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:
 DP Processor:
  DPs:
   a____#(__(X,Y),Z) -> mark#(Z)
   a____#(__(X,Y),Z) -> mark#(Y)
   a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
   a____#(__(X,Y),Z) -> mark#(X)
   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#(__(V1,V2)) -> a__isList#(V1)
   a__isList#(__(V1,V2)) -> a__and#(a__isList(V1),isList(V2))
   a__isNeList#(V) -> a__isQid#(V)
   a__isNeList#(__(V1,V2)) -> a__isList#(V1)
   a__isNeList#(__(V1,V2)) -> a__and#(a__isList(V1),isNeList(V2))
   a__isNeList#(__(V1,V2)) -> a__isNeList#(V1)
   a__isNeList#(__(V1,V2)) -> a__and#(a__isNeList(V1),isList(V2))
   a__isNePal#(V) -> a__isQid#(V)
   a__isNePal#(__(I,__(P,I))) -> a__isQid#(I)
   a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPal(P))
   a__isPal#(V) -> a__isNePal#(V)
   mark#(__(X1,X2)) -> mark#(X2)
   mark#(__(X1,X2)) -> mark#(X1)
   mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
   mark#(and(X1,X2)) -> mark#(X1)
   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)
  TRS:
   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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a__isPal#](x0) = x0 + 4,
    
    [a__isNePal#](x0) = x0 + 2,
    
    [a__isQid#](x0) = x0,
    
    [a__isNeList#](x0) = x0 + 1,
    
    [a__isList#](x0) = x0 + 2,
    
    [a__and#](x0, x1) = 2x0 + x1,
    
    [mark#](x0) = x0 + 3,
    
    [a____#](x0, x1) = 2x0 + x1,
    
    [isNePal](x0) = x0,
    
    [isQid](x0) = x0,
    
    [and](x0, x1) = 2x0 + x1 + 2,
    
    [u] = 4,
    
    [o] = 4,
    
    [i] = 2,
    
    [e] = 2,
    
    [a] = 2,
    
    [a__isPal](x0) = x0 + 4,
    
    [isPal](x0) = x0 + 4,
    
    [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 + 2,
    
    [tt] = 2,
    
    [nil] = 4,
    
    [mark](x0) = x0,
    
    [a____](x0, x1) = 2x0 + x1 + 3,
    
    [__](x0, x1) = 2x0 + x1 + 3
   orientation:
    a____#(__(X,Y),Z) = 4X + 2Y + Z + 6 >= Z + 3 = mark#(Z)
    
    a____#(__(X,Y),Z) = 4X + 2Y + Z + 6 >= Y + 3 = mark#(Y)
    
    a____#(__(X,Y),Z) = 4X + 2Y + Z + 6 >= 2Y + Z = a____#(mark(Y),mark(Z))
    
    a____#(__(X,Y),Z) = 4X + 2Y + Z + 6 >= X + 3 = mark#(X)
    
    a____#(__(X,Y),Z) = 4X + 2Y + Z + 6 >= 2X + 2Y + Z + 3 = a____#(mark(X),a____(mark(Y),mark(Z)))
    
    a____#(X,nil()) = 2X + 4 >= X + 3 = mark#(X)
    
    a____#(nil(),X) = X + 8 >= X + 3 = mark#(X)
    
    a__and#(tt(),X) = X + 4 >= X + 3 = mark#(X)
    
    a__isList#(V) = V + 2 >= V + 1 = a__isNeList#(V)
    
    a__isList#(__(V1,V2)) = 2V1 + V2 + 5 >= V1 + 2 = a__isList#(V1)
    
    a__isList#(__(V1,V2)) = 2V1 + V2 + 5 >= 2V1 + V2 = a__and#(a__isList(V1),isList(V2))
    
    a__isNeList#(V) = V + 1 >= V = a__isQid#(V)
    
    a__isNeList#(__(V1,V2)) = 2V1 + V2 + 4 >= V1 + 2 = a__isList#(V1)
    
    a__isNeList#(__(V1,V2)) = 2V1 + V2 + 4 >= 2V1 + V2 = a__and#(a__isList(V1),isNeList(V2))
    
    a__isNeList#(__(V1,V2)) = 2V1 + V2 + 4 >= V1 + 1 = a__isNeList#(V1)
    
