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

Proof:
 Church Rosser Transformation Processor:
  strict:
   
  weak:
   
  critical peaks: 2
   f(g(y),g(y)) <-0|[]- f(y,y) -1|[]-> f(h(y),h(y))
   f(h(x),h(x)) <-1|[]- f(x,x) -0|[]-> f(g(x),g(x))
  Redundant Rules Transformation:
   f(x,y) -> f(h(x),h(y))
   g(x) -> p(x)
   h(x) -> p(x)
   Qed (ToyamaOyamaguchi95Cor22)