YES
(ignored inputs)COMMENT Example 2 of \cite{Gra96caap}
Rewrite Rules:
   [ f(a,a) -> b,
     a -> a',
     f(a',?x) -> f(?x,?x),
     f(?x,a') -> f(?x,?x),
     f(a',a') -> b,
     b -> f(a',a') ]
Apply Direct Methods...
Inner CPs:
   [ f(a',a) = b,
     f(a,a') = b ]
Outer CPs:
   [ f(a',a') = f(a',a'),
     f(a',a') = b,
     f(a',a') = b ]
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:
   [ f(a,a') = b {},
     f(a',a) = b {},
     f(a',a') = b {} ]
Toyama (Parallel CPs)
Direct Methods: CR

Final result: CR
30.trs: Success(CR)
(17 msec.)