MAYBE

Problem:
 app(g(),app(h(),app(g(),x))) -> app(g(),x)
 app(g(),app(g(),x)) -> app(g(),app(h(),app(g(),x)))
 app(h(),app(h(),x)) -> app(h(),app(app(f(),app(h(),x)),x))
 app(app(map(),fun),nil()) -> nil()
 app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
 app(app(filter(),fun),nil()) -> nil()
 app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
 app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
 app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)

Proof:
 DP Processor:
  DPs:
   app#(g(),app(g(),x)) -> app#(h(),app(g(),x))
   app#(g(),app(g(),x)) -> app#(g(),app(h(),app(g(),x)))
   app#(h(),app(h(),x)) -> app#(f(),app(h(),x))
   app#(h(),app(h(),x)) -> app#(app(f(),app(h(),x)),x)
   app#(h(),app(h(),x)) -> app#(h(),app(app(f(),app(h(),x)),x))
   app#(app(map(),fun),app(app(cons(),x),xs)) -> app#(app(map(),fun),xs)
   app#(app(map(),fun),app(app(cons(),x),xs)) -> app#(fun,x)
   app#(app(map(),fun),app(app(cons(),x),xs)) -> app#(cons(),app(fun,x))
   app#(app(map(),fun),app(app(cons(),x),xs)) ->
   app#(app(cons(),app(fun,x)),app(app(map(),fun),xs))
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(fun,x)
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(filter2(),app(fun,x))
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(app(filter2(),app(fun,x)),fun)
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(fun,x)),fun),x)
   app#(app(filter(),fun),app(app(cons(),x),xs)) ->
   app#(app(app(app(filter2(),app(fun,x)),fun),x),xs)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(filter(),fun)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(app(filter(),fun),xs)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(cons(),x)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(app(cons(),x),app(app(filter(),fun),xs))
   app#(app(app(app(filter2(),false()),fun),x),xs) -> app#(filter(),fun)
   app#(app(app(app(filter2(),false()),fun),x),xs) -> app#(app(filter(),fun),xs)
  TRS:
   app(g(),app(h(),app(g(),x))) -> app(g(),x)
   app(g(),app(g(),x)) -> app(g(),app(h(),app(g(),x)))
   app(h(),app(h(),x)) -> app(h(),app(app(f(),app(h(),x)),x))
   app(app(map(),fun),nil()) -> nil()
   app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
   app(app(filter(),fun),nil()) -> nil()
   app(app(filter(),fun),app(app(cons(),x),xs)) ->
   app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
   app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
   app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)
  Open