?x_5)))) = c(b(a(c(?x_5)))),
     b(b(c(?x_8))) = c(b(b(?x_8))),
     b(d(c(?x_12))) = c(b(d(?x_12))),
     a(b(a(a(c(a(?x_5)))))) = b(a(c(b(a(c(?x_5)))))),
     a(b(a(b(c(?x_8))))) = b(a(c(b(b(?x_8))))),
     a(b(a(d(c(?x_12))))) = b(a(c(b(d(?x_12))))),
     b(c(a(c(a(?x_5))))) = c(c(b(a(c(?x_5))))),
     b(c(b(c(?x_8)))) = c(c(b(b(?x_8)))),
     b(c(d(c(?x_12)))) = c(c(b(d(?x_12)))),
     b(d(a(c(a(?x_5))))) = d(c(b(a(c(?x_5))))),
     b(d(b(c(?x_8)))) = d(c(b(b(?x_8)))),
     b(d(d(c(?x_12)))) = d(c(b(d(?x_12)))),
     a(b(a(c(?x)))) = b(a(c(b(?x)))),
     b(c(c(?x))) = c(c(b(?x))),
     b(d(c(?x))) = d(c(b(?x))),
     c(a(b(a(?x_3)))) = b(c(a(b(?x_3)))),
     c(c(b(?x_8))) = b(c(c(?x_8))),
     c(d(b(?x_9))) = b(c(d(?x_9))),
     a(c(a(a(b(a(?x_3)))))) = c(a(b(c(a(b(?x_3)))))),
     a(c(a(c(b(?x_8))))) = c(a(b(c(c(?x_8))))),
     a(c(a(d(b(?x_9))))) = c(a(b(c(d(?x_9))))),
     c(b(a(b(a(?x_3))))) = b(b(c(a(b(?x_3))))),
     c(b(c(b(?x_8)))) = b(b(c(c(?x_8)))),
     c(b(d(b(?x_9)))) = b(b(c(d(?x_9)))),
     c(d(a(b(a(?x_3))))) = d(b(c(a(b(?x_3))))),
     c(d(c(b(?x_8)))) = d(b(c(c(?x_8)))),
     c(d(d(b(?x_9)))) = d(b(c(d(?x_9)))),
     a(c(a(b(?x)))) = c(a(b(c(?x)))),
     c(b(b(?x))) = b(b(c(?x))),
     c(d(b(?x))) = d(b(c(?x))),
     b(a(d(a(?x_7)))) = d(b(a(d(?x_7)))),
     b(b(d(?x_10))) = d(b(b(?x_10))),
     b(c(d(?x_11))) = d(b(c(?x_11))),
     a(b(a(a(d(a(?x_7)))))) = b(a(d(b(a(d(?x_7)))))),
     a(b(a(b(d(?x_10))))) = b(a(d(b(b(?x_10))))),
     a(b(a(c(d(?x_11))))) = b(a(d(b(c(?x_11))))),
     b(c(a(d(a(?x_7))))) = c(d(b(a(d(?x_7))))),
     b(c(b(d(?x_10)))) = c(d(b(b(?x_10)))),
     b(c(c(d(?x_11)))) = c(d(b(c(?x_11)))),
     b(d(a(d(a(?x_7))))) = d(d(b(a(d(?x_7))))),
     b(d(b(d(?x_10)))) = d(d(b(b(?x_10)))),
     b(d(c(d(?x_11)))) = d(d(b(c(?x_11)))),
     a(b(a(d(?x)))) = b(a(d(b(?x)))),
     b(c(d(?x))) = c(d(b(?x))),
     b(d(d(?x))) = d(d(b(?x))),
     d(a(b(a(?x_3)))) = b(d(a(b(?x_3)))),
     d(c(b(?x_8))) = b(d(c(?x_8))),
     d(d(b(?x_10))) = b(d(d(?x_10))),
     a(d(a(a(b(a(?x_3)))))) = d(a(b(d(a(b(?x_3)))))),
     a(d(a(c(b(?x_8))))) = d(a(b(d(c(?x_8))))),
     a(d(a(d(b(?x_10))))) = d(a(b(d(d(?x_10))))),
     d(b(a(b(a(?x_3))))) = b(b(d(a(b(?x_3))))),
     d(b(c(b(?x_8)))) = b(b(d(c(?x_8)))),
     d(b(d(b(?x_10)))) = b(b(d(d(?x_10)))),
     d(c(a(b(a(?x_3))))) = c(b(d(a(b(?x_3))))),
     d(c(c(b(?x_8)))) = c(b(d(c(?x_8)))),
     d(c(d(b(?x_10)))) = c(b(d(d(?x_10)))),
     a(d(a(b(?x)))) = d(a(b(d(?x)))),
     d(b(b(?x))) = b(b(d(?x))),
     d(c(b(?x))) = c(b(d(?x))),
     d(a(c(a(?x_5)))) = c(d(a(c(?x_5)))),
     d(b(c(?x_9))) = c(d(b(?x_9))),
     d(d(c(?x_12))) = c(d(d(?x_12))),
     a(d(a(a(c(a(?x_5)))))) = d(a(c(d(a(c(?x_5)))))),
     a(d(a(b(c(?x_9))))) = d(a(c(d(b(?x_9))))),
     a(d(a(d(c(?x_12))))) = d(a(c(d(d(?x_12))))),
     d(b(a(c(a(?x_5))))) = b(c(d(a(c(?x_5))))),
     d(b(b(c(?x_9)))) = b(c(d(b(?x_9)))),
     d(b(d(c(?x_12)))) = b(c(d(d(?x_12)))),
     d(c(a(c(a(?x_5))))) = c(c(d(a(c(?x_5))))),
     d(c(b(c(?x_9)))) = c(c(d(b(?x_9)))),
     d(c(d(c(?x_12)))) = c(c(d(d(?x_12)))),
     a(d(a(c(?x)))) = d(a(c(d(?x)))),
     d(b(c(?x))) = b(c(d(?x))),
     d(c(c(?x))) = c(c(d(?x))),
     c(a(d(a(?x_7)))) = d(c(a(d(?x_7)))),
     c(b(d(?x_11))) = d(c(b(?x_11))),
     c(c(d(?x_12))) = d(c(c(?x_12))),
     a(c(a(a(d(a(?x_7)))))) = c(a(d(c(a(d(?x_7)))))),
     a(c(a(b(d(?x_11))))) = c(a(d(c(b(?x_11))))),
     a(c(a(c(d(?x_12))))) = c(a(d(c(c(?x_12))))),
     c(b(a(d(a(?x_7))))) = b(d(c(a(d(?x_7))))),
     c(b(b(d(?x_11)))) = b(d(c(b(?x_11)))),
     c(b(c(d(?x_12)))) = b(d(c(c(?x_12)))),
     c(d(a(d(a(?x_7))))) = d(d(c(a(d(?x_7))))),
