MAYBE

Problem:
 app(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
 app(app(:(),app(app(:(),x),z)),app(app(:(),app(app(:(),app(app(:(),x),y)),z)),u))
 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(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) -> app#(app(:(),x),y)
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app#(:(),app(app(:(),x),y))
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app#(app(:(),app(app(:(),x),y)),z)
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app#(:(),app(app(:(),app(app(:(),x),y)),z))
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app#(app(:(),app(app(:(),app(app(:(),x),y)),z)),u)
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) -> app#(:(),x)
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) -> app#(app(:(),x),z)
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app#(:(),app(app(:(),x),z))
   app#(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app#(app(:(),app(app(:(),x),z)),app(app(:(),app(app(:(),app(app(:(),x),y)),z)),u))
   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(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
   app(app(:(),app(app(:(),x),z)),app(app(:(),app(app(:(),app(app(:(),x),y)),z)),u))
   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