(ignored inputs)COMMENT TPDB SRS_Standard/Zantema_04/z108
Rewrite Rules:
   [ a(a(?x)) -> b(c(?x)),
     b(b(?x)) -> c(d(?x)),
     c(c(?x)) -> d(d(d(?x))),
     d(d(d(?x))) -> a(c(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ a(b(c(?x))) = b(c(a(?x))),
     b(c(d(?x))) = c(d(b(?x))),
     c(d(d(d(?x)))) = d(d(d(c(?x)))),
     d(a(c(?x))) = a(c(d(?x))),
     d(d(a(c(?x)))) = a(c(d(d(?x)))) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ a(b(c(?x_1))) = b(c(a(?x_1))),
     b(c(b(c(?x_1)))) = a(b(c(a(?x_1)))),
     b(c(a(?x))) = a(b(c(?x))),
     b(c(d(?x_1))) = c(d(b(?x_1))),
     c(d(c(d(?x_1)))) = b(c(d(b(?x_1)))),
     c(d(b(?x))) = b(c(d(?x))),
     c(d(d(d(?x_1)))) = d(d(d(c(?x_1)))),
     d(d(d(d(d(d(?x_1)))))) = c(d(d(d(c(?x_1))))),
     d(d(d(c(?x)))) = c(d(d(d(?x)))),
     d(a(c(?x_1))) = a(c(d(?x_1))),
     d(d(a(c(?x_1)))) = a(c(d(d(?x_1)))),
     a(c(a(c(?x_1)))) = d(a(c(d(d(?x_1))))),
     a(c(a(c(?x_1)))) = d(d(a(c(d(?x_1))))),
     a(c(d(a(c(?x_1))))) = d(d(a(c(d(d(?x_1)))))),
     a(c(d(?x))) = d(a(c(?x))),
     a(c(d(d(?x)))) = d(d(a(c(?x)))) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
Direct Methods: CR

Combined result: CR
943.trs: Success(CR)
YES
(54 msec.)