YES

Problem:
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(X,nil()) -> X
 __(nil(),X) -> X
 and(tt(),X) -> activate(X)
 isList(V) -> isNeList(activate(V))
 isList(n__nil()) -> tt()
 isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
 isNeList(V) -> isQid(activate(V))
 isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
 isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
 isNePal(V) -> isQid(activate(V))
 isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
 isPal(V) -> 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)
 isList(X) -> n__isList(X)
 isNeList(X) -> n__isNeList(X)
 isPal(X) -> n__isPal(X)
 a() -> n__a()
 e() -> n__e()
 i() -> n__i()
 o() -> n__o()
 u() -> n__u()
 activate(n__nil()) -> nil()
 activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
 activate(n__isList(X)) -> isList(X)
 activate(n__isNeList(X)) -> isNeList(X)
 activate(n__isPal(X)) -> isPal(X)
 activate(n__a()) -> a()
 activate(n__e()) -> e()
 activate(n__i()) -> i()
 activate(n__o()) -> o()
 activate(n__u()) -> u()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [u] = 1,
   
   [o] = 0,
   
   [i] = 0,
   
   [e] = 0,
   
   [a] = 0,
   
   [n__u] = 1,
   
   [n__o] = 0,
   
   [n__i] = 0,
   
   [n__e] = 0,
   
   [n__a] = 0,
   
   [isPal](x0) = 2x0 + 3,
   
   [n__isPal](x0) = 2x0 + 3,
   
   [isNePal](x0) = x0 + 3,
   
   [n__isNeList](x0) = x0,
   
   [isQid](x0) = x0,
   
   [n__isList](x0) = x0,
   
   [n____](x0, x1) = 2x0 + x1,
   
   [n__nil] = 0,
   
   [isNeList](x0) = x0,
   
   [isList](x0) = x0,
   
   [activate](x0) = x0,
   
   [and](x0, x1) = 2x0 + x1,
   
   [tt] = 0,
   
   [nil] = 0,
   
   [__](x0, x1) = 2x0 + x1
  orientation:
   __(__(X,Y),Z) = 4X + 2Y + Z >= 2X + 2Y + Z = __(X,__(Y,Z))
   
   __(X,nil()) = 2X >= X = X
   
   __(nil(),X) = X >= X = X
   
   and(tt(),X) = X >= X = activate(X)
   
   isList(V) = V >= V = isNeList(activate(V))
   
   isList(n__nil()) = 0 >= 0 = tt()
   
   isList(n____(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = and(isList(activate(V1)),n__isList(activate(V2)))
   
   isNeList(V) = V >= V = isQid(activate(V))
   
   isNeList(n____(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = and(isList(activate(V1)),n__isNeList(activate(V2)))
   
   isNeList(n____(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = and(isNeList(activate(V1)),n__isList(activate(V2)))
   
   isNePal(V) = V + 3 >= V = isQid(activate(V))
   
   isNePal(n____(I,n____(P,I))) = 3I + 2P + 3 >= 2I + 2P + 3 = and(isQid(activate(I)),n__isPal(activate(P)))
   
   isPal(V) = 2V + 3 >= V + 3 = isNePal(activate(V))
   
   isPal(n__nil()) = 3 >= 0 = tt()
   
   isQid(n__a()) = 0 >= 0 = tt()
   
   isQid(n__e()) = 0 >= 0 = tt()
   
   isQid(n__i()) = 0 >= 0 = tt()
   
   isQid(n__o()) = 0 >= 0 = tt()
   
   isQid(n__u()) = 1 >= 0 = tt()
   
   nil() = 0 >= 0 = n__nil()
   
