(ignored inputs)COMMENT experiments for [36] submitted by: Takahito Aoto
Rewrite Rules:
   [ +(0,?y) -> ?y,
     +(s(?x),?y) -> s(+(?x,?y)),
     +(?x,+(?y,?z)) -> +(+(?z,?y),?x),
     s(s(?x)) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [ +(?x_3,?y_1) = s(+(s(?x_3),?y_1)),
     +(?x_2,?y) = +(+(?y,0),?x_2),
     +(?x_2,s(+(?x_1,?y_1))) = +(+(?y_1,s(?x_1)),?x_2),
     +(?x_1,+(+(?z,?y),?x)) = +(+(+(?y,?z),?x),?x_1),
     s(?x) = s(?x) ]
Outer CPs:
   [ +(?y_2,?z_2) = +(+(?z_2,?y_2),0),
     s(+(?x_1,+(?y_2,?z_2))) = +(+(?z_2,?y_2),s(?x_1)) ]
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:
   [ +(+(?z_2,?y_2),0) = +(?y_2,?z_2),
     +(+(?y,0),?x_3) = +(?x_3,?y),
     +(+(?z_2,?y_2),?x_6) = s(+(s(?x_6),+(?y_2,?z_2))),
     +(+(?z_2,?y_2),s(?x)) = s(+(?x,+(?y_2,?z_2))),
     +(?x_4,?y) = s(+(s(?x_4),?y)),
     +(+(?y,?x_7),?x_3) = +(?x_3,s(+(s(?x_7),?y))),
     +(+(?y,s(?x)),?x_3) = +(?x_3,s(+(?x,?y))),
     +(+(?z_1,?y_1),?y) = +(+(+(?y_1,?z_1),?y),0),
     ?z = +(+(?z,0),0),
     s(+(?x_3,?z)) = +(+(?z,s(?x_3)),0),
     s(+(?x_2,+(+(?z_3,?y_3),?y))) = +(+(+(?y_3,?z_3),?y),s(?x_2)),
     s(+(?x_2,?z)) = +(+(?z,0),s(?x_2)),
     s(+(?x_2,s(+(?x_5,?z)))) = +(+(?z,s(?x_5)),s(?x_2)),
     +(?y,?z) = +(+(?z,?y),0),
     s(+(?x_2,+(?y,?z))) = +(+(?z,?y),s(?x_2)),
     +(?x,+(+(?z_1,?y_1),?y)) = +(+(+(?y_1,?z_1),?y),?x),
     +(?x,?z) = +(+(?z,0),?x),
     +(?x,s(+(?x_3,?z))) = +(+(?z,s(?x_3)),?x),
     +(+(+(+(?z_2,?y_2),?y),?x),?x_1) = +(?x_1,+(+(+(?y_2,?z_2),?y),?x)),
     +(+(?z,?x),?x_1) = +(?x_1,+(+(?z,0),?x)),
     +(+(s(+(?x_4,?z)),?x),?x_1) = +(?x_1,+(+(?z,s(?x_4)),?x)),
     +(+(+(?y,?z),?x),?x_1) = +(?x_1,+(+(?z,?y),?x)),
     s(?x_1) = s(?x_1),
     ?x_1 = s(s(?x_1)),
     s(+(?x_4,?y_3)) = +(s(?x_4),?y_3),
     s(+(s(?x),?y_3)) = +(?x,?y_3) ]
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 <+(?x_3,?y_1), s(+(s(?x_3),?y_1))> by Rules <3, 1> preceded by [(+,1)]
 joinable by a reduction of rules <[], [([(s,1)],1),([],3)]>
Critical Pair <+(?x_2,?y), +(+(?y,0),?x_2)> by Rules <0, 2> preceded by [(+,2)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 7 rules by 3 steps unfolding
obtain 30 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <+(c_1,0) <- +(c_1,+(0,0)) -> c_1>
Direct Methods: not CR

Combined result: not CR
582.trs: Success(not CR)
NO
(71 msec.)