(ignored inputs)COMMENT submitted by: Johannes Waldmann
Rewrite Rules:
   [ b(b(?x)) -> b(a(?x)),
     a(c(?x)) -> b(a(?x)),
     a(c(?x)) -> c(b(?x)),
     c(c(?x)) -> b(c(?x)),
     b(c(?x)) -> b(c(?x)),
     c(b(?x)) -> b(a(?x)),
     a(b(?x)) -> a(c(?x)),
     a(a(?x)) -> a(a(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ b(b(c(?x_4))) = b(a(c(?x_4))),
     a(b(c(?x_3))) = b(a(c(?x_3))),
     a(b(a(?x_5))) = b(a(b(?x_5))),
     a(b(c(?x_3))) = c(b(c(?x_3))),
     a(b(a(?x_5))) = c(b(b(?x_5))),
     c(b(a(?x_5))) = b(c(b(?x_5))),
     b(b(c(?x_3))) = b(c(c(?x_3))),
     b(b(a(?x_5))) = b(c(b(?x_5))),
     c(b(a(?x))) = b(a(b(?x))),
     c(b(c(?x_4))) = b(a(c(?x_4))),
     a(b(a(?x))) = a(c(b(?x))),
     a(b(c(?x_4))) = a(c(c(?x_4))),
     a(b(a(?x_1))) = a(a(c(?x_1))),
     a(c(b(?x_2))) = a(a(c(?x_2))),
     a(a(c(?x_6))) = a(a(b(?x_6))),
     b(b(a(?x))) = b(a(b(?x))),
     c(b(c(?x))) = b(c(c(?x))),
     a(a(a(?x))) = a(a(a(?x))) ]
Outer CPs:
   [ b(a(?x_1)) = c(b(?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
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:
   [ b(b(a(?x_1))) = b(a(b(?x_1))),
     b(b(c(?x_5))) = b(a(c(?x_5))),
     b(a(b(a(?x_1)))) = b(b(a(b(?x_1)))),
     b(a(b(c(?x_5)))) = b(b(a(c(?x_5)))),
     b(a(b(a(?x_1)))) = c(b(a(b(?x_1)))),
     b(a(b(c(?x_5)))) = c(b(a(c(?x_5)))),
     a(c(b(a(?x_1)))) = a(b(a(b(?x_1)))),
     a(c(b(c(?x_5)))) = a(b(a(c(?x_5)))),
     b(a(b(?x))) = b(b(a(?x))),
     b(a(b(?x))) = c(b(a(?x))),
     a(c(b(?x))) = a(b(a(?x))),
     c(b(?x)) = b(a(?x)),
     a(b(c(?x_4))) = b(a(c(?x_4))),
     a(b(a(?x_6))) = b(a(b(?x_6))),
     a(a(b(c(?x_4)))) = a(b(a(c(?x_4)))),
     a(a(b(a(?x_6)))) = a(b(a(b(?x_6)))),
     a(a(c(?x))) = a(b(a(?x))),
     b(a(?x)) = c(b(?x)),
     a(b(c(?x_4))) = c(b(c(?x_4))),
     a(b(a(?x_6))) = c(b(b(?x_6))),
     a(a(b(c(?x_4)))) = a(c(b(c(?x_4)))),
     a(a(b(a(?x_6)))) = a(c(b(b(?x_6)))),
     a(a(c(?x))) = a(c(b(?x))),
     c(b(c(?x_1))) = b(c(c(?x_1))),
     c(b(a(?x_6))) = b(c(b(?x_6))),
     b(c(b(c(?x_1)))) = c(b(c(c(?x_1)))),
     b(c(b(a(?x_6)))) = c(b(c(b(?x_6)))),
     b(a(b(c(?x_1)))) = a(b(c(c(?x_1)))),
     b(a(b(a(?x_6)))) = a(b(c(b(?x_6)))),
     c(b(b(c(?x_1)))) = a(b(c(c(?x_1)))),
     c(b(b(a(?x_6)))) = a(b(c(b(?x_6)))),
     b(c(b(c(?x_1)))) = b(b(c(c(?x_1)))),
     b(c(b(a(?x_6)))) = b(b(c(b(?x_6)))),