     c(d(b(d(?x_11)))) = d(d(c(b(?x_11)))),
     c(d(c(d(?x_12)))) = d(d(c(c(?x_12)))),
     a(c(a(d(?x)))) = c(a(d(c(?x)))),
     c(b(d(?x))) = b(d(c(?x))),
     c(d(d(?x))) = d(d(c(?x))),
     b(p) = a(p),
     c(p) = a(p),
     d(p) = a(p),
     a(p) = b(p),
     c(p) = b(p),
     d(p) = b(p),
     a(p) = c(p),
     b(p) = c(p),
     d(p) = c(p),
     a(p) = d(p),
     b(p) = d(p),
     c(p) = d(p) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <a(a(b(a(?x_1)))), b(a(b(b(?x_1))))> by Rules <1, 0> preceded by [(a,1)]
 joinable by a reduction of rules <[([(a,1)],0)], [([],1)]>
Critical Pair <a(b(c(a(c(?x_2))))), b(a(b(c(a(?x_2)))))> by Rules <2, 0> preceded by [(a,1),(b,1)]
 joinable by a reduction of rules <[([(a,1),(b,1)],3)], [([],1)]>
Critical Pair <a(b(d(a(d(?x_4))))), b(a(b(d(a(?x_4)))))> by Rules <4, 0> preceded by [(a,1),(b,1)]
 joinable by a reduction of rules <[([(a,1),(b,1)],5)], [([],1)]>
Critical Pair <b(b(a(b(?x)))), a(b(a(a(?x))))> by Rules <0, 1> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],1)], [([],0)]>
Critical Pair <b(a(c(b(?x_6)))), a(b(a(c(?x_6))))> by Rules <6, 1> preceded by [(b,1),(a,1)]
 joinable by a reduction of rules <[([(b,1),(a,1)],7)], [([],0)]>
Critical Pair <b(a(d(b(?x_8)))), a(b(a(d(?x_8))))> by Rules <8, 1> preceded by [(b,1),(a,1)]
 joinable by a reduction of rules <[([(b,1),(a,1)],9)], [([],0)]>
Critical Pair <a(c(b(a(b(?x))))), c(a(c(b(a(?x)))))> by Rules <0, 2> preceded by [(a,1),(c,1)]
 joinable by a reduction of rules <[([(a,1),(c,1)],1)], [([],3)]>
Critical Pair <a(a(c(a(?x_3)))), c(a(c(c(?x_3))))> by Rules <3, 2> preceded by [(a,1)]
 joinable by a reduction of rules <[([(a,1)],2)], [([],3)]>
Critical Pair <a(c(d(a(d(?x_4))))), c(a(c(d(a(?x_4)))))> by Rules <4, 2> preceded by [(a,1),(c,1)]
 joinable by a reduction of rules <[([(a,1),(c,1)],5)], [([],3)]>
Critical Pair <c(c(a(c(?x_2)))), a(c(a(a(?x_2))))> by Rules <2, 3> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],3)], [([],2)]>
Critical Pair <c(a(b(c(?x_7)))), a(c(a(b(?x_7))))> by Rules <7, 3> preceded by [(c,1),(a,1)]
 joinable by a reduction of rules <[([(c,1),(a,1)],6)], [([],2)]>
Critical Pair <c(a(d(c(?x_11)))), a(c(a(d(?x_11))))> by Rules <11, 3> preceded by [(c,1),(a,1)]
 joinable by a reduction of rules <[([(c,1),(a,1)],10)], [([],2)]>
Critical Pair <a(d(b(a(b(?x))))), d(a(d(b(a(?x)))))> by Rules <0, 4> preceded by [(a,1),(d,1)]
 joinable by a reduction of rules <[([(a,1),(d,1)],1)], [([],5)]>
Critical Pair <a(d(c(a(c(?x_2))))), d(a(d(c(a(?x_2)))))> by Rules <2, 4> preceded by [(a,1),(d,1)]
 joinable by a reduction of rules <[([(a,1),(d,1)],3)], [([],5)]>
Critical Pair <a(a(d(a(?x_5)))), d(a(d(d(?x_5))))> by Rules <5, 4> preceded by [(a,1)]
 joinable by a reduction of rules <[([(a,1)],4)], [([],5)]>
Critical Pair <d(d(a(d(?x_4)))), a(d(a(a(?x_4))))> by Rules <4, 5> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],5)], [([],4)]>
Critical Pair <d(a(b(d(?x_9)))), a(d(a(b(?x_9))))> by Rules <9, 5> preceded by [(d,1),(a,1)]
 joinable by a reduction of rules <[([(d,1),(a,1)],8)], [([],4)]>
Critical Pair <d(a(c(d(?x_10)))), a(d(a(c(?x_10))))> by Rules <10, 5> preceded by [(d,1),(a,1)]
 joinable by a reduction of rules <[([(d,1),(a,1)],11)], [([],4)]>
Critical Pair <b(a(c(a(?x_3)))), c(b(a(c(?x_3))))> by Rules <3, 6> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],2)], [([],7)]>
Critical Pair <b(b(c(?x_7))), c(b(b(?x_7)))> by Rules <7, 6> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],6)], [([],7)]>
Critical Pair <b(d(c(?x_11))), c(b(d(?x_11)))> by Rules <11, 6> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],10)], [([],7)]>
