YES
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ a(s(?x)) -> s(a(?x)),
     b(a(b(s(?x)))) -> a(b(s(a(?x)))),
     b(a(b(b(?x)))) -> a(b(a(b(?x)))),
     a(b(a(a(?x)))) -> b(a(b(a(?x)))) ]
Apply Direct Methods...
Inner CPs:
   [ b(a(b(a(b(s(a(?x_1))))))) = a(b(a(b(a(b(s(?x_1))))))),
     a(b(a(s(a(?x))))) = b(a(b(a(s(?x))))),
     b(a(b(a(b(a(b(?x))))))) = a(b(a(b(a(b(b(?x))))))),
     a(b(a(b(a(b(a(?x))))))) = b(a(b(a(b(a(a(?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:
   [ b(a(b(a(s(?x))))) = a(b(a(s(a(?x))))),
     a(b(a(b(a(b(s(?x))))))) = b(a(b(a(b(s(a(?x))))))),
     b(a(b(a(b(a(b(?x_1))))))) = a(b(a(b(a(b(b(?x_1))))))),
     b(a(b(a(b(s(a(?x_3))))))) = a(b(a(b(a(b(s(?x_3))))))),
     a(b(a(b(a(b(a(b(a(b(?x_1)))))))))) = b(a(b(a(b(a(b(a(b(b(?x_1)))))))))),
     a(b(a(b(a(b(a(b(s(a(?x_3)))))))))) = b(a(b(a(b(a(b(a(b(s(?x_3)))))))))),
     a(b(a(b(a(b(b(?x))))))) = b(a(b(a(b(a(b(?x))))))),
     a(b(a(b(a(b(a(?x_1))))))) = b(a(b(a(b(a(a(?x_1))))))),
     a(b(a(s(a(?x_2))))) = b(a(b(a(s(?x_2))))),
     b(a(b(a(b(a(b(a(b(a(?x_1)))))))))) = a(b(a(b(a(b(a(b(a(a(?x_1)))))))))),
     b(a(b(a(b(a(s(a(?x_2)))))))) = a(b(a(b(a(b(a(s(?x_2)))))))),
     b(a(b(a(b(a(a(?x))))))) = a(b(a(b(a(b(a(?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 <b(a(b(a(b(s(a(?x_1))))))), a(b(a(b(a(b(s(?x_1)))))))> by Rules <1, 2> preceded by [(b,1),(a,1),(b,1)]
 joinable by a reduction of rules <[], [([(a,1),(b,1),(a,1)],1),([],3)]>
Critical Pair <a(b(a(s(a(?x))))), b(a(b(a(s(?x)))))> by Rules <0, 3> preceded by [(a,1),(b,1),(a,1)]
 joinable by a reduction of rules <[([(a,1),(b,1)],0)], [([(b,1),(a,1),(b,1)],0),([],1)]>
Critical Pair <b(a(b(a(b(a(b(?x))))))), a(b(a(b(a(b(b(?x)))))))> by Rules <2, 2> preceded by [(b,1),(a,1),(b,1)]
 joinable by a reduction of rules <[], [([(a,1),(b,1),(a,1)],2),([],3)]>
Critical Pair <a(b(a(b(a(b(a(?x))))))), b(a(b(a(b(a(a(?x)))))))> by Rules <3, 3> preceded by [(a,1),(b,1),(a,1)]
 joinable by a reduction of rules <[], [([(b,1),(a,1),(b,1)],3),([],2)]>
Satisfiable by 4,3>1>2; a(1)b(1)s(0); 3>2>1>4
Diagram Decreasing
Direct Methods: CR

Combined result: CR
/tmp/filemTRWj6.trs: Success(CR)
(45 msec.)