YES

TRS:

  +(*(x,y),*(x,z)) -> *(x,+(y,z))
  +(+(x,y),z) -> +(x,+(y,z))
  +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = x1 + x2
  *_A(x1,x2) = x1 + x2 + 4
  *#_A(x1,x2) = 7
  u_A = 1
  u#_A = 6

precedence:

  * > + > u