NO

Problem:
 bt(0(),x) -> x
 bt(x,bt(y,z)) -> bt(plus(x,y),z)
 plus(0(),x) -> x
 plus(x,0()) -> x
 plus(1(),1()) -> bt(1(),0())
 plus(x,bt(y,z)) -> bt(y,plus(x,z))
 plus(bt(x,y),z) -> bt(x,plus(y,z))
 mult(x,0()) -> 0()
 mult(0(),x) -> 0()
 mult(1(),1()) -> 1()
 mult(x,bt(y,z)) -> bt(mult(x,y),mult(x,z))
 mult(bt(x,y),z) -> bt(mult(x,z),mult(y,z))

Proof:
 Nonconfluence Processor:
  terms: bt(plus(x,plus(y,x533)),x534) *<- bt(x,bt(y,bt(x533,x534))) ->* 
  bt(plus(plus(x,y),x533),x534)
  Qed