YES
(ignored inputs)COMMENT Example 6 of \cite{Gra96caap}
Rewrite Rules:
   [ f(a) -> f(g(b,b)),
     a -> g(c,c),
     c -> d,
     d -> b,
     b -> d ]
Apply Direct Methods...
Inner CPs:
   [ f(g(c,c)) = f(g(b,b)) ]
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:
   [ f(g(c,c)) = f(g(b,b)) {} ]
Toyama (Parallel CPs)
Direct Methods: CR

Final result: CR
33.trs: Success(CR)
(15 msec.)