     b(c(c(?x))) = c(b(c(?x))),
     b(a(c(?x))) = a(b(c(?x))),
     c(b(c(?x))) = a(b(c(?x))),
     b(c(c(?x))) = b(b(c(?x))),
     b(b(c(?x_5))) = b(c(c(?x_5))),
     b(b(a(?x_6))) = b(c(b(?x_6))),
     b(a(b(c(?x_5)))) = b(b(c(c(?x_5)))),
     b(a(b(a(?x_6)))) = b(b(c(b(?x_6)))),
     b(a(b(c(?x_5)))) = c(b(c(c(?x_5)))),
     b(a(b(a(?x_6)))) = c(b(c(b(?x_6)))),
     a(c(b(c(?x_5)))) = a(b(c(c(?x_5)))),
     a(c(b(a(?x_6)))) = a(b(c(b(?x_6)))),
     b(a(c(?x))) = b(b(c(?x))),
     b(a(c(?x))) = c(b(c(?x))),
     a(c(c(?x))) = a(b(c(?x))),
     c(b(a(?x_2))) = b(a(b(?x_2))),
     c(b(c(?x_6))) = b(a(c(?x_6))),
     b(a(b(a(?x_2)))) = a(b(a(b(?x_2)))),
     b(a(b(c(?x_6)))) = a(b(a(c(?x_6)))),
     c(b(b(a(?x_2)))) = a(b(a(b(?x_2)))),
     c(b(b(c(?x_6)))) = a(b(a(c(?x_6)))),
     b(c(b(a(?x_2)))) = c(b(a(b(?x_2)))),
     b(c(b(c(?x_6)))) = c(b(a(c(?x_6)))),
     b(c(b(a(?x_2)))) = b(b(a(b(?x_2)))),
     b(c(b(c(?x_6)))) = b(b(a(c(?x_6)))),
     b(a(b(?x))) = a(b(a(?x))),
     c(b(b(?x))) = a(b(a(?x))),
     b(c(b(?x))) = c(b(a(?x))),
     b(c(b(?x))) = b(b(a(?x))),
     a(b(a(?x_2))) = a(c(b(?x_2))),
     a(b(c(?x_6))) = a(c(c(?x_6))),
     a(a(b(a(?x_2)))) = a(a(c(b(?x_2)))),
     a(a(b(c(?x_6)))) = a(a(c(c(?x_6)))),
     a(a(b(?x))) = a(a(c(?x))),
     a(a(a(?x_1))) = a(a(a(?x_1))),
     a(b(a(?x_3))) = a(a(c(?x_3))),
     a(c(b(?x_4))) = a(a(c(?x_4))),
     a(a(c(?x_8))) = a(a(b(?x_8))),
     a(a(a(a(?x_1)))) = a(a(a(a(?x_1)))),
     a(a(b(a(?x_3)))) = a(a(a(c(?x_3)))),
     a(a(c(b(?x_4)))) = a(a(a(c(?x_4)))),
     a(a(a(c(?x_8)))) = a(a(a(b(?x_8)))) ]
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 <b(b(c(?x_4))), b(a(c(?x_4)))> by Rules <4, 0> preceded by [(b,1)]
 joinable by a reduction of rules <[([],0)], []>
Critical Pair <a(b(c(?x_3))), b(a(c(?x_3)))> by Rules <3, 1> preceded by [(a,1)]
 joinable by a reduction of rules <[([],6),([],1)], []>
Critical Pair <a(b(a(?x_5))), b(a(b(?x_5)))> by Rules <5, 1> preceded by [(a,1)]
 joinable by a reduction of rules <[([],6),([],1)], [([(b,1)],6),([(b,1)],1),([],0)]>
 joinable by a reduction of rules <[([],6),([],2),([],5)], [([(b,1)],6),([(b,1)],1),([],0)]>
Critical Pair <a(b(c(?x_3))), c(b(c(?x_3)))> by Rules <3, 2> preceded by [(a,1)]
 joinable by a reduction of rules <[([],6),([],2)], []>
 joinable by a reduction of rules <[([],6),([],1)], [([],5)]>