   __(X1,X2) = 2X1 + X2 >= 2X1 + X2 = n____(X1,X2)
   
   isList(X) = X >= X = n__isList(X)
   
   isNeList(X) = X >= X = n__isNeList(X)
   
   isPal(X) = 2X + 3 >= 2X + 3 = n__isPal(X)
   
   a() = 0 >= 0 = n__a()
   
   e() = 0 >= 0 = n__e()
   
   i() = 0 >= 0 = n__i()
   
   o() = 0 >= 0 = n__o()
   
   u() = 1 >= 1 = n__u()
   
   activate(n__nil()) = 0 >= 0 = nil()
   
   activate(n____(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(activate(X1),activate(X2))
   
   activate(n__isList(X)) = X >= X = isList(X)
   
   activate(n__isNeList(X)) = X >= X = isNeList(X)
   
   activate(n__isPal(X)) = 2X + 3 >= 2X + 3 = isPal(X)
   
   activate(n__a()) = 0 >= 0 = a()
   
   activate(n__e()) = 0 >= 0 = e()
   
   activate(n__i()) = 0 >= 0 = i()
   
   activate(n__o()) = 0 >= 0 = o()
   
   activate(n__u()) = 1 >= 1 = u()
   
   activate(X) = X >= X = X
  problem:
   __(__(X,Y),Z) -> __(X,__(Y,Z))
   __(X,nil()) -> X
   __(nil(),X) -> X
   and(tt(),X) -> activate(X)
   isList(V) -> isNeList(activate(V))
   isList(n__nil()) -> tt()
   isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
   isNeList(V) -> isQid(activate(V))
   isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
   isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
   isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
   isPal(V) -> isNePal(activate(V))
   isQid(n__a()) -> tt()
   isQid(n__e()) -> tt()
   isQid(n__i()) -> tt()
   isQid(n__o()) -> tt()
   nil() -> n__nil()
   __(X1,X2) -> n____(X1,X2)
   isList(X) -> n__isList(X)
   isNeList(X) -> n__isNeList(X)
   isPal(X) -> n__isPal(X)
   a() -> n__a()
   e() -> n__e()
   i() -> n__i()
   o() -> n__o()
   u() -> n__u()
   activate(n__nil()) -> nil()
   activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
   activate(n__isList(X)) -> isList(X)
   activate(n__isNeList(X)) -> isNeList(X)
   activate(n__isPal(X)) -> isPal(X)
   activate(n__a()) -> a()
   activate(n__e()) -> e()
   activate(n__i()) -> i()
   activate(n__o()) -> o()
   activate(n__u()) -> u()
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [u] = 4,
    
    [o] = 0,
    
    [i] = 4,
    
    [e] = 0,
    
    [a] = 4,
    
    [n__u] = 4,
    
    [n__o] = 0,
    
    [n__i] = 4,
    
    [n__e] = 0,
    
    [n__a] = 4,
    
    [isPal](x0) = x0,
    
    [n__isPal](x0) = x0,
    
    [isNePal](x0) = x0,
    
    [n__isNeList](x0) = x0,
    
    [isQid](x0) = x0,
    
    [n__isList](x0) = x0,
    
    [n____](x0, x1) = x0 + x1,
    
    [n__nil] = 0,
    
    [isNeList](x0) = x0,
    
    [isList](x0) = x0,
    
    [activate](x0) = x0,
    
    [and](x0, x1) = x0 + x1,
    
    [tt] = 0,
    
    [nil] = 0,
    
    [__](x0, x1) = x0 + x1
   orientation:
    __(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
    
    __(X,nil()) = X >= X = X
    
    __(nil(),X) = X >= X = X
    
    and(tt(),X) = X >= X = activate(X)
    
    isList(V) = V >= V = isNeList(activate(V))
    
    isList(n__nil()) = 0 >= 0 = tt()
    
    isList(n____(V1,V2)) = V1 + V2 >= V1 + V2 = and(isList(activate(V1)),n__isList(activate(V2)))
    
    isNeList(V) = V >= V = isQid(activate(V))
    
    isNeList(n____(V1,V2)) = V1 + V2 >= V1 + V2 = and(isList(activate(V1)),n__isNeList(activate(V2)))
    
    isNeList(n____(V1,V2)) = V1 + V2 >= V1 + V2 = and(isNeList(activate(V1)),n__isList(activate(V2)))
    
    isNePal(n____(I,n____(P,I))) = 2I + P >= I + P = and(isQid(activate(I)),n__isPal(activate(P)))
    
    isPal(V) = V >= V = isNePal(activate(V))
    
    isQid(n__a()) = 4 >= 0 = tt()
    
    isQid(n__e()) = 0 >= 0 = tt()
    
    isQid(n__i()) = 4 >= 0 = tt()
    
    isQid(n__o()) = 0 >= 0 = tt()
    
    nil() = 0 >= 0 = n__nil()
    
