YES

TRS:

  p(s(x)) -> x
  s(p(x)) -> x
  +(0(),y) -> y
  +(s(x),y) -> s(+(x,y))
  +(p(x),y) -> p(+(x,y))
  minus(0()) -> 0()
  minus(s(x)) -> p(minus(x))
  minus(p(x)) -> s(minus(x))
  *(0(),y) -> 0()
  *(s(x),y) -> +(*(x,y),y)
  *(p(x),y) -> +(*(x,y),minus(y))

max/plus interpretations on N:

  p_A(x1) = max{7, x1}
  p#_A(x1) = max{4, 2}
  s_A(x1) = max{3, x1}
  s#_A(x1) = max{1, 6}
  +_A(x1,x2) = max{9, 9, 1 + x2}
  +#_A(x1,x2) = max{0, 7, 7}
  0_A = 3
  0#_A = 4
  minus_A(x1) = max{2, 7}
  minus#_A(x1) = max{5, x1}
  *_A(x1,x2) = max{2, 8, 9 + x2}
  *#_A(x1,x2) = max{7, 7, 7 + x2}

precedence:

  0 > * > + = minus > p > s