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

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