MAYBE

Problem:
 app(app(app(sort(),f),g),nil()) -> nil()
 app(app(app(sort(),f),g),app(app(cons(),x),y)) ->
 app(app(app(app(insert(),f),g),app(app(app(sort(),f),g),y)),x)
 app(app(app(app(insert(),f),g),nil()),y) -> app(app(cons(),y),nil())
 app(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) ->
 app(app(cons(),app(app(f,x),y)),app(app(app(app(insert(),f),g),z),app(app(g,x),y)))
 app(app(max(),0()),y) -> y
 app(app(max(),x),0()) -> x
 app(app(max(),app(s(),x)),app(s(),y)) -> app(app(max(),x),y)
 app(app(min(),0()),y) -> 0()
 app(app(min(),x),0()) -> 0()
 app(app(min(),app(s(),x)),app(s(),y)) -> app(app(min(),x),y)
 app(asort(),z) -> app(app(app(sort(),min()),max()),z)
 app(dsort(),z) -> app(app(app(sort(),max()),min()),z)

Proof:
 DP Processor:
  DPs:
   app#(app(app(sort(),f),g),app(app(cons(),x),y)) -> app#(app(app(sort(),f),g),y)
   app#(app(app(sort(),f),g),app(app(cons(),x),y)) -> app#(insert(),f)
   app#(app(app(sort(),f),g),app(app(cons(),x),y)) -> app#(app(insert(),f),g)
   app#(app(app(sort(),f),g),app(app(cons(),x),y)) ->
   app#(app(app(insert(),f),g),app(app(app(sort(),f),g),y))
   app#(app(app(sort(),f),g),app(app(cons(),x),y)) ->
   app#(app(app(app(insert(),f),g),app(app(app(sort(),f),g),y)),x)
   app#(app(app(app(insert(),f),g),nil()),y) -> app#(cons(),y)
   app#(app(app(app(insert(),f),g),nil()),y) -> app#(app(cons(),y),nil())
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) -> app#(g,x)
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) -> app#(app(g,x),y)
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) -> app#(app(app(insert(),f),g),z)
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) ->
   app#(app(app(app(insert(),f),g),z),app(app(g,x),y))
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) -> app#(f,x)
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) -> app#(app(f,x),y)
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) -> app#(cons(),app(app(f,x),y))
   app#(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) ->
   app#(app(cons(),app(app(f,x),y)),app(app(app(app(insert(),f),g),z),app(app(g,x),y)))
   app#(app(max(),app(s(),x)),app(s(),y)) -> app#(max(),x)
   app#(app(max(),app(s(),x)),app(s(),y)) -> app#(app(max(),x),y)
   app#(app(min(),app(s(),x)),app(s(),y)) -> app#(min(),x)
   app#(app(min(),app(s(),x)),app(s(),y)) -> app#(app(min(),x),y)
   app#(asort(),z) -> app#(sort(),min())
   app#(asort(),z) -> app#(app(sort(),min()),max())
   app#(asort(),z) -> app#(app(app(sort(),min()),max()),z)
   app#(dsort(),z) -> app#(sort(),max())
   app#(dsort(),z) -> app#(app(sort(),max()),min())
   app#(dsort(),z) -> app#(app(app(sort(),max()),min()),z)
  TRS:
   app(app(app(sort(),f),g),nil()) -> nil()
   app(app(app(sort(),f),g),app(app(cons(),x),y)) ->
   app(app(app(app(insert(),f),g),app(app(app(sort(),f),g),y)),x)
   app(app(app(app(insert(),f),g),nil()),y) -> app(app(cons(),y),nil())
   app(app(app(app(insert(),f),g),app(app(cons(),x),z)),y) ->
   app(app(cons(),app(app(f,x),y)),app(app(app(app(insert(),f),g),z),app(app(g,x),y)))
   app(app(max(),0()),y) -> y
   app(app(max(),x),0()) -> x
   app(app(max(),app(s(),x)),app(s(),y)) -> app(app(max(),x),y)
   app(app(min(),0()),y) -> 0()
   app(app(min(),x),0()) -> 0()
   app(app(min(),app(s(),x)),app(s(),y)) -> app(app(min(),x),y)
   app(asort(),z) -> app(app(app(sort(),min()),max()),z)
   app(dsort(),z) -> app(app(app(sort(),max()),min()),z)
  Open