Critical Pair <a(b(a(?x_5))), c(b(b(?x_5)))> by Rules <5, 2> preceded by [(a,1)]
 joinable by a reduction of rules <[([],6),([],2)], [([(c,1)],0)]>
 joinable by a reduction of rules <[([],6),([],1)], [([(c,1)],0),([],5)]>
Critical Pair <c(b(a(?x_5))), b(c(b(?x_5)))> by Rules <5, 3> preceded by [(c,1)]
 joinable by a reduction of rules <[([],5)], [([(b,1)],5),([],0)]>
Critical Pair <b(b(c(?x_3))), b(c(c(?x_3)))> by Rules <3, 4> preceded by [(b,1)]
 joinable by a reduction of rules <[], [([(b,1)],3)]>
Critical Pair <b(b(a(?x_5))), b(c(b(?x_5)))> by Rules <5, 4> preceded by [(b,1)]
 joinable by a reduction of rules <[], [([(b,1)],5)]>
Critical Pair <c(b(a(?x))), b(a(b(?x)))> by Rules <0, 5> preceded by [(c,1)]
 joinable by a reduction of rules <[([],5)], [([(b,1)],6),([(b,1)],1),([],0)]>
Critical Pair <c(b(c(?x_4))), b(a(c(?x_4)))> by Rules <4, 5> preceded by [(c,1)]
 joinable by a reduction of rules <[([],5)], []>
Critical Pair <a(b(a(?x))), a(c(b(?x)))> by Rules <0, 6> preceded by [(a,1)]
 joinable by a reduction of rules <[], [([(a,1)],5)]>
Critical Pair <a(b(c(?x_4))), a(c(c(?x_4)))> by Rules <4, 6> preceded by [(a,1)]
 joinable by a reduction of rules <[([],6)], []>
 joinable by a reduction of rules <[], [([(a,1)],3)]>
Critical Pair <a(b(a(?x_1))), a(a(c(?x_1)))> by Rules <1, 7> preceded by [(a,1)]
 joinable by a reduction of rules <[], [([(a,1)],1)]>
Critical Pair <a(c(b(?x_2))), a(a(c(?x_2)))> by Rules <2, 7> preceded by [(a,1)]
 joinable by a reduction of rules <[], [([(a,1)],2)]>
 joinable by a reduction of rules <[([(a,1)],5)], [([(a,1)],1)]>
Critical Pair <a(a(c(?x_6))), a(a(b(?x_6)))> by Rules <6, 7> preceded by [(a,1)]
 joinable by a reduction of rules <[], [([(a,1)],6)]>
Critical Pair <b(b(a(?x))), b(a(b(?x)))> by Rules <0, 0> preceded by [(b,1)]
 joinable by a reduction of rules <[], [([(b,1)],6),([(b,1)],1)]>
Critical Pair <c(b(c(?x))), b(c(c(?x)))> by Rules <3, 3> preceded by [(c,1)]
 joinable by a reduction of rules <[([],5)], [([(b,1)],3),([],0)]>
Critical Pair <a(a(a(?x))), a(a(a(?x)))> by Rules <7, 7> preceded by [(a,1)]
 joinable by a reduction of rules <[], []>
Critical Pair <c(b(?x_2)), b(a(?x_2))> by Rules <2, 1> preceded by []
 joinable by a reduction of rules <[([],5)], []>
Satisfiable by 6,4,3,2,1>5,8,7; a(1)b(1)c(1); 7>6,2,1>4>5,8,3
Diagram Decreasing
Direct Methods: CR

Combined result: CR
1013.trs: Success(CR)
YES
(10 msec.)