YES

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)) -> ba0(plus(x,y))
 plus(ba0(x),ba1(y)) -> S(ba0(plus(x,y)))
 plus(ba1(x),ba0(y)) -> ba1(plus(x,y))
 plus(ba1(x),ba1(y)) -> S(ba1(plus(x,y)))
 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()))

Proof:
 Church Rosser Transformation Processor (kb):
  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)) -> ba0(plus(x,y))
  plus(ba0(x),ba1(y)) -> S(ba0(plus(x,y)))
  plus(ba1(x),ba0(y)) -> ba1(plus(x,y))
  plus(ba1(x),ba1(y)) -> S(ba1(plus(x,y)))
  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()))
  critical peaks: joinable
   LPO Processor:
    precedence:
     mult > plus > S > ba0 > ba1 > 1 ~ 0
    problem:
     
    Qed