YES

TRS:

  f(x,0(),0()) -> s(x)
  f(0(),y,0()) -> s(y)
  f(0(),0(),z) -> s(z)
  f(s(0()),y,z) -> f(0(),s(y),s(z))
  f(s(x),s(y),0()) -> f(x,y,s(0()))
  f(s(x),0(),s(z)) -> f(x,s(0()),z)
  f(0(),s(0()),s(0())) -> s(s(0()))
  f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
  f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
  f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
  f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))

linear polynomial interpretations on N:

  f_A(x1,x2,x3) = 1
  f#_A(x1,x2,x3) = 2
  0_A = 2
  0#_A = 0
  s_A(x1) = 1
  s#_A(x1) = 1

precedence:

  f > s > 0