    __(X1,X2) = X1 + X2 >= X1 + X2 = n____(X1,X2)
    
    isList(X) = X >= X = n__isList(X)
    
    isNeList(X) = X >= X = n__isNeList(X)
    
    isPal(X) = X >= X = n__isPal(X)
    
    a() = 4 >= 4 = n__a()
    
    e() = 0 >= 0 = n__e()
    
    i() = 4 >= 4 = n__i()
    
    o() = 0 >= 0 = n__o()
    
    u() = 4 >= 4 = n__u()
    
    activate(n__nil()) = 0 >= 0 = nil()
    
    activate(n____(X1,X2)) = X1 + X2 >= X1 + X2 = __(activate(X1),activate(X2))
    
    activate(n__isList(X)) = X >= X = isList(X)
    
    activate(n__isNeList(X)) = X >= X = isNeList(X)
    
    activate(n__isPal(X)) = X >= X = isPal(X)
    
    activate(n__a()) = 4 >= 4 = a()
    
    activate(n__e()) = 0 >= 0 = e()
    
    activate(n__i()) = 4 >= 4 = i()
    
    activate(n__o()) = 0 >= 0 = o()
    
    activate(n__u()) = 4 >= 4 = u()
    
    activate(X) = X >= X = X
   problem:
    __(__(X,Y),Z) -> __(X,__(Y,Z))
    __(X,nil()) -> X
    __(nil(),X) -> X
    and(tt(),X) -> activate(X)
    isList(V) -> isNeList(activate(V))
    isList(n__nil()) -> tt()
    isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
    isNeList(V) -> isQid(activate(V))
    isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
    isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
    isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
    isPal(V) -> isNePal(activate(V))
    isQid(n__e()) -> tt()
    isQid(n__o()) -> tt()
    nil() -> n__nil()
    __(X1,X2) -> n____(X1,X2)
    isList(X) -> n__isList(X)
    isNeList(X) -> n__isNeList(X)
    isPal(X) -> n__isPal(X)
    a() -> n__a()
    e() -> n__e()
    i() -> n__i()
    o() -> n__o()
    u() -> n__u()
    activate(n__nil()) -> nil()
    activate(n____(X1,X2)) -> __(activate(X1),activate(X2))
    activate(n__isList(X)) -> isList(X)
    activate(n__isNeList(X)) -> isNeList(X)
    activate(n__isPal(X)) -> isPal(X)
    activate(n__a()) -> a()
    activate(n__e()) -> e()
    activate(n__i()) -> i()
    activate(n__o()) -> o()
    activate(n__u()) -> u()
    activate(X) -> X
   KBO Processor:
    weight function:
     w0 = 1
     w(u) = w(o) = w(i) = w(e) = w(a) = w(n__u) = w(n__o) = w(n__i) = w(
     n__e) = w(n__a) = w(isPal) = w(n__isPal) = w(isNePal) = w(n__isNeList) = w(
     isQid) = w(n__isList) = w(n____) = w(n__nil) = w(isNeList) = w(isList) = w(
     tt) = w(nil) = w(__) = 1
     w(activate) = w(and) = 0
    precedence:
     activate > nil > isList > isNeList > u ~ o ~ i ~ e ~ a ~ isPal ~ 
     __ > n__u ~ n__o ~ n__i ~ n__e ~ n__a ~ n__isPal ~ isNePal ~ n__isNeList ~ 
     isQid ~ n__isList ~ n____ ~ n__nil ~ and ~ tt
    problem:
     
    Qed