Critical Pair <c(a(b(a(?x_1)))), b(c(a(b(?x_1))))> by Rules <1, 7> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],0)], [([],6)]>
Critical Pair <c(c(b(?x_6))), b(c(c(?x_6)))> by Rules <6, 7> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],7)], [([],6)]>
Critical Pair <c(d(b(?x_8))), b(c(d(?x_8)))> by Rules <8, 7> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],9)], [([],6)]>
Critical Pair <b(a(d(a(?x_5)))), d(b(a(d(?x_5))))> by Rules <5, 8> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],4)], [([],9)]>
Critical Pair <b(b(d(?x_9))), d(b(b(?x_9)))> by Rules <9, 8> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],8)], [([],9)]>
Critical Pair <b(c(d(?x_10))), d(b(c(?x_10)))> by Rules <10, 8> preceded by [(b,1)]
 joinable by a reduction of rules <[([(b,1)],11)], [([],9)]>
Critical Pair <d(a(b(a(?x_1)))), b(d(a(b(?x_1))))> by Rules <1, 9> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],0)], [([],8)]>
Critical Pair <d(c(b(?x_6))), b(d(c(?x_6)))> by Rules <6, 9> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],7)], [([],8)]>
Critical Pair <d(d(b(?x_8))), b(d(d(?x_8)))> by Rules <8, 9> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],9)], [([],8)]>
Critical Pair <d(a(c(a(?x_3)))), c(d(a(c(?x_3))))> by Rules <3, 10> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],2)], [([],11)]>
Critical Pair <d(b(c(?x_7))), c(d(b(?x_7)))> by Rules <7, 10> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],6)], [([],11)]>
Critical Pair <d(d(c(?x_11))), c(d(d(?x_11)))> by Rules <11, 10> preceded by [(d,1)]
 joinable by a reduction of rules <[([(d,1)],10)], [([],11)]>
Critical Pair <c(a(d(a(?x_5)))), d(c(a(d(?x_5))))> by Rules <5, 11> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],4)], [([],10)]>
Critical Pair <c(b(d(?x_9))), d(c(b(?x_9)))> by Rules <9, 11> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],8)], [([],10)]>
Critical Pair <c(c(d(?x_10))), d(c(c(?x_10)))> by Rules <10, 11> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],11)], [([],10)]>
Critical Pair <a(b(b(a(b(?x))))), b(a(b(b(a(?x)))))> by Rules <0, 0> preceded by [(a,1),(b,1)]
 joinable by a reduction of rules <[([(a,1),(b,1)],1)], [([],1)]>
Critical Pair <b(a(a(b(a(?x))))), a(b(a(a(b(?x)))))> by Rules <1, 1> preceded by [(b,1),(a,1)]
 joinable by a reduction of rules <[([(b,1),(a,1)],0)], [([],0)]>
Critical Pair <a(c(c(a(c(?x))))), c(a(c(c(a(?x)))))> by Rules <2, 2> preceded by [(a,1),(c,1)]
 joinable by a reduction of rules <[([(a,1),(c,1)],3)], [([],3)]>
Critical Pair <c(a(a(c(a(?x))))), a(c(a(a(c(?x)))))> by Rules <3, 3> preceded by [(c,1),(a,1)]
 joinable by a reduction of rules <[([(c,1),(a,1)],2)], [([],2)]>
Critical Pair <a(d(d(a(d(?x))))), d(a(d(d(a(?x)))))> by Rules <4, 4> preceded by [(a,1),(d,1)]
 joinable by a reduction of rules <[([(a,1),(d,1)],5)], [([],5)]>
Critical Pair <d(a(a(d(a(?x))))), a(d(a(a(d(?x)))))> by Rules <5, 5> preceded by [(d,1),(a,1)]
 joinable by a reduction of rules <[([(d,1),(a,1)],4)], [([],4)]>
Critical Pair <b(p), a(p)> by Rules <13, 12> preceded by []
 joinable by a reduction of rules <[([(b,1)],12),([(b,1),(a,1)],13),([],1)], [([(a,1)],13),([(a,1),(b,1)],12)]>
 joinable by a reduction of rules <[([(b,1)],12),([(b,1),(a,1)],13)], [([(a,1)],13),([(a,1),(b,1)],12),([],0)]>
Critical Pair <c(p), a(p)> by Rules <14, 12> preceded by []
 joinable by a reduction of rules <[([(c,1)],12),([(c,1),(a,1)],14),([],3)], [([(a,1)],14),([(a,1),(c,1)],12)]>
 joinable by a reduction of rules <[([(c,1)],12),([(c,1),(a,1)],14)], [([(a,1)],14),([(a,1),(c,1)],12),([],2)]>
Critical Pair <d(p), a(p)> by Rules <15, 12> preceded by []
