YES

TRS:

  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(0(),y) -> 0()
  minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
  if_minus(true(),s(x),y) -> 0()
  if_minus(false(),s(x),y) -> s(minus(x,y))
  gcd(0(),y) -> y
  gcd(s(x),0()) -> s(x)
  gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
  if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
  if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))

linear polynomial interpretations on N:

  le_A(x1,x2) = x1 + 1
  le#_A(x1,x2) = x1 + 8
  0_A = 6
  0#_A = 0
  true_A = 7
  true#_A = 1
  s_A(x1) = x1 + 5
  s#_A(x1) = 11
  false_A = 1
  false#_A = 12
  minus_A(x1,x2) = x1 + 1
  minus#_A(x1,x2) = x1 + 9
  if_minus_A(x1,x2,x3) = x2 + 1
  if_minus#_A(x1,x2,x3) = x2 + 7
  gcd_A(x1,x2) = x1 + x2
  gcd#_A(x1,x2) = x1 + x2 + 1
  if_gcd_A(x1,x2,x3) = x2 + x3
  if_gcd#_A(x1,x2,x3) = x2 + x3

precedence:

  if_gcd > minus > false = if_minus > s = gcd > le > true > 0