YES

weighted path orer with linear polynomial on natural numbers:

  seven_A = 2
  s_A(x1) = x1
  O_A = 1
  isNat_A(x1) = x1 + 4
  false_A = 7
  true_A = 4
  ack_A(x1,x2) = x2


precedence:

  false > O > ack > true > isNat > s > seven


status:
seven: []
s: []
O: []
isNat: []
false: []
true: []
ack: []

the condition isNat(ack(seven(),seven())) ->> false() is unsatisfiable for all substitutions.