MAYBE

Problem:
 app(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
 app(app(*(),app(app(+(),y),z)),x) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
 app(app(*(),app(app(*(),x),y)),z) -> app(app(*(),x),app(app(*(),y),z))
 app(app(+(),app(app(+(),x),y)),z) -> app(app(+(),x),app(app(+(),y),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#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
   app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
   app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
   app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
   app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
   app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
   app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
   app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
   app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
   app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
   app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
   app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
   app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
   app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
   app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),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(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
   app(app(*(),app(app(+(),y),z)),x) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
   app(app(*(),app(app(*(),x),y)),z) -> app(app(*(),x),app(app(*(),y),z))
   app(app(+(),app(app(+(),x),y)),z) -> app(app(+(),x),app(app(+(),y),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)
  EDG Processor:
   DPs:
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),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(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app(app(*(),app(app(+(),y),z)),x) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app(app(*(),app(app(*(),x),y)),z) -> app(app(*(),x),app(app(*(),y),z))
    app(app(+(),app(app(+(),x),y)),z) -> app(app(+(),x),app(app(+(),y),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)
   graph:
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(filter(),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(filter(),f),app(app(cons(),x),xs)) -> 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#(f,x)
    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#(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#(f,x) ->
    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#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    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#(app(map(),f),xs) ->
    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(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    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#(f,x)
    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#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),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(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    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(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z)) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(+(),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z)) ->
    app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(*(),x)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(+(),y),z)),x) -> app#(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(*(),y)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
    app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y) ->
    app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
   SCC Processor:
    #sccs: 3
    #rules: 13
    #arcs: 158/900
    DPs:
     app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
     app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
     app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    TRS:
     app(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
     app(app(*(),app(app(+(),y),z)),x) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
     app(app(*(),app(app(*(),x),y)),z) -> app(app(*(),x),app(app(*(),y),z))
     app(app(+(),app(app(+(),x),y)),z) -> app(app(+(),x),app(app(+(),y),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
    
    DPs:
     app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),x),app(app(*(),y),z))
     app#(app(*(),app(app(*(),x),y)),z) -> app#(app(*(),y),z)
     app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),y)
     app#(app(*(),app(app(+(),y),z)),x) -> app#(app(*(),x),z)
     app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),y)
     app#(app(*(),x),app(app(+(),y),z)) -> app#(app(*(),x),z)
    TRS:
     app(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
     app(app(*(),app(app(+(),y),z)),x) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
     app(app(*(),app(app(*(),x),y)),z) -> app(app(*(),x),app(app(*(),y),z))
     app(app(+(),app(app(+(),x),y)),z) -> app(app(+(),x),app(app(+(),y),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
    
    DPs:
     app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),x),app(app(+(),y),z))
     app#(app(+(),app(app(+(),x),y)),z) -> app#(app(+(),y),z)
    TRS:
     app(app(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
     app(app(*(),app(app(+(),y),z)),x) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
     app(app(*(),app(app(*(),x),y)),z) -> app(app(*(),x),app(app(*(),y),z))
     app(app(+(),app(app(+(),x),y)),z) -> app(app(+(),x),app(app(+(),y),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