MAYBE

Problem:
 app(app(h(),z),app(e(),x)) -> app(app(h(),app(c(),z)),app(app(d(),z),x))
 app(app(d(),z),app(app(g(),0()),0())) -> app(e(),0())
 app(app(d(),z),app(app(g(),x),y)) -> app(app(g(),app(e(),x)),app(app(d(),z),y))
 app(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
 app(app(g(),app(app(d(),app(c(),z)),app(app(g(),x),y))),app(app(d(),z),app(app(g(),x),y)))
 app(app(g(),app(e(),x)),app(e(),y)) -> app(e(),app(app(g(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 DP Processor:
  DPs:
   app#(app(h(),z),app(e(),x)) -> app#(d(),z)
   app#(app(h(),z),app(e(),x)) -> app#(app(d(),z),x)
   app#(app(h(),z),app(e(),x)) -> app#(c(),z)
   app#(app(h(),z),app(e(),x)) -> app#(h(),app(c(),z))
   app#(app(h(),z),app(e(),x)) -> app#(app(h(),app(c(),z)),app(app(d(),z),x))
   app#(app(d(),z),app(app(g(),0()),0())) -> app#(e(),0())
   app#(app(d(),z),app(app(g(),x),y)) -> app#(app(d(),z),y)
   app#(app(d(),z),app(app(g(),x),y)) -> app#(e(),x)
   app#(app(d(),z),app(app(g(),x),y)) -> app#(g(),app(e(),x))
   app#(app(d(),z),app(app(g(),x),y)) -> app#(app(g(),app(e(),x)),app(app(d(),z),y))
   app#(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) -> app#(d(),z)
   app#(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
   app#(app(d(),z),app(app(g(),x),y))
   app#(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
   app#(app(d(),app(c(),z)),app(app(g(),x),y))
   app#(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
   app#(g(),app(app(d(),app(c(),z)),app(app(g(),x),y)))
   app#(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
   app#(app(g(),app(app(d(),app(c(),z)),app(app(g(),x),y))),app(app(d(),z),app(app(g(),x),y)))
   app#(app(g(),app(e(),x)),app(e(),y)) -> app#(g(),x)
   app#(app(g(),app(e(),x)),app(e(),y)) -> app#(app(g(),x),y)
   app#(app(g(),app(e(),x)),app(e(),y)) -> app#(e(),app(app(g(),x),y))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs))
   app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
   app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
  TRS:
   app(app(h(),z),app(e(),x)) -> app(app(h(),app(c(),z)),app(app(d(),z),x))
   app(app(d(),z),app(app(g(),0()),0())) -> app(e(),0())
   app(app(d(),z),app(app(g(),x),y)) -> app(app(g(),app(e(),x)),app(app(d(),z),y))
   app(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
   app(app(g(),app(app(d(),app(c(),z)),app(app(g(),x),y))),app(app(d(),z),app(app(g(),x),y)))
   app(app(g(),app(e(),x)),app(e(),y)) -> app(e(),app(app(g(),x),y))
   app(app(map(),f),nil()) -> nil()
   app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
   app(app(filter(),f),nil()) -> nil()
   app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
   app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
   app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
  Open