    a__isNeList#(__(V1,V2)) = 2V1 + V2 + 4 >= 2V1 + V2 = a__and#(a__isNeList(V1),isList(V2))
    
    a__isNePal#(V) = V + 2 >= V = a__isQid#(V)
    
    a__isNePal#(__(I,__(P,I))) = 3I + 2P + 8 >= I = a__isQid#(I)
    
    a__isNePal#(__(I,__(P,I))) = 3I + 2P + 8 >= 2I + P + 4 = a__and#(a__isQid(I),isPal(P))
    
    a__isPal#(V) = V + 4 >= V + 2 = a__isNePal#(V)
    
    mark#(__(X1,X2)) = 2X1 + X2 + 6 >= X2 + 3 = mark#(X2)
    
    mark#(__(X1,X2)) = 2X1 + X2 + 6 >= X1 + 3 = mark#(X1)
    
    mark#(__(X1,X2)) = 2X1 + X2 + 6 >= 2X1 + X2 = a____#(mark(X1),mark(X2))
    
    mark#(and(X1,X2)) = 2X1 + X2 + 5 >= X1 + 3 = mark#(X1)
    
    mark#(and(X1,X2)) = 2X1 + X2 + 5 >= 2X1 + X2 = a__and#(mark(X1),X2)
    
    mark#(isList(X)) = X + 3 >= X + 2 = a__isList#(X)
    
    mark#(isNeList(X)) = X + 3 >= X + 1 = a__isNeList#(X)
    
    mark#(isQid(X)) = X + 3 >= X = a__isQid#(X)
    
    mark#(isNePal(X)) = X + 3 >= X + 2 = a__isNePal#(X)
    
    mark#(isPal(X)) = X + 7 >= X + 4 = a__isPal#(X)
    
    a____(__(X,Y),Z) = 4X + 2Y + Z + 9 >= 2X + 2Y + Z + 6 = a____(mark(X),a____(mark(Y),mark(Z)))
    
    a____(X,nil()) = 2X + 7 >= X = mark(X)
    
    a____(nil(),X) = X + 11 >= X = mark(X)
    
    a__and(tt(),X) = X + 6 >= X = mark(X)
    
    a__isList(V) = V >= V = a__isNeList(V)
    
    a__isList(nil()) = 4 >= 2 = tt()
    
    a__isList(__(V1,V2)) = 2V1 + V2 + 3 >= 2V1 + V2 + 2 = a__and(a__isList(V1),isList(V2))
    
    a__isNeList(V) = V >= V = a__isQid(V)
    
    a__isNeList(__(V1,V2)) = 2V1 + V2 + 3 >= 2V1 + V2 + 2 = a__and(a__isList(V1),isNeList(V2))
    
    a__isNeList(__(V1,V2)) = 2V1 + V2 + 3 >= 2V1 + V2 + 2 = a__and(a__isNeList(V1),isList(V2))
    
    a__isNePal(V) = V >= V = a__isQid(V)
    
    a__isNePal(__(I,__(P,I))) = 3I + 2P + 6 >= 2I + P + 6 = a__and(a__isQid(I),isPal(P))
    
    a__isPal(V) = V + 4 >= V = a__isNePal(V)
    
    a__isPal(nil()) = 8 >= 2 = tt()
    
    a__isQid(a()) = 2 >= 2 = tt()
    
    a__isQid(e()) = 2 >= 2 = tt()
    
    a__isQid(i()) = 2 >= 2 = tt()
    
    a__isQid(o()) = 4 >= 2 = tt()
    
    a__isQid(u()) = 4 >= 2 = tt()
    
    mark(__(X1,X2)) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = a____(mark(X1),mark(X2))
    
    mark(and(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = 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)) = X + 4 >= X + 4 = a__isPal(X)
    
    mark(nil()) = 4 >= 4 = nil()
    
    mark(tt()) = 2 >= 2 = tt()
    
    mark(a()) = 2 >= 2 = a()
    
    mark(e()) = 2 >= 2 = e()
    
    mark(i()) = 2 >= 2 = i()
    
    mark(o()) = 4 >= 4 = o()
    
    mark(u()) = 4 >= 4 = u()
    
    a____(X1,X2) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = __(X1,X2)
    
    a__and(X1,X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = 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) = X + 4 >= X + 4 = isPal(X)
   problem:
    DPs:
     
    TRS:
     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)
   Qed