 joinable by a reduction of rules <[([(d,1)],12),([(d,1),(a,1)],15),([],5)], [([(a,1)],15),([(a,1),(d,1)],12)]>
 joinable by a reduction of rules <[([(d,1)],12),([(d,1),(a,1)],15)], [([(a,1)],15),([(a,1),(d,1)],12),([],4)]>
Critical Pair <c(p), b(p)> by Rules <14, 13> preceded by []
 joinable by a reduction of rules <[([(c,1)],13),([],7)], [([(b,1)],14)]>
 joinable by a reduction of rules <[([(c,1)],13)], [([(b,1)],14),([],6)]>
Critical Pair <d(p), b(p)> by Rules <15, 13> preceded by []
 joinable by a reduction of rules <[([(d,1)],13),([],9)], [([(b,1)],15)]>
 joinable by a reduction of rules <[([(d,1)],13)], [([(b,1)],15),([],8)]>
Critical Pair <d(p), c(p)> by Rules <15, 14> preceded by []
 joinable by a reduction of rules <[([(d,1)],14),([],10)], [([(c,1)],15)]>
 joinable by a reduction of rules <[([(d,1)],14)], [([(c,1)],15),([],11)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 22 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
unknown Huet (modulo AC)
check by Reduction-Preserving Completion...
STEP: 1 (parallel)
S:
   [ p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
P:
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)) ]
S: unknown termination
failure(Step 1)
STEP: 2 (linear)
S:
   [ p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
P:
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)) ]
S: unknown termination
failure(Step 2)
STEP: 3 (relative)
S:
   [ p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
P:
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)) ]
Check relative termination:
   [ p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)) ]
not relatively terminatiing
S/P: unknown relative termination
failure(Step 3)
failure(no possibility remains)
unknown Reduction-Preserving Completion
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)),
     p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
Sort Assignment:
 a : 22=>22
 b : 22=>22
 c : 22=>22
 d : 22=>22
 p : =>22
maximal types: {22}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)),
     p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     c(a(c(?x))) -> a(c(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     d(a(d(?x))) -> a(d(a(?x))),
     b(c(?x)) -> c(b(?x)),
     c(b(?x)) -> b(c(?x)),
     b(d(?x)) -> d(b(?x)),
     d(b(?x)) -> b(d(?x)),
     d(c(?x)) -> c(d(?x)),
     c(d(?x)) -> d(c(?x)),
     p -> a(p),
     p -> b(p),
     p -> c(p),
     p -> d(p) ]
Outside Critical Pair: <b(p), a(p)> by Rules <13, 12>
develop reducts from lhs term...
<{15}, b(d(p))>
<{14}, b(c(p))>
<{13}, b(b(p))>
<{12}, b(a(p))>
<{}, b(p)>
develop reducts from rhs term...
<{15}, a(d(p))>
<{14}, a(c(p))>
<{13}, a(b(p))>
<{12}, a(a(p))>
<{}, a(p)>
Outside Critical Pair: <c(p), a(p)> by Rules <14, 12>
develop reducts from lhs term...
<{15}, c(d(p))>
<{14}, c(c(p))>
<{13}, c(b(p))>
<{12}, c(a(p))>
<{}, c(p)>
develop reducts from rhs term...
<{15}, a(d(p))>
<{14}, a(c(p))>
<{13}, a(b(p))>
<{12}, a(a(p))>
<{}, a(p)>
Outside Critical Pair: <d(p), a(p)> by Rules <15, 12>
develop reducts from lhs term...
<{15}, d(d(p))>
<{14}, d(c(p))>
<{13}, d(b(p))>
<{12}, d(a(p))>
<{}, d(p)>
develop reducts from rhs term...
<{15}, a(d(p))>
<{14}, a(c(p))>
<{13}, a(b(p))>
<{12}, a(a(p))>
<{}, a(p)>
Outside Critical Pair: <c(p), b(p)> by Rules <14, 13>
develop reducts from lhs term...
<{15}, c(d(p))>
<{14}, c(c(p))>
<{13}, c(b(p))>
<{12}, c(a(p))>
<{}, c(p)>
develop reducts from rhs term...
<{15}, b(d(p))>
<{14}, b(c(p))>
<{13}, b(b(p))>
<{12}, b(a(p))>
<{}, b(p)>
Outside Critical Pair: <d(p), b(p)> by Rules <15, 13>
develop reducts from lhs term...
