YES
(ignored inputs)COMMENT doi:10.1007/BFb0052357 [21] TRS R_1 , attributed to Middeldorp submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Rewrite Rules:
   [ f(g(g(?x))) -> a,
     f(g(h(?x))) -> b,
     f(h(g(?x))) -> b,
     f(h(h(?x))) -> c,
     g(?x) -> h(?x),
     a -> b,
     b -> c ]
Apply Direct Methods...
Inner CPs:
   [ f(h(g(?x))) = a,
     f(g(h(?x_4))) = a,
     f(h(h(?x_1))) = b,
     f(h(h(?x_4))) = b ]
Outer CPs:
   [  ]
not Overlay, check Termination...
Terminating, WCR
Knuth & Bendix
Direct Methods: CR

Combined result: CR
73.trs: Success(CR)
(0 msec.)