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__U11(tt()) -> tt()
  a__U21(tt(),V2) -> a__U22(a__isList(V2))
  a__U22(tt()) -> tt()
  a__U31(tt()) -> tt()
  a__U41(tt(),V2) -> a__U42(a__isNeList(V2))
  a__U42(tt()) -> tt()
  a__U51(tt(),V2) -> a__U52(a__isList(V2))
  a__U52(tt()) -> tt()
  a__U61(tt()) -> tt()
  a__U71(tt(),P) -> a__U72(a__isPal(P))
  a__U72(tt()) -> tt()
  a__U81(tt()) -> tt()
  a__isList(V) -> a__U11(a__isNeList(V))
  a__isList(nil()) -> tt()
  a__isList(__(V1,V2)) -> a__U21(a__isList(V1),V2)
  a__isNeList(V) -> a__U31(a__isQid(V))
  a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2)
  a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2)
  a__isNePal(V) -> a__U61(a__isQid(V))
  a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),P)
  a__isPal(V) -> a__U81(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(U11(X)) -> a__U11(mark(X))
  mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
  mark(U22(X)) -> a__U22(mark(X))
  mark(isList(X)) -> a__isList(X)
  mark(U31(X)) -> a__U31(mark(X))
  mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
  mark(U42(X)) -> a__U42(mark(X))
  mark(isNeList(X)) -> a__isNeList(X)
  mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
  mark(U52(X)) -> a__U52(mark(X))
  mark(U61(X)) -> a__U61(mark(X))
  mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
  mark(U72(X)) -> a__U72(mark(X))
  mark(isPal(X)) -> a__isPal(X)
  mark(U81(X)) -> a__U81(mark(X))
  mark(isQid(X)) -> a__isQid(X)
  mark(isNePal(X)) -> a__isNePal(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__U11(X) -> U11(X)
  a__U21(X1,X2) -> U21(X1,X2)
  a__U22(X) -> U22(X)
  a__isList(X) -> isList(X)
  a__U31(X) -> U31(X)
  a__U41(X1,X2) -> U41(X1,X2)
  a__U42(X) -> U42(X)
  a__isNeList(X) -> isNeList(X)
  a__U51(X1,X2) -> U51(X1,X2)
  a__U52(X) -> U52(X)
  a__U61(X) -> U61(X)
  a__U71(X1,X2) -> U71(X1,X2)
  a__U72(X) -> U72(X)
  a__isPal(X) -> isPal(X)
  a__U81(X) -> U81(X)
  a__isQid(X) -> isQid(X)
  a__isNePal(X) -> isNePal(X)

linear polynomial interpretations on N:

  a_____A(x1,x2) = x1 + x2 + 3
  a____#_A(x1,x2) = x1 + x2 + 3
  ___A(x1,x2) = x1 + x2 + 3
  __#_A(x1,x2) = x1 + x2 + 3
  mark_A(x1) = x1
  mark#_A(x1) = x1
  nil_A = 4
  nil#_A = 4
  a__U11_A(x1) = x1
  a__U11#_A(x1) = x1
  tt_A = 3
  tt#_A = 3
  a__U21_A(x1,x2) = x1 + x2
  a__U21#_A(x1,x2) = x1 + x2
  a__U22_A(x1) = x1
  a__U22#_A(x1) = x1
  a__isList_A(x1) = x1 + 2
  a__isList#_A(x1) = x1 + 2
  a__U31_A(x1) = x1
  a__U31#_A(x1) = x1
  a__U41_A(x1,x2) = x1 + x2
  a__U41#_A(x1,x2) = x1 + x2
  a__U42_A(x1) = x1
  a__U42#_A(x1) = x1
  a__isNeList_A(x1) = x1 + 1
  a__isNeList#_A(x1) = x1 + 1
  a__U51_A(x1,x2) = x1 + x2
  a__U51#_A(x1,x2) = x1 + x2
  a__U52_A(x1) = x1
  a__U52#_A(x1) = x1
  a__U61_A(x1) = x1
  a__U61#_A(x1) = x1
  a__U71_A(x1,x2) = x1 + x2
  a__U71#_A(x1,x2) = x1 + x2
  a__U72_A(x1) = x1
  a__U72#_A(x1) = x1
  a__isPal_A(x1) = x1 + 2
  a__isPal#_A(x1) = x1 + 2
  a__U81_A(x1) = x1
  a__U81#_A(x1) = x1
  a__isQid_A(x1) = x1
  a__isQid#_A(x1) = x1
  a__isNePal_A(x1) = x1 + 1
  a__isNePal#_A(x1) = x1 + 1
  a_A = 4
  a#_A = 4
  e_A = 4
  e#_A = 4
  i_A = 4
  i#_A = 4
  o_A = 4
  o#_A = 4
  u_A = 4
  u#_A = 4
  U11_A(x1) = x1
  U11#_A(x1) = x1
  U21_A(x1,x2) = x1 + x2
  U21#_A(x1,x2) = x1 + x2
  U22_A(x1) = x1
  U22#_A(x1) = x1
  isList_A(x1) = x1 + 2
  isList#_A(x1) = x1 + 2
  U31_A(x1) = x1
  U31#_A(x1) = x1
  U41_A(x1,x2) = x1 + x2
  U41#_A(x1,x2) = x1 + x2
  U42_A(x1) = x1
  U42#_A(x1) = x1
  isNeList_A(x1) = x1 + 1
  isNeList#_A(x1) = x1 + 1
  U51_A(x1,x2) = x1 + x2
  U51#_A(x1,x2) = x1 + x2
  U52_A(x1) = x1
  U52#_A(x1) = x1
  U61_A(x1) = x1
  U61#_A(x1) = x1
  U71_A(x1,x2) = x1 + x2
  U71#_A(x1,x2) = x1 + x2
  U72_A(x1) = x1
  U72#_A(x1) = x1
  isPal_A(x1) = x1 + 2
  isPal#_A(x1) = x1 + 2
  U81_A(x1) = x1
  U81#_A(x1) = x1
  isQid_A(x1) = x1
  isQid#_A(x1) = x1
  isNePal_A(x1) = x1 + 1
  isNePal#_A(x1) = x1 + 1

precedence:

  a = e = i = o = u > tt > mark > a____ = nil = a__isPal > __ = a__U81 = a__isNePal = isPal > a__isNeList = a__U61 = a__U71 = U81 = isNePal > a__U31 = a__U41 = a__U51 = a__U72 = a__isQid = isNeList = U61 = U71 > a__isList = a__U42 = a__U52 = U31 = U41 = U51 = U72 = isQid > a__U11 = a__U21 = isList = U42 = U52 > a__U22 = U11 = U21 > U22