<{15}, d(d(p))>
<{14}, d(c(p))>
<{13}, d(b(p))>
<{12}, d(a(p))>
<{}, d(p)>
develop reducts from rhs term...
<{15}, b(d(p))>
<{14}, b(c(p))>
<{13}, b(b(p))>
<{12}, b(a(p))>
<{}, b(p)>
Outside Critical Pair: <d(p), c(p)> by Rules <15, 14>
develop reducts from lhs term...
<{15}, d(d(p))>
<{14}, d(c(p))>
<{13}, d(b(p))>
<{12}, d(a(p))>
<{}, d(p)>
develop reducts from rhs term...
<{15}, c(d(p))>
<{14}, c(c(p))>
<{13}, c(b(p))>
<{12}, c(a(p))>
<{}, c(p)>
Inside Critical Pair: <a(a(b(a(?x_1)))), b(a(b(b(?x_1))))> by Rules <1, 0>
develop reducts from lhs term...
<{0}, a(b(a(b(?x_1))))>
<{}, a(a(b(a(?x_1))))>
develop reducts from rhs term...
<{1}, a(b(a(b(?x_1))))>
<{}, b(a(b(b(?x_1))))>
Inside Critical Pair: <a(b(c(a(c(?x_2))))), b(a(b(c(a(?x_2)))))> by Rules <2, 0>
develop reducts from lhs term...
<{6}, a(c(b(a(c(?x_2)))))>
<{3}, a(b(a(c(a(?x_2)))))>
<{}, a(b(c(a(c(?x_2)))))>
develop reducts from rhs term...
<{1}, a(b(a(c(a(?x_2)))))>
<{6}, b(a(c(b(a(?x_2)))))>
<{}, b(a(b(c(a(?x_2)))))>
Inside Critical Pair: <a(b(d(a(d(?x_4))))), b(a(b(d(a(?x_4)))))> by Rules <4, 0>
develop reducts from lhs term...
<{8}, a(d(b(a(d(?x_4)))))>
<{5}, a(b(a(d(a(?x_4)))))>
<{}, a(b(d(a(d(?x_4)))))>
develop reducts from rhs term...
<{1}, a(b(a(d(a(?x_4)))))>
<{8}, b(a(d(b(a(?x_4)))))>
<{}, b(a(b(d(a(?x_4)))))>
Inside Critical Pair: <b(b(a(b(?x)))), a(b(a(a(?x))))> by Rules <0, 1>
develop reducts from lhs term...
<{1}, b(a(b(a(?x))))>
<{}, b(b(a(b(?x))))>
develop reducts from rhs term...
<{0}, b(a(b(a(?x))))>
<{}, a(b(a(a(?x))))>
Inside Critical Pair: <b(a(c(b(?x_6)))), a(b(a(c(?x_6))))> by Rules <6, 1>
develop reducts from lhs term...
<{7}, b(a(b(c(?x_6))))>
<{}, b(a(c(b(?x_6))))>
develop reducts from rhs term...
<{0}, b(a(b(c(?x_6))))>
<{}, a(b(a(c(?x_6))))>
Inside Critical Pair: <b(a(d(b(?x_8)))), a(b(a(d(?x_8))))> by Rules <8, 1>
develop reducts from lhs term...
<{9}, b(a(b(d(?x_8))))>
<{}, b(a(d(b(?x_8))))>
develop reducts from rhs term...
<{0}, b(a(b(d(?x_8))))>
<{}, a(b(a(d(?x_8))))>
Inside Critical Pair: <a(c(b(a(b(?x))))), c(a(c(b(a(?x)))))> by Rules <0, 2>
develop reducts from lhs term...
<{7}, a(b(c(a(b(?x)))))>
<{1}, a(c(a(b(a(?x)))))>
<{}, a(c(b(a(b(?x)))))>
develop reducts from rhs term...
<{3}, a(c(a(b(a(?x)))))>
<{7}, c(a(b(c(a(?x)))))>
<{}, c(a(c(b(a(?x)))))>
Inside Critical Pair: <a(a(c(a(?x_3)))), c(a(c(c(?x_3))))> by Rules <3, 2>
develop reducts from lhs term...
<{2}, a(c(a(c(?x_3))))>
<{}, a(a(c(a(?x_3))))>
develop reducts from rhs term...
<{3}, a(c(a(c(?x_3))))>
<{}, c(a(c(c(?x_3))))>
Inside Critical Pair: <a(c(d(a(d(?x_4))))), c(a(c(d(a(?x_4)))))> by Rules <4, 2>
develop reducts from lhs term...
<{11}, a(d(c(a(d(?x_4)))))>
<{5}, a(c(a(d(a(?x_4)))))>
<{}, a(c(d(a(d(?x_4)))))>
develop reducts from rhs term...
<{3}, a(c(a(d(a(?x_4)))))>
<{11}, c(a(d(c(a(?x_4)))))>
<{}, c(a(c(d(a(?x_4)))))>
Inside Critical Pair: <c(c(a(c(?x_2)))), a(c(a(a(?x_2))))> by Rules <2, 3>
develop reducts from lhs term...
<{3}, c(a(c(a(?x_2))))>
<{}, c(c(a(c(?x_2))))>
develop reducts from rhs term...
