YES
(ignored inputs)COMMENT doi:10.1007/11805618_6 [7] Example 1 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Rewrite Rules:
   [ g(a) -> f(g(a)),
     g(b) -> c,
     a -> b,
     f(?x) -> h(?x,?x),
     h(?x,?y) -> c ]
Apply Direct Methods...
Inner CPs:
   [ g(b) = f(g(a)) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Left-Linear, not Right-Linear
unknown Development 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:
   [ g(b) = f(g(a)),
     f(g(a)) = g(b) ]
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 <g(b), f(g(a))> by Rules <2, 0> preceded by [(g,1)]
 joinable by a reduction of rules <[([],1)], [([],3),([],4)]>
Satisfiable by 3,5>1>4,2; f(1)g(0)h(0,0); 1>4>3,5>2
Diagram Decreasing
Direct Methods: CR

Combined result: CR
19.trs: Success(CR)
(1 msec.)