YES

Problem:
 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)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [isNePal](x0) = x0,
   
   [isQid](x0) = x0,
   
   [and](x0, x1) = 2x0 + x1,
   
   [u] = 1,
   
   [o] = 1,
   
   [i] = 4,
   
   [e] = 1,
   
   [a] = 4,
   
   [a__isPal](x0) = 2x0,
   
   [isPal](x0) = 2x0,
   
   [a__isNePal](x0) = x0,
   
   [isNeList](x0) = x0,
   
   [a__isQid](x0) = x0,
   
   [isList](x0) = x0,
   
   [a__isNeList](x0) = x0,
   
   [a__isList](x0) = x0,
   
   [a__and](x0, x1) = 2x0 + x1,
   
   [tt] = 0,
   
   [nil] = 1,
   
   [mark](x0) = x0,
   
   [a____](x0, x1) = 2x0 + x1,
   
   [__](x0, x1) = 2x0 + x1
  orientation:
   a____(__(X,Y),Z) = 4X + 2Y + Z >= 2X + 2Y + Z = a____(mark(X),a____(mark(Y),mark(Z)))
   
   a____(X,nil()) = 2X + 1 >= X = mark(X)
   
   a____(nil(),X) = X + 2 >= X = mark(X)
   
   a__and(tt(),X) = X >= X = mark(X)
   
   a__isList(V) = V >= V = a__isNeList(V)
   
   a__isList(nil()) = 1 >= 0 = tt()
   
   a__isList(__(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = a__and(a__isList(V1),isList(V2))
   
   a__isNeList(V) = V >= V = a__isQid(V)
   
   a__isNeList(__(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = a__and(a__isList(V1),isNeList(V2))
   
   a__isNeList(__(V1,V2)) = 2V1 + V2 >= 2V1 + V2 = a__and(a__isNeList(V1),isList(V2))
   
   a__isNePal(V) = V >= V = a__isQid(V)
   
   a__isNePal(__(I,__(P,I))) = 3I + 2P >= 2I + 2P = a__and(a__isQid(I),isPal(P))
   
   a__isPal(V) = 2V >= V = a__isNePal(V)
   
   a__isPal(nil()) = 2 >= 0 = tt()
   
   a__isQid(a()) = 4 >= 0 = tt()
   
   a__isQid(e()) = 1 >= 0 = tt()
   
   a__isQid(i()) = 4 >= 0 = tt()
   
   a__isQid(o()) = 1 >= 0 = tt()
   
   a__isQid(u()) = 1 >= 0 = tt()
   
   mark(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a____(mark(X1),mark(X2))
   
   mark(and(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a__and(mark(X1),X2)
   
   mark(isList(X)) = X >= X = a__isList(X)
   
   mark(isNeList(X)) = X >= X = a__isNeList(X)
   
   mark(isQid(X)) = X >= X = a__isQid(X)
   
   mark(isNePal(X)) = X >= X = a__isNePal(X)
   
   mark(isPal(X)) = 2X >= 2X = a__isPal(X)
   
   mark(nil()) = 1 >= 1 = nil()
   
   mark(tt()) = 0 >= 0 = tt()
   
   mark(a()) = 4 >= 4 = a()
   
   mark(e()) = 1 >= 1 = e()
   
   mark(i()) = 4 >= 4 = i()
   
   mark(o()) = 1 >= 1 = o()
   
   mark(u()) = 1 >= 1 = u()
   
   a____(X1,X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2)
   
   a__and(X1,X2) = 2X1 + X2 >= 2X1 + X2 = and(X1,X2)
   
   a__isList(X) = X >= X = isList(X)
   
   a__isNeList(X) = X >= X = isNeList(X)
   
   a__isQid(X) = X >= X = isQid(X)
   
   a__isNePal(X) = X >= X = isNePal(X)
   
   a__isPal(X) = 2X >= 2X = isPal(X)
  problem:
   a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
   a__and(tt(),X) -> mark(X)
   a__isList(V) -> a__isNeList(V)
   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)
   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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [isNePal](x0) = x0 + 1,
    