<{2}, c(a(c(a(?x_2))))>
<{}, a(c(a(a(?x_2))))>
Inside Critical Pair: <c(a(b(c(?x_7)))), a(c(a(b(?x_7))))> by Rules <7, 3>
develop reducts from lhs term...
<{6}, c(a(c(b(?x_7))))>
<{}, c(a(b(c(?x_7))))>
develop reducts from rhs term...
<{2}, c(a(c(b(?x_7))))>
<{}, a(c(a(b(?x_7))))>
Inside Critical Pair: <c(a(d(c(?x_11)))), a(c(a(d(?x_11))))> by Rules <11, 3>
develop reducts from lhs term...
<{10}, c(a(c(d(?x_11))))>
<{}, c(a(d(c(?x_11))))>
develop reducts from rhs term...
<{2}, c(a(c(d(?x_11))))>
<{}, a(c(a(d(?x_11))))>
Inside Critical Pair: <a(d(b(a(b(?x))))), d(a(d(b(a(?x)))))> by Rules <0, 4>
develop reducts from lhs term...
<{9}, a(b(d(a(b(?x)))))>
<{1}, a(d(a(b(a(?x)))))>
<{}, a(d(b(a(b(?x)))))>
develop reducts from rhs term...
<{5}, a(d(a(b(a(?x)))))>
<{9}, d(a(b(d(a(?x)))))>
<{}, d(a(d(b(a(?x)))))>
Inside Critical Pair: <a(d(c(a(c(?x_2))))), d(a(d(c(a(?x_2)))))> by Rules <2, 4>
develop reducts from lhs term...
<{10}, a(c(d(a(c(?x_2)))))>
<{3}, a(d(a(c(a(?x_2)))))>
<{}, a(d(c(a(c(?x_2)))))>
develop reducts from rhs term...
<{5}, a(d(a(c(a(?x_2)))))>
<{10}, d(a(c(d(a(?x_2)))))>
<{}, d(a(d(c(a(?x_2)))))>
Inside Critical Pair: <a(a(d(a(?x_5)))), d(a(d(d(?x_5))))> by Rules <5, 4>
develop reducts from lhs term...
<{4}, a(d(a(d(?x_5))))>
<{}, a(a(d(a(?x_5))))>
develop reducts from rhs term...
<{5}, a(d(a(d(?x_5))))>
<{}, d(a(d(d(?x_5))))>
Inside Critical Pair: <d(d(a(d(?x_4)))), a(d(a(a(?x_4))))> by Rules <4, 5>
develop reducts from lhs term...
<{5}, d(a(d(a(?x_4))))>
<{}, d(d(a(d(?x_4))))>
develop reducts from rhs term...
<{4}, d(a(d(a(?x_4))))>
<{}, a(d(a(a(?x_4))))>
Inside Critical Pair: <d(a(b(d(?x_9)))), a(d(a(b(?x_9))))> by Rules <9, 5>
develop reducts from lhs term...
<{8}, d(a(d(b(?x_9))))>
<{}, d(a(b(d(?x_9))))>
develop reducts from rhs term...
<{4}, d(a(d(b(?x_9))))>
<{}, a(d(a(b(?x_9))))>
Inside Critical Pair: <d(a(c(d(?x_10)))), a(d(a(c(?x_10))))> by Rules <10, 5>
develop reducts from lhs term...
<{11}, d(a(d(c(?x_10))))>
<{}, d(a(c(d(?x_10))))>
develop reducts from rhs term...
<{4}, d(a(d(c(?x_10))))>
<{}, a(d(a(c(?x_10))))>
Inside Critical Pair: <b(a(c(a(?x_3)))), c(b(a(c(?x_3))))> by Rules <3, 6>
develop reducts from lhs term...
<{2}, b(c(a(c(?x_3))))>
<{}, b(a(c(a(?x_3))))>
develop reducts from rhs term...
<{7}, b(c(a(c(?x_3))))>
<{}, c(b(a(c(?x_3))))>
Inside Critical Pair: <b(b(c(?x_7))), c(b(b(?x_7)))> by Rules <7, 6>
develop reducts from lhs term...
<{6}, b(c(b(?x_7)))>
<{}, b(b(c(?x_7)))>
develop reducts from rhs term...
<{7}, b(c(b(?x_7)))>
<{}, c(b(b(?x_7)))>
Inside Critical Pair: <b(d(c(?x_11))), c(b(d(?x_11)))> by Rules <11, 6>
develop reducts from lhs term...
<{8}, d(b(c(?x_11)))>
<{10}, b(c(d(?x_11)))>
<{}, b(d(c(?x_11)))>
develop reducts from rhs term...
<{7}, b(c(d(?x_11)))>
<{8}, c(d(b(?x_11)))>
<{}, c(b(d(?x_11)))>
Inside Critical Pair: <c(a(b(a(?x_1)))), b(c(a(b(?x_1))))> by Rules <1, 7>
develop reducts from lhs term...
<{0}, c(b(a(b(?x_1))))>
<{}, c(a(b(a(?x_1))))>
develop reducts from rhs term...
<{6}, c(b(a(b(?x_1))))>
<{}, b(c(a(b(?x_1))))>
Inside Critical Pair: <c(c(b(?x_6))), b(c(c(?x_6)))> by Rules <6, 7>
develop reducts from lhs term...
<{7}, c(b(c(?x_6)))>
<{}, c(c(b(?x_6)))>
develop reducts from rhs term...
