MAYBE

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

Proof:
 DP Processor:
  DPs:
   h#(x,x) -> h#(a(),b())
   g#(g(x,a()),y) -> g#(a(),x)
   g#(g(x,a()),y) -> g#(a(),y)
   g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
   f#(g(x,y)) -> h#(a(),a())
   f#(g(x,y)) -> f#(y)
   f#(g(x,y)) -> f#(f(y))
   f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
   f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
   h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
   h#(h(f(f(x)),y),h(z,v)) -> f#(y)
   h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
   h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
   h#(h(f(f(x)),y),h(z,v)) -> f#(z)
   h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
   h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
  TRS:
   h(x,x) -> h(a(),b())
   g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
   f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
   h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
  Open