YES

TRS:

  p(0()) -> 0()
  p(s(x)) -> x
  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(x,0()) -> x
  minus(x,s(y)) -> if(le(x,s(y)),0(),p(minus(x,p(s(y)))))
  if(true(),x,y) -> x
  if(false(),x,y) -> y

max/plus interpretations on N:

  p_A(x1) = max{3, -7 + x1}
  p#_A(x1) = max{9, 9}
  0_A = 3
  0#_A = 7
  s_A(x1) = max{10, 8 + x1}
  s#_A(x1) = max{5, 8}
  le_A(x1,x2) = max{1, -1, -2}
  le#_A(x1,x2) = max{12, 1, 3}
  true_A = 1
  true#_A = 2
  false_A = 0
  false#_A = 0
  minus_A(x1,x2) = max{12, 8 + x1, 9}
  minus#_A(x1,x2) = max{6, 4, 2 + x2}
  if_A(x1,x2,x3) = max{10, 11 + x1, 7 + x2, 7 + x3}
  if#_A(x1,x2,x3) = max{12, 5, 3, 3}

precedence:

  minus > s = if > p = le > 0 > true = false