YES

TRS:

  __(__(X,Y),Z) -> __(X,__(Y,Z))
  __(X,nil()) -> X
  __(nil(),X) -> X
  U11(tt()) -> tt()
  U21(tt(),V2) -> U22(isList(activate(V2)))
  U22(tt()) -> tt()
  U31(tt()) -> tt()
  U41(tt(),V2) -> U42(isNeList(activate(V2)))
  U42(tt()) -> tt()
  U51(tt(),V2) -> U52(isList(activate(V2)))
  U52(tt()) -> tt()
  U61(tt()) -> tt()
  U71(tt(),P) -> U72(isPal(activate(P)))
  U72(tt()) -> tt()
  U81(tt()) -> tt()
  isList(V) -> U11(isNeList(activate(V)))
  isList(n__nil()) -> tt()
  isList(n____(V1,V2)) -> U21(isList(activate(V1)),activate(V2))
  isNeList(V) -> U31(isQid(activate(V)))
  isNeList(n____(V1,V2)) -> U41(isList(activate(V1)),activate(V2))
  isNeList(n____(V1,V2)) -> U51(isNeList(activate(V1)),activate(V2))
  isNePal(V) -> U61(isQid(activate(V)))
  isNePal(n____(I,__(P,I))) -> U71(isQid(activate(I)),activate(P))
  isPal(V) -> U81(isNePal(activate(V)))
  isPal(n__nil()) -> tt()
  isQid(n__a()) -> tt()
  isQid(n__e()) -> tt()
  isQid(n__i()) -> tt()
  isQid(n__o()) -> tt()
  isQid(n__u()) -> tt()
  nil() -> n__nil()
  __(X1,X2) -> n____(X1,X2)
  a() -> n__a()
  e() -> n__e()
  i() -> n__i()
  o() -> n__o()
  u() -> n__u()
  activate(n__nil()) -> nil()
  activate(n____(X1,X2)) -> __(X1,X2)
  activate(n__a()) -> a()
  activate(n__e()) -> e()
  activate(n__i()) -> i()
  activate(n__o()) -> o()
  activate(n__u()) -> u()
  activate(X) -> X

linear polynomial interpretations on N:

  ___A(x1,x2) = x1 + x2 + 6
  __#_A(x1,x2) = 4
  nil_A = 1
  nil#_A = 4
  U11_A(x1) = x1
  U11#_A(x1) = x1
  tt_A = 1
  tt#_A = 2
  U21_A(x1,x2) = x1
  U21#_A(x1,x2) = x1 + x2 + 9
  U22_A(x1) = 1
  U22#_A(x1) = x1
  isList_A(x1) = x1 + 2
  isList#_A(x1) = x1 + 8
  activate_A(x1) = x1 + 1
  activate#_A(x1) = 5
  U31_A(x1) = 1
  U31#_A(x1) = 3
  U41_A(x1,x2) = x1
  U41#_A(x1,x2) = x2 + 8
  U42_A(x1) = 1
  U42#_A(x1) = x1 + 2
  isNeList_A(x1) = x1 + 1
  isNeList#_A(x1) = x1 + 6
  U51_A(x1,x2) = x1
  U51#_A(x1,x2) = x2 + 10
  U52_A(x1) = 1
  U52#_A(x1) = x1 + 2
  U61_A(x1) = 1
  U61#_A(x1) = 1
  U71_A(x1,x2) = 1
  U71#_A(x1,x2) = x2 + 10
  U72_A(x1) = 1
  U72#_A(x1) = 0
  isPal_A(x1) = 1
  isPal#_A(x1) = x1 + 8
  U81_A(x1) = 1
  U81#_A(x1) = 3
  n__nil_A = 1
  n__nil#_A = 3
  n_____A(x1,x2) = x1 + x2 + 6
  n____#_A(x1,x2) = 2
  isQid_A(x1) = 1
  isQid#_A(x1) = 3
  isNePal_A(x1) = 1
  isNePal#_A(x1) = x1 + 6
  n__a_A = 1
  n__a#_A = 3
  n__e_A = 1
  n__e#_A = 3
  n__i_A = 1
  n__i#_A = 3
  n__o_A = 1
  n__o#_A = 3
  n__u_A = 1
  n__u#_A = 0
  a_A = 1
  a#_A = 4
  e_A = 1
  e#_A = 4
  i_A = 1
  i#_A = 4
  o_A = 1
  o#_A = 4
  u_A = 1
  u#_A = 1

precedence:

  n____ > isNeList > U51 > isList > U21 = U41 > activate = n__e > nil = isNePal = a = e = i > __ = U11 = U71 = n__nil = n__a = n__i > isPal = isQid > U31 = U42 = U52 = U81 = n__o > tt = o > U22 = U61 = U72 = n__u > u