YES

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

Proof:
 Church Rosser Transformation Processor (no redundant rules):
  strict:
   a() -> b()
   g(x) -> x
   h(x,y) -> h(g(x),g(y))
   b() -> a()
   f(x) -> h(x,x)
   g(a()) -> b()
   f(g(x)) -> h(x,x)
  weak:
   
  critical peaks: 7
   g(b()) <-0|0[]- g(a()) -5|[]-> b()
   a() <-1|[]- g(a()) -5|[]-> b()
   f(x) <-1|0[]- f(g(x)) -6|[]-> h(x,x)
   h(g(x),g(x)) <-4|[]- f(g(x)) -6|[]-> h(x,x)
   b() <-5|[]- g(a()) -1|[]-> a()
   f(b()) <-5|0[]- f(g(a())) -6|[]-> h(a(),a())
   h(x50,x50) <-6|[]- f(g(x50)) -4|[]-> h(g(x50),g(x50))
  Closedness Processor (*development*):
   
   Qed