(ignored inputs)COMMENT TPDB SRS_Standard/Secret_06_SRS/aprove04
Rewrite Rules:
   [ sq(0(?x)) -> p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(?x))))))))))))))))),
     sq(s(?x)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(?x))))))))))))))))))))))))))))))))),
     twice(0(?x)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(?x))))))))))))))))))))))))))),
     twice(s(?x)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(?x))))))))))))))),
     p(p(s(?x))) -> p(?x),
     p(s(?x)) -> ?x,
     p(0(?x)) -> 0(s(s(s(s(s(s(s(s(s(s(s(?x)))))))))))),
     0(?x) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [ sq(?x_7) = p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(?x_7))))))))))))))))),
     twice(?x_7) = p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(?x_7))))))))))))))))))))))))))),
     p(?x_5) = p(?x_5),
     p(?x_7) = 0(s(s(s(s(s(s(s(s(s(s(s(?x_7)))))))))))) ]
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:
   [ sq(?x) = p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(?x))))))))))))))))),
     twice(?x) = p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(?x))))))))))))))))))))))))))),
     p(?x) = p(?x),
     p(?x) = 0(s(s(s(s(s(s(s(s(s(s(s(?x)))))))))))),
     p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(?x))))))))))))))))) = sq(?x),
     p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(?x))))))))))))))))))))))))))) = twice(?x),
     0(s(s(s(s(s(s(s(s(s(s(s(?x)))))))))))) = p(?x) ]
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 <sq(?x_7), p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(?x_7)))))))))))))))))> by Rules <7, 0> preceded by [(sq,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 69 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <s(s(s(s(s(s(s(s(s(s(s(c_1))))))))))) <- p(0(0(0(c_1)))) -> p(c_1)>
Direct Methods: not CR

Combined result: not CR
954.trs: Success(not CR)
NO
(146 msec.)