YES

TRS:

  __(__(X,Y),Z) -> __(X,__(Y,Z))
  __(X,nil()) -> X
  __(nil(),X) -> X
  U11(tt(),V) -> U12(isNeList(activate(V)))
  U12(tt()) -> tt()
  U21(tt(),V1,V2) -> U22(isList(activate(V1)),activate(V2))
  U22(tt(),V2) -> U23(isList(activate(V2)))
  U23(tt()) -> tt()
  U31(tt(),V) -> U32(isQid(activate(V)))
  U32(tt()) -> tt()
  U41(tt(),V1,V2) -> U42(isList(activate(V1)),activate(V2))
  U42(tt(),V2) -> U43(isNeList(activate(V2)))
  U43(tt()) -> tt()
  U51(tt(),V1,V2) -> U52(isNeList(activate(V1)),activate(V2))
  U52(tt(),V2) -> U53(isList(activate(V2)))
  U53(tt()) -> tt()
  U61(tt(),V) -> U62(isQid(activate(V)))
  U62(tt()) -> tt()
  U71(tt(),V) -> U72(isNePal(activate(V)))
  U72(tt()) -> tt()
  and(tt(),X) -> activate(X)
  isList(V) -> U11(isPalListKind(activate(V)),activate(V))
  isList(n__nil()) -> tt()
  isList(n____(V1,V2)) -> U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2))
  isNeList(V) -> U31(isPalListKind(activate(V)),activate(V))
  isNeList(n____(V1,V2)) -> U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2))
  isNeList(n____(V1,V2)) -> U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2))
  isNePal(V) -> U61(isPalListKind(activate(V)),activate(V))
  isNePal(n____(I,__(P,I))) -> and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)),n__isPalListKind(activate(P))))
  isPal(V) -> U71(isPalListKind(activate(V)),activate(V))
  isPal(n__nil()) -> tt()
  isPalListKind(n__a()) -> tt()
  isPalListKind(n__e()) -> tt()
  isPalListKind(n__i()) -> tt()
  isPalListKind(n__nil()) -> tt()
  isPalListKind(n__o()) -> tt()
  isPalListKind(n__u()) -> tt()
  isPalListKind(n____(V1,V2)) -> and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2)))
  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)
  isPalListKind(X) -> n__isPalListKind(X)
  and(X1,X2) -> n__and(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__isPalListKind(X)) -> isPalListKind(X)
  activate(n__and(X1,X2)) -> and(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 + 23
  __#_A(x1,x2) = x1 + x2 + 25
  nil_A = 1
  nil#_A = 3
  U11_A(x1,x2) = 2
  U11#_A(x1,x2) = x2 + 10
  tt_A = 2
  tt#_A = 1
  U12_A(x1) = 2
  U12#_A(x1) = 2
  isNeList_A(x1) = 2
  isNeList#_A(x1) = x1 + 7
  activate_A(x1) = x1 + 2
  activate#_A(x1) = x1 + 3
  U21_A(x1,x2,x3) = x2 + 2
  U21#_A(x1,x2,x3) = x1 + x2 + x3 + 17
  U22_A(x1,x2) = 2
  U22#_A(x1,x2) = x2 + 16
  isList_A(x1) = x1 + 2
  isList#_A(x1) = x1 + 13
  U23_A(x1) = 2
  U23#_A(x1) = x1
  U31_A(x1,x2) = 2
  U31#_A(x1,x2) = x2 + 4
  U32_A(x1) = x1
  U32#_A(x1) = 2
  isQid_A(x1) = 2
  isQid#_A(x1) = 2
  U41_A(x1,x2,x3) = 2
  U41#_A(x1,x2,x3) = x2 + x3 + 16
  U42_A(x1,x2) = 2
  U42#_A(x1,x2) = x2 + 10
  U43_A(x1) = 2
  U43#_A(x1) = 0
  U51_A(x1,x2,x3) = 2
  U51#_A(x1,x2,x3) = x2 + x3 + 19
  U52_A(x1,x2) = x1
  U52#_A(x1,x2) = x2 + 16
  U53_A(x1) = 2
  U53#_A(x1) = x1
  U61_A(x1,x2) = 2
  U61#_A(x1,x2) = x2 + 3
  U62_A(x1) = 2
  U62#_A(x1) = 2
  U71_A(x1,x2) = 2
  U71#_A(x1,x2) = x2 + 9
  U72_A(x1) = 2
  U72#_A(x1) = x1
  isNePal_A(x1) = x1 + 2
  isNePal#_A(x1) = x1 + 6
  and_A(x1,x2) = x1 + x2
  and#_A(x1,x2) = x1 + x2 + 2
  isPalListKind_A(x1) = 2
  isPalListKind#_A(x1) = 2
  n__nil_A = 1
  n__nil#_A = 2
  n_____A(x1,x2) = x1 + x2 + 23
  n____#_A(x1,x2) = x1 + x2 + 24
  n__isPalListKind_A(x1) = 0
  n__isPalListKind#_A(x1) = 0
  n__and_A(x1,x2) = x1 + x2
  n__and#_A(x1,x2) = x1 + 1
  isPal_A(x1) = x1 + 40
  isPal#_A(x1) = x1 + 22
  n__a_A = 1
  n__a#_A = 2
  n__e_A = 1
  n__e#_A = 2
  n__i_A = 1
  n__i#_A = 2
  n__o_A = 1
  n__o#_A = 2
  n__u_A = 1
  n__u#_A = 0
  a_A = 1
  a#_A = 3
  e_A = 1
  e#_A = 3
  i_A = 1
  i#_A = 3
  o_A = 1
  o#_A = 3
  u_A = 1
  u#_A = 1

precedence:

  isNeList = U21 > U22 = U31 = U41 = U52 > isList = U42 = isNePal > U11 = U43 = U61 = a > activate = U62 > __ = nil = i = o > n____ = n__i = n__o > isQid = U51 = n__and = isPal > U12 = U71 = isPalListKind = n__a = e = u > U23 = U32 = U72 = and = n__nil = n__isPalListKind = n__e = n__u > tt > U53