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))
 lambda(x) -> x
 a(x,y) -> x
 a(x,y) -> y
 p(x,y) -> x
 p(x,y) -> y

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