YES

Problem:
 a() -> a'()
 h(x,a'(),y) -> h(x,y,y)
 h(x,y,a'()) -> h(x,y,y)
 g() -> f()
 h(f(),a(),a()) -> h(g(),a(),a())
 h(g(),a(),a()) -> h(f(),a(),a())

Proof:
 Church Rosser Transformation Processor (no redundant rules):
  strict:
   h(f(),a(),a()) -> h(g(),a(),a())
   g() -> f()
   h(x,y,a'()) -> h(x,y,y)
   h(x,a'(),y) -> h(x,y,y)
   a() -> a'()
  weak:
   
  critical peaks: 4
   h(x,a'(),a'()) <-2|[]- h(x,a'(),a'()) -3|[]-> h(x,a'(),a'())
   h(x,a'(),a'()) <-3|[]- h(x,a'(),a'()) -2|[]-> h(x,a'(),a'())
   h(f(),a'(),a()) <-4|1[]- h(f(),a(),a()) -0|[]-> h(g(),a(),a())
   h(f(),a(),a'()) <-4|2[]- h(f(),a(),a()) -0|[]-> h(g(),a(),a())
  Closedness Processor (*upside-parallel*):
   
   Qed