    [isQid](x0) = x0,
    
    [and](x0, x1) = x0 + x1,
    
    [u] = 2,
    
    [o] = 1,
    
    [i] = 1,
    
    [e] = 0,
    
    [a] = 7,
    
    [a__isPal](x0) = 2x0 + 1,
    
    [isPal](x0) = 2x0 + 1,
    
    [a__isNePal](x0) = x0 + 1,
    
    [isNeList](x0) = x0,
    
    [a__isQid](x0) = x0,
    
    [isList](x0) = x0,
    
    [a__isNeList](x0) = x0,
    
    [a__isList](x0) = x0,
    
    [a__and](x0, x1) = x0 + x1,
    
    [tt] = 6,
    
    [nil] = 5,
    
    [mark](x0) = x0,
    
    [a____](x0, x1) = 4x0 + x1,
    
    [__](x0, x1) = 4x0 + x1
   orientation:
    a____(__(X,Y),Z) = 16X + 4Y + Z >= 4X + 4Y + Z = a____(mark(X),a____(mark(Y),mark(Z)))
    
    a__and(tt(),X) = X + 6 >= X = mark(X)
    
    a__isList(V) = V >= V = a__isNeList(V)
    
    a__isList(__(V1,V2)) = 4V1 + V2 >= V1 + V2 = a__and(a__isList(V1),isList(V2))
    
    a__isNeList(V) = V >= V = a__isQid(V)
    
    a__isNeList(__(V1,V2)) = 4V1 + V2 >= V1 + V2 = a__and(a__isList(V1),isNeList(V2))
    
    a__isNeList(__(V1,V2)) = 4V1 + V2 >= V1 + V2 = a__and(a__isNeList(V1),isList(V2))
    
    a__isNePal(V) = V + 1 >= V = a__isQid(V)
    
    a__isNePal(__(I,__(P,I))) = 5I + 4P + 1 >= I + 2P + 1 = a__and(a__isQid(I),isPal(P))
    
    a__isPal(V) = 2V + 1 >= V + 1 = a__isNePal(V)
    
    mark(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = a____(mark(X1),mark(X2))
    
    mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2)
    
    mark(isList(X)) = X >= X = a__isList(X)
    
    mark(isNeList(X)) = X >= X = a__isNeList(X)
    
    mark(isQid(X)) = X >= X = a__isQid(X)
    
    mark(isNePal(X)) = X + 1 >= X + 1 = a__isNePal(X)
    
    mark(isPal(X)) = 2X + 1 >= 2X + 1 = a__isPal(X)
    
    mark(nil()) = 5 >= 5 = nil()
    
    mark(tt()) = 6 >= 6 = tt()
    
    mark(a()) = 7 >= 7 = a()
    
    mark(e()) = 0 >= 0 = e()
    
    mark(i()) = 1 >= 1 = i()
    
    mark(o()) = 1 >= 1 = o()
    
    mark(u()) = 2 >= 2 = u()
    
    a____(X1,X2) = 4X1 + X2 >= 4X1 + X2 = __(X1,X2)
    
    a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2)
    
    a__isList(X) = X >= X = isList(X)
    
    a__isNeList(X) = X >= X = isNeList(X)
    
    a__isQid(X) = X >= X = isQid(X)
    
    a__isNePal(X) = X + 1 >= X + 1 = isNePal(X)
    
    a__isPal(X) = 2X + 1 >= 2X + 1 = isPal(X)
   problem:
    a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
    a__isList(V) -> a__isNeList(V)
    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(__(I,__(P,I))) -> a__and(a__isQid(I),isPal(P))
    a__isPal(V) -> a__isNePal(V)
    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)
   KBO Processor:
    weight function:
     w0 = 1
     w(isNePal) = w(isQid) = w(u) = w(o) = w(i) = w(e) = w(a) = w(a__isPal) = w(
     isPal) = w(a__isNePal) = w(isNeList) = w(a__isQid) = w(isList) = w(
     a__isNeList) = w(a__isList) = w(tt) = w(nil) = w(a____) = w(__) = 1
     w(and) = w(a__and) = w(mark) = 0
    precedence:
     mark > a__isPal > a__isNePal > a__isList > a__isNeList > a__isQid ~ 
     a__and ~ a____ > isNePal ~ isQid ~ and ~ u ~ o ~ i ~ e ~ a ~ isPal ~ 
     isNeList ~ isList ~ tt ~ nil ~ __
    problem:
     
    Qed