<{6}, c(b(c(?x_6)))>
<{}, b(c(c(?x_6)))>
Inside Critical Pair: <c(d(b(?x_8))), b(c(d(?x_8)))> by Rules <8, 7>
develop reducts from lhs term...
<{11}, d(c(b(?x_8)))>
<{9}, c(b(d(?x_8)))>
<{}, c(d(b(?x_8)))>
develop reducts from rhs term...
<{6}, c(b(d(?x_8)))>
<{11}, b(d(c(?x_8)))>
<{}, b(c(d(?x_8)))>
Inside Critical Pair: <b(a(d(a(?x_5)))), d(b(a(d(?x_5))))> by Rules <5, 8>
develop reducts from lhs term...
<{4}, b(d(a(d(?x_5))))>
<{}, b(a(d(a(?x_5))))>
develop reducts from rhs term...
<{9}, b(d(a(d(?x_5))))>
<{}, d(b(a(d(?x_5))))>
Inside Critical Pair: <b(b(d(?x_9))), d(b(b(?x_9)))> by Rules <9, 8>
develop reducts from lhs term...
<{8}, b(d(b(?x_9)))>
<{}, b(b(d(?x_9)))>
develop reducts from rhs term...
<{9}, b(d(b(?x_9)))>
<{}, d(b(b(?x_9)))>
Inside Critical Pair: <b(c(d(?x_10))), d(b(c(?x_10)))> by Rules <10, 8>
develop reducts from lhs term...
<{6}, c(b(d(?x_10)))>
<{11}, b(d(c(?x_10)))>
<{}, b(c(d(?x_10)))>
develop reducts from rhs term...
<{9}, b(d(c(?x_10)))>
<{6}, d(c(b(?x_10)))>
<{}, d(b(c(?x_10)))>
Inside Critical Pair: <d(a(b(a(?x_1)))), b(d(a(b(?x_1))))> by Rules <1, 9>
develop reducts from lhs term...
<{0}, d(b(a(b(?x_1))))>
<{}, d(a(b(a(?x_1))))>
develop reducts from rhs term...
<{8}, d(b(a(b(?x_1))))>
<{}, b(d(a(b(?x_1))))>
Inside Critical Pair: <d(c(b(?x_6))), b(d(c(?x_6)))> by Rules <6, 9>
develop reducts from lhs term...
<{10}, c(d(b(?x_6)))>
<{7}, d(b(c(?x_6)))>
<{}, d(c(b(?x_6)))>
develop reducts from rhs term...
<{8}, d(b(c(?x_6)))>
<{10}, b(c(d(?x_6)))>
<{}, b(d(c(?x_6)))>
Inside Critical Pair: <d(d(b(?x_8))), b(d(d(?x_8)))> by Rules <8, 9>
develop reducts from lhs term...
<{9}, d(b(d(?x_8)))>
<{}, d(d(b(?x_8)))>
develop reducts from rhs term...
<{8}, d(b(d(?x_8)))>
<{}, b(d(d(?x_8)))>
Inside Critical Pair: <d(a(c(a(?x_3)))), c(d(a(c(?x_3))))> by Rules <3, 10>
develop reducts from lhs term...
<{2}, d(c(a(c(?x_3))))>
<{}, d(a(c(a(?x_3))))>
develop reducts from rhs term...
<{11}, d(c(a(c(?x_3))))>
<{}, c(d(a(c(?x_3))))>
Inside Critical Pair: <d(b(c(?x_7))), c(d(b(?x_7)))> by Rules <7, 10>
develop reducts from lhs term...
<{9}, b(d(c(?x_7)))>
<{6}, d(c(b(?x_7)))>
<{}, d(b(c(?x_7)))>
develop reducts from rhs term...
<{11}, d(c(b(?x_7)))>
<{9}, c(b(d(?x_7)))>
<{}, c(d(b(?x_7)))>
Inside Critical Pair: <d(d(c(?x_11))), c(d(d(?x_11)))> by Rules <11, 10>
develop reducts from lhs term...
<{10}, d(c(d(?x_11)))>
<{}, d(d(c(?x_11)))>
develop reducts from rhs term...
<{11}, d(c(d(?x_11)))>
<{}, c(d(d(?x_11)))>
Inside Critical Pair: <c(a(d(a(?x_5)))), d(c(a(d(?x_5))))> by Rules <5, 11>
develop reducts from lhs term...
<{4}, c(d(a(d(?x_5))))>
<{}, c(a(d(a(?x_5))))>
develop reducts from rhs term...
<{10}, c(d(a(d(?x_5))))>
<{}, d(c(a(d(?x_5))))>
Inside Critical Pair: <c(b(d(?x_9))), d(c(b(?x_9)))> by Rules <9, 11>
develop reducts from lhs term...
<{7}, b(c(d(?x_9)))>
<{8}, c(d(b(?x_9)))>
<{}, c(b(d(?x_9)))>
develop reducts from rhs term...
<{10}, c(d(b(?x_9)))>
<{7}, d(b(c(?x_9)))>
<{}, d(c(b(?x_9)))>
Inside Critical Pair: <c(c(d(?x_10))), d(c(c(?x_10)))> by Rules <10, 11>
develop reducts from lhs term...
<{11}, c(d(c(?x_10)))>
<{}, c(c(d(?x_10)))>
develop reducts from rhs term...
