YES

TRS:

  a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
  a____(X,nil()) -> mark(X)
  a____(nil(),X) -> mark(X)
  a__and(tt(),X) -> mark(X)
  a__isList(V) -> a__isNeList(V)
  a__isList(nil()) -> tt()
  a__isList(__(V1,V2)) -> a__and(a__isList(V1),isList(V2))
  a__isNeList(V) -> a__isQid(V)
  a__isNeList(__(V1,V2)) -> a__and(a__isList(V1),isNeList(V2))
  a__isNeList(__(V1,V2)) -> a__and(a__isNeList(V1),isList(V2))
  a__isNePal(V) -> a__isQid(V)
  a__isNePal(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P))
  a__isPal(V) -> a__isNePal(V)
  a__isPal(nil()) -> tt()
  a__isQid(a()) -> tt()
  a__isQid(e()) -> tt()
  a__isQid(i()) -> tt()
  a__isQid(o()) -> tt()
  a__isQid(u()) -> tt()
  mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
  mark(and(X1,X2)) -> a__and(mark(X1),X2)
  mark(isList(X)) -> a__isList(X)
  mark(isNeList(X)) -> a__isNeList(X)
  mark(isQid(X)) -> a__isQid(X)
  mark(isNePal(X)) -> a__isNePal(X)
  mark(isPal(X)) -> a__isPal(X)
  mark(nil()) -> nil()
  mark(tt()) -> tt()
  mark(a()) -> a()
  mark(e()) -> e()
  mark(i()) -> i()
  mark(o()) -> o()
  mark(u()) -> u()
  a____(X1,X2) -> __(X1,X2)
  a__and(X1,X2) -> and(X1,X2)
  a__isList(X) -> isList(X)
  a__isNeList(X) -> isNeList(X)
  a__isQid(X) -> isQid(X)
  a__isNePal(X) -> isNePal(X)
  a__isPal(X) -> isPal(X)

linear polynomial interpretations on N:

  a_____A(x1,x2) = x1 + x2 + 6
  a____#_A(x1,x2) = x1 + x2 + 14
  ___A(x1,x2) = x1 + x2 + 6
  __#_A(x1,x2) = x1 + x2 + 13
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 9
  nil_A = 0
  nil#_A = 8
  a__and_A(x1,x2) = x1 + x2 + 3
  a__and#_A(x1,x2) = x2 + 11
  tt_A = 0
  tt#_A = 1
  a__isList_A(x1) = x1 + 1
  a__isList#_A(x1) = 9
  a__isNeList_A(x1) = x1 + 1
  a__isNeList#_A(x1) = 8
  isList_A(x1) = x1 + 1
  isList#_A(x1) = 0
  a__isQid_A(x1) = x1 + 1
  a__isQid#_A(x1) = 2
  isNeList_A(x1) = x1 + 1
  isNeList#_A(x1) = 7
  a__isNePal_A(x1) = x1 + 1
  a__isNePal#_A(x1) = x1 + 3
  isPal_A(x1) = x1 + 7
  isPal#_A(x1) = 14
  a__isPal_A(x1) = x1 + 7
  a__isPal#_A(x1) = x1 + 15
  a_A = 0
  a#_A = 2
  e_A = 0
  e#_A = 2
  i_A = 0
  i#_A = 0
  o_A = 0
  o#_A = 0
  u_A = 0
  u#_A = 2
  and_A(x1,x2) = x1 + x2 + 3
  and#_A(x1,x2) = x2 + 10
  isQid_A(x1) = x1 + 1
  isQid#_A(x1) = 0
  isNePal_A(x1) = x1 + 1
  isNePal#_A(x1) = x1

precedence:

  __ > a__isList = o = and > mark = a__isNeList > a____ = a__and = isList = isNeList = a = e = i = u = isNePal > a__isNePal > a__isQid > tt = isQid > nil = a__isPal > isPal