(ignored inputs)COMMENT experiments for [125] submitted by: Takahito Aoto
Rewrite Rules:
   [ +(0,?y) -> ?y,
     +(s(?x),?y) -> s(+(?x,?y)),
     +(p(?x),?y) -> +(?x,p(?y)),
     p(s(?x)) -> s(p(?x)),
     s(p(?x)) -> p(s(?x)),
     p(s(0)) -> 0 ]
Apply Direct Methods...
Inner CPs:
   [ +(p(s(?x_4)),?y_1) = s(+(p(?x_4),?y_1)),
     +(s(p(?x_3)),?y_2) = +(s(?x_3),p(?y_2)),
     +(0,?y_2) = +(s(0),p(?y_2)),
     p(p(s(?x_4))) = s(p(p(?x_4))),
     s(s(p(?x_3))) = p(s(s(?x_3))),
     s(0) = p(s(s(0))) ]
Outer CPs:
   [ s(p(0)) = 0 ]
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:
   [ +(p(s(?x_5)),?y) = s(+(p(?x_5),?y)),
     +(s(p(?x_4)),?y) = +(s(?x_4),p(?y)),
     +(0,?y) = +(s(0),p(?y)),
     0 = s(p(0)),
     p(p(s(?x_5))) = s(p(p(?x_5))),
     +(p(s(?x_9)),p(?y_4)) = +(s(p(p(?x_9))),?y_4),
     p(s(p(s(?x_5)))) = s(s(p(p(?x_5)))),
     +(s(?x),p(?y_4)) = +(s(p(?x)),?y_4),
     p(s(s(?x))) = s(s(p(?x))),
     s(s(p(?x_5))) = p(s(s(?x_5))),
     s(0) = p(s(s(0))),
     s(+(s(p(?x_8)),?y_3)) = +(p(s(s(?x_8))),?y_3),
     s(+(0,?y_3)) = +(p(s(s(0))),?y_3),
     s(p(s(p(?x_5)))) = p(p(s(s(?x_5)))),
     s(p(0)) = p(p(s(s(0)))),
     s(+(p(?x),?y_3)) = +(p(s(?x)),?y_3),
     s(p(p(?x))) = p(p(s(?x))),
     s(p(0)) = 0,
     +(s(0),p(?y_2)) = +(0,?y_2),
     p(s(s(0))) = s(0) ]
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 <+(p(s(?x_4)),?y_1), s(+(p(?x_4),?y_1))> by Rules <4, 1> preceded by [(+,1)]
 joinable by a reduction of rules <[([(+,1)],3),([],1)], []>
 joinable by a reduction of rules <[([],2),([],1)], [([(s,1)],2)]>
Critical Pair <+(s(p(?x_3)),?y_2), +(s(?x_3),p(?y_2))> by Rules <3, 2> preceded by [(+,1)]
 joinable by a reduction of rules <[([(+,1)],4),([],2)], []>
 joinable by a reduction of rules <[([],1),([(s,1)],2)], [([],1)]>
Critical Pair <+(0,?y_2), +(s(0),p(?y_2))> by Rules <5, 2> preceded by [(+,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 45 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <p(s(c_1)) <- +(s(p(0)),c_1) -> c_1>
Direct Methods: not CR

Combined result: not CR
614.trs: Success(not CR)
NO
(95 msec.)