MAYBE

Problem:
 a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t()))))
 a(p(x,y),z) -> p(a(x,z),a(y,z))
 a(a(x,y),z) -> a(x,a(y,z))
 a(id(),x) -> x
 a(1(),id()) -> 1()
 a(t(),id()) -> t()
 a(1(),p(x,y)) -> x
 a(t(),p(x,y)) -> y

Proof:
 DP Processor:
  DPs:
   a#(lambda(x),y) -> a#(y,t())
   a#(lambda(x),y) -> a#(x,p(1(),a(y,t())))
   a#(p(x,y),z) -> a#(y,z)
   a#(p(x,y),z) -> a#(x,z)
   a#(a(x,y),z) -> a#(y,z)
   a#(a(x,y),z) -> a#(x,a(y,z))
  TRS:
   a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t()))))
   a(p(x,y),z) -> p(a(x,z),a(y,z))
   a(a(x,y),z) -> a(x,a(y,z))
   a(id(),x) -> x
   a(1(),id()) -> 1()
   a(t(),id()) -> t()
   a(1(),p(x,y)) -> x
   a(t(),p(x,y)) -> y
  Open