YES

TRS:

  if(true(),t,e) -> t
  if(false(),t,e) -> e
  member(x,nil()) -> false()
  member(x,cons(y,ys)) -> if(eq(x,y),true(),member(x,ys))
  eq(nil(),nil()) -> true()
  eq(O(x),0(y)) -> eq(x,y)
  eq(0(x),1(y)) -> false()
  eq(1(x),0(y)) -> false()
  eq(1(x),1(y)) -> eq(x,y)
  negate(0(x)) -> 1(x)
  negate(1(x)) -> 0(x)
  choice(cons(x,xs)) -> x
  choice(cons(x,xs)) -> choice(xs)
  guess(nil()) -> nil()
  guess(cons(clause,cnf)) -> cons(choice(clause),guess(cnf))
  verify(nil()) -> true()
  verify(cons(l,ls)) -> if(member(negate(l),ls),false(),verify(ls))
  sat(cnf) -> satck(cnf,guess(cnf))
  satck(cnf,assign) -> if(verify(assign),assign,unsat())

linear polynomial interpretations on N:

  if_A(x1,x2,x3) = x2 + x3
  if#_A(x1,x2,x3) = 0
  true_A = 1
  true#_A = 2
  false_A = 1
  false#_A = 0
  member_A(x1,x2) = x2 + 1
  member#_A(x1,x2) = 5
  nil_A = 1
  nil#_A = 1
  cons_A(x1,x2) = x1 + x2 + 2
  cons#_A(x1,x2) = 6
  eq_A(x1,x2) = x1 + 1
  eq#_A(x1,x2) = 3
  O_A(x1) = x1 + 1
  O#_A(x1) = 0
  0_A(x1) = x1 + 1
  0#_A(x1) = 1
  1_A(x1) = x1 + 1
  1#_A(x1) = 2
  negate_A(x1) = x1
  negate#_A(x1) = 3
  choice_A(x1) = x1
  choice#_A(x1) = x1 + 7
  guess_A(x1) = x1 + 1
  guess#_A(x1) = x1 + 6
  verify_A(x1) = x1 + 1
  verify#_A(x1) = 4
  sat_A(x1) = x1 + 2
  sat#_A(x1) = x1 + 7
  satck_A(x1,x2) = x2 + 1
  satck#_A(x1,x2) = x2 + 5
  unsat_A = 1
  unsat#_A = 0

precedence:

  sat > guess > cons = O > member = choice = satck > eq = verify = unsat > if = true > nil > false > 0 > negate > 1