<{10}, c(d(c(?x_10)))>
<{}, d(c(c(?x_10)))>
Try A Minimal Decomposition {15,14,12,13}{10,9,5,4,11,7,3,2,8,6,0,1}
{15,14,12,13}
(cm)Rewrite Rules:
   [ p -> d(p),
     p -> c(p),
     p -> a(p),
     p -> b(p) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ d(p) = c(p),
     d(p) = a(p),
     d(p) = b(p),
     c(p) = a(p),
     c(p) = b(p),
     a(p) = b(p) ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ c(p) = d(p),
     a(p) = d(p),
     b(p) = d(p),
     d(p) = c(p),
     a(p) = c(p),
     b(p) = c(p),
     d(p) = a(p),
     c(p) = a(p),
     b(p) = a(p),
     d(p) = b(p),
     c(p) = b(p),
     a(p) = b(p) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <c(p), d(p)> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <a(p) <- p -> b(p)>
Direct Methods: not CR
{10,9,5,4,11,7,3,2,8,6,0,1}
(cm)Rewrite Rules:
   [ d(c(?x)) -> c(d(?x)),
     d(b(?x)) -> b(d(?x)),
     d(a(d(?x))) -> a(d(a(?x))),
     a(d(a(?x))) -> d(a(d(?x))),
     c(d(?x)) -> d(c(?x)),
     c(b(?x)) -> b(c(?x)),
     c(a(c(?x))) -> a(c(a(?x))),
     a(c(a(?x))) -> c(a(c(?x))),
     b(d(?x)) -> d(b(?x)),
     b(c(?x)) -> c(b(?x)),
     a(b(a(?x))) -> b(a(b(?x))),
     b(a(b(?x))) -> a(b(a(?x))) ]
Apply Direct Methods...
Inner CPs:
   [ d(d(c(?x_4))) = c(d(d(?x_4))),
     d(b(c(?x_5))) = c(d(b(?x_5))),
     d(a(c(a(?x_6)))) = c(d(a(c(?x_6)))),
     d(d(b(?x_8))) = b(d(d(?x_8))),
     d(c(b(?x_9))) = b(d(c(?x_9))),
     d(a(b(a(?x_11)))) = b(d(a(b(?x_11)))),
     d(a(c(d(?x)))) = a(d(a(c(?x)))),
     d(a(b(d(?x_1)))) = a(d(a(b(?x_1)))),
     d(d(a(d(?x_3)))) = a(d(a(a(?x_3)))),
     a(a(d(a(?x_2)))) = d(a(d(d(?x_2)))),
     a(d(c(a(c(?x_7))))) = d(a(d(c(a(?x_7))))),
     a(d(b(a(b(?x_10))))) = d(a(d(b(a(?x_10))))),
     c(c(d(?x))) = d(c(c(?x))),
     c(b(d(?x_1))) = d(c(b(?x_1))),
     c(a(d(a(?x_2)))) = d(c(a(d(?x_2)))),
     c(d(b(?x_8))) = b(c(d(?x_8))),
     c(c(b(?x_9))) = b(c(c(?x_9))),
     c(a(b(a(?x_11)))) = b(c(a(b(?x_11)))),
     c(a(d(c(?x_4)))) = a(c(a(d(?x_4)))),
     c(a(b(c(?x_5)))) = a(c(a(b(?x_5)))),
     c(c(a(c(?x_7)))) = a(c(a(a(?x_7)))),
     a(c(d(a(d(?x_3))))) = c(a(c(d(a(?x_3))))),
     a(a(c(a(?x_6)))) = c(a(c(c(?x_6)))),
     a(c(b(a(b(?x_10))))) = c(a(c(b(a(?x_10))))),
     b(c(d(?x))) = d(b(c(?x))),
     b(b(d(?x_1))) = d(b(b(?x_1))),
     b(a(d(a(?x_2)))) = d(b(a(d(?x_2)))),
     b(d(c(?x_4))) = c(b(d(?x_4))),
     b(b(c(?x_5))) = c(b(b(?x_5))),
     b(a(c(a(?x_6)))) = c(b(a(c(?x_6)))),
     a(b(d(a(d(?x_3))))) = b(a(b(d(a(?x_3))))),
     a(b(c(a(c(?x_7))))) = b(a(b(c(a(?x_7))))),
     a(a(b(a(?x_11)))) = b(a(b(b(?x_11)))),
     b(a(d(b(?x_8)))) = a(b(a(d(?x_8)))),
     b(a(c(b(?x_9)))) = a(b(a(c(?x_9)))),
     b(b(a(b(?x_10)))) = a(b(a(a(?x_10)))),
     d(a(a(d(a(?x))))) = a(d(a(a(d(?x))))),
     a(d(d(a(d(?x))))) = d(a(d(d(a(?x))))),
     c(a(a(c(a(?x))))) = a(c(a(a(c(?x))))),
     a(c(c(a(c(?x))))) = c(a(c(c(a(?x))))),
     a(b(b(a(b(?x))))) = b(a(b(b(a(?x))))),
     b(a(a(b(a(?x))))) = a(b(a(a(b(?x))))) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
Strongly Closed
Direct Methods: CR
Commutative Decomposition failed: Can't judge
No further decomposition possible


Combined result: Can't judge
1283.trs: Failure(unknown CR)
MAYBE
(12464 msec.)