YES

TRS:

  admit(x,nil()) -> nil()
  admit(x,.(u,.(v,.(w(),z)))) -> cond(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
  cond(true(),y) -> y

max/plus interpretations on N:

  admit_A(x1,x2) = max{28, 35 + x1, 7 + x2}
  admit#_A(x1,x2) = max{0, -2 + x1, -24 + x2}
  nil_A = 36
  nil#_A = 1
  ._A(x1,x2) = max{38, -4 + x1, 9 + x2}
  .#_A(x1,x2) = max{24, -29, 1}
  w_A = 3
  w#_A = 2
  cond_A(x1,x2) = max{55, 62 + x1, x2}
  cond#_A(x1,x2) = max{32, 31 + x1, -3}
  =_A(x1,x2) = max{1, -7 + x1, -7}
  =#_A(x1,x2) = max{32, 23 + x1, 32}
  sum_A(x1,x2,x3) = max{1, -26 + x1, -52 + x2, -43 + x3}
  sum#_A(x1,x2,x3) = max{31, 24, -29, -29}
  carry_A(x1,x2,x3) = max{1, -27 + x1, -34, -34}
  carry#_A(x1,x2,x3) = max{32, -29, -29, -29}
  true_A = 0
  true#_A = 0

precedence:

  admit > . = cond = = = carry > nil = w = sum = true