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:
 Open