NO

Problem:
 ba0(0()) -> 0()
 ba1(0()) -> 1()
 S(0()) -> 1()
 S(1()) -> ba0(1())
 S(ba0(x)) -> ba1(x)
 S(ba1(x)) -> ba0(S(x))
 plus(x,0()) -> x
 plus(0(),x) -> x
 plus(x,1()) -> S(x)
 plus(1(),x) -> S(x)
 plus(ba0(x),ba0(y)) -> plus(ba0(plus(x,y)),0())
 plus(ba0(x),ba1(y)) -> plus(ba0(plus(x,y)),1())
 plus(ba1(x),ba0(y)) -> plus(ba1(plus(x,y)),0())
 plus(ba1(x),ba1(y)) -> plus(ba1(plus(x,y)),1())
 mult(x,0()) -> 0()
 mult(x,1()) -> x
 mult(x,ba0(y)) -> plus(ba0(mult(x,y)),mult(x,0()))
 mult(x,ba1(y)) -> plus(ba0(mult(x,y)),mult(x,1()))
 neg(0()) -> 0()
 neg(neg(x)) -> x
 P(0()) -> neg(1())
 P(1()) -> 0()
 P(ba0(x)) -> ba1(P(x))
 P(ba1(x)) -> ba0(x)
 P(neg(x)) -> neg(S(x))
 S(neg(1())) -> 0()
 S(neg(ba0(x))) -> neg(ba1(P(x)))
 S(neg(ba1(x))) -> neg(ba0(x))
 ba0(neg(x)) -> neg(ba0(x))
 ba1(neg(x)) -> neg(ba1(P(x)))
 plus(x,neg(1())) -> P(x)
 plus(neg(1()),x) -> P(x)
 plus(ba0(x),neg(ba0(y))) -> ba0(plus(x,neg(y)))
 plus(ba0(x),neg(ba1(y))) -> plus(ba0(plus(x,neg(y))),neg(1()))
 plus(ba1(x),neg(ba0(y))) -> plus(ba1(plus(x,neg(y))),neg(0()))
 plus(ba1(x),neg(ba1(y))) -> plus(ba1(plus(x,neg(y))),neg(1()))
 plus(neg(ba0(y)),ba0(x)) -> plus(ba0(plus(x,neg(y))),neg(0()))
 plus(neg(ba1(y)),ba0(x)) -> plus(ba0(plus(x,neg(y))),neg(1()))
 plus(neg(ba0(y)),ba1(x)) -> plus(ba1(plus(x,neg(y))),neg(0()))
 plus(neg(ba1(y)),ba1(x)) -> plus(ba1(plus(x,neg(y))),neg(1()))
 plus(neg(x),neg(y)) -> neg(plus(x,y))
 mult(x,neg(y)) -> neg(mult(x,y))

Proof:
 Nonconfluence Processor:
  terms: P(x5515) *<- P(neg(neg(x5515))) ->* neg(S(neg(x5515)))
  Qed