MAYBE

Problem:
 app(not(),app(not(),x)) -> x
 app(not(),app(app(or(),x),y)) -> app(app(and(),app(not(),x)),app(not(),y))
 app(not(),app(app(and(),x),y)) -> app(app(or(),app(not(),x)),app(not(),y))
 app(app(and(),x),app(app(or(),y),z)) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
 app(app(and(),app(app(or(),y),z)),x) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
 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#(not(),app(app(or(),x),y)) -> app#(not(),y)
   app#(not(),app(app(or(),x),y)) -> app#(not(),x)
   app#(not(),app(app(or(),x),y)) -> app#(and(),app(not(),x))
   app#(not(),app(app(or(),x),y)) -> app#(app(and(),app(not(),x)),app(not(),y))
   app#(not(),app(app(and(),x),y)) -> app#(not(),y)
   app#(not(),app(app(and(),x),y)) -> app#(not(),x)
   app#(not(),app(app(and(),x),y)) -> app#(or(),app(not(),x))
   app#(not(),app(app(and(),x),y)) -> app#(app(or(),app(not(),x)),app(not(),y))
   app#(app(and(),x),app(app(or(),y),z)) -> app#(app(and(),x),z)
   app#(app(and(),x),app(app(or(),y),z)) -> app#(app(and(),x),y)
   app#(app(and(),x),app(app(or(),y),z)) -> app#(or(),app(app(and(),x),y))
   app#(app(and(),x),app(app(or(),y),z)) -> app#(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
   app#(app(and(),app(app(or(),y),z)),x) -> app#(app(and(),x),z)
   app#(app(and(),app(app(or(),y),z)),x) -> app#(and(),x)
   app#(app(and(),app(app(or(),y),z)),x) -> app#(app(and(),x),y)
   app#(app(and(),app(app(or(),y),z)),x) -> app#(or(),app(app(and(),x),y))
   app#(app(and(),app(app(or(),y),z)),x) -> app#(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
   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(not(),app(not(),x)) -> x
   app(not(),app(app(or(),x),y)) -> app(app(and(),app(not(),x)),app(not(),y))
   app(not(),app(app(and(),x),y)) -> app(app(or(),app(not(),x)),app(not(),y))
   app(app(and(),x),app(app(or(),y),z)) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
   app(app(and(),app(app(or(),y),z)),x) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
   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