YES

Problem:
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(X,nil())) -> mark(X)
 active(__(nil(),X)) -> mark(X)
 active(and(tt(),X)) -> mark(X)
 active(isList(V)) -> mark(isNeList(V))
 active(isList(nil())) -> mark(tt())
 active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2)))
 active(isNeList(V)) -> mark(isQid(V))
 active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2)))
 active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2)))
 active(isNePal(V)) -> mark(isQid(V))
 active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P)))
 active(isPal(V)) -> mark(isNePal(V))
 active(isPal(nil())) -> mark(tt())
 active(isQid(a())) -> mark(tt())
 active(isQid(e())) -> mark(tt())
 active(isQid(i())) -> mark(tt())
 active(isQid(o())) -> mark(tt())
 active(isQid(u())) -> mark(tt())
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(isList(X)) -> active(isList(X))
 mark(isNeList(X)) -> active(isNeList(X))
 mark(isQid(X)) -> active(isQid(X))
 mark(isNePal(X)) -> active(isNePal(X))
 mark(isPal(X)) -> active(isPal(X))
 mark(a()) -> active(a())
 mark(e()) -> active(e())
 mark(i()) -> active(i())
 mark(o()) -> active(o())
 mark(u()) -> active(u())
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 __(active(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 isList(mark(X)) -> isList(X)
 isList(active(X)) -> isList(X)
 isNeList(mark(X)) -> isNeList(X)
 isNeList(active(X)) -> isNeList(X)
 isQid(mark(X)) -> isQid(X)
 isQid(active(X)) -> isQid(X)
 isNePal(mark(X)) -> isNePal(X)
 isNePal(active(X)) -> isNePal(X)
 isPal(mark(X)) -> isPal(X)
 isPal(active(X)) -> isPal(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [u] = 0,
   
   [o] = 0,
   
   [i] = 4,
   
   [e] = 2,
   
   [a] = 4,
   
   [isPal](x0) = 3x0 + 3,
   
   [isNePal](x0) = 3x0 + 1,
   
   [isQid](x0) = 2x0,
   
   [isNeList](x0) = 2x0 + 2,
   
   [isList](x0) = 2x0 + 5,
   
   [and](x0, x1) = x0 + x1 + 5,
   
   [tt] = 0,
   
   [nil] = 3,
   
   [mark](x0) = x0,
   
   [active](x0) = x0,
   
   [__](x0, x1) = 2x0 + x1 + 5
  orientation:
   active(__(__(X,Y),Z)) = 4X + 2Y + Z + 15 >= 2X + 2Y + Z + 10 = mark(__(X,__(Y,Z)))
   
   active(__(X,nil())) = 2X + 8 >= X = mark(X)
   
   active(__(nil(),X)) = X + 11 >= X = mark(X)
   
   active(and(tt(),X)) = X + 5 >= X = mark(X)
   
   active(isList(V)) = 2V + 5 >= 2V + 2 = mark(isNeList(V))
   
   active(isList(nil())) = 11 >= 0 = mark(tt())
   
   active(isList(__(V1,V2))) = 4V1 + 2V2 + 15 >= 2V1 + 2V2 + 15 = mark(and(isList(V1),isList(V2)))
   
   active(isNeList(V)) = 2V + 2 >= 2V = mark(isQid(V))
   
   active(isNeList(__(V1,V2))) = 4V1 + 2V2 + 12 >= 2V1 + 2V2 + 12 = mark(and(isList(V1),isNeList(V2)))
   
   active(isNeList(__(V1,V2))) = 4V1 + 2V2 + 12 >= 2V1 + 2V2 + 12 = mark(and(isNeList(V1),isList(V2)))
   
   active(isNePal(V)) = 3V + 1 >= 2V = mark(isQid(V))
   
   active(isNePal(__(I,__(P,I)))) = 9I + 6P + 31 >= 2I + 3P + 8 = mark(and(isQid(I),isPal(P)))
   
   active(isPal(V)) = 3V + 3 >= 3V + 1 = mark(isNePal(V))
   
   active(isPal(nil())) = 12 >= 0 = mark(tt())
   
   active(isQid(a())) = 8 >= 0 = mark(tt())
   
   active(isQid(e())) = 4 >= 0 = mark(tt())
   
   active(isQid(i())) = 8 >= 0 = mark(tt())
   
   active(isQid(o())) = 0 >= 0 = mark(tt())
   
   active(isQid(u())) = 0 >= 0 = mark(tt())
   
   mark(__(X1,X2)) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = active(__(mark(X1),mark(X2)))
   
   mark(nil()) = 3 >= 3 = active(nil())
   
   mark(and(X1,X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = active(and(mark(X1),X2))
   
   mark(tt()) = 0 >= 0 = active(tt())
   
   mark(isList(X)) = 2X + 5 >= 2X + 5 = active(isList(X))
   
   mark(isNeList(X)) = 2X + 2 >= 2X + 2 = active(isNeList(X))
   
   mark(isQid(X)) = 2X >= 2X = active(isQid(X))
   
   mark(isNePal(X)) = 3X + 1 >= 3X + 1 = active(isNePal(X))
   
   mark(isPal(X)) = 3X + 3 >= 3X + 3 = active(isPal(X))
   
   mark(a()) = 4 >= 4 = active(a())
   
   mark(e()) = 2 >= 2 = active(e())
   
   mark(i()) = 4 >= 4 = active(i())
   
   mark(o()) = 0 >= 0 = active(o())
   
   mark(u()) = 0 >= 0 = active(u())
   
   __(mark(X1),X2) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = __(X1,X2)
   
   __(X1,mark(X2)) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = __(X1,X2)
   
   __(active(X1),X2) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = __(X1,X2)
   
   __(X1,active(X2)) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = __(X1,X2)
   
   and(mark(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2)
   
   and(X1,mark(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2)
   
   and(active(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2)
   
   and(X1,active(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2)
   
   isList(mark(X)) = 2X + 5 >= 2X + 5 = isList(X)
   
   isList(active(X)) = 2X + 5 >= 2X + 5 = isList(X)
   
   isNeList(mark(X)) = 2X + 2 >= 2X + 2 = isNeList(X)
   
   isNeList(active(X)) = 2X + 2 >= 2X + 2 = isNeList(X)
   
   isQid(mark(X)) = 2X >= 2X = isQid(X)
   
   isQid(active(X)) = 2X >= 2X = isQid(X)
   
   isNePal(mark(X)) = 3X + 1 >= 3X + 1 = isNePal(X)
   
   isNePal(active(X)) = 3X + 1 >= 3X + 1 = isNePal(X)
   
   isPal(mark(X)) = 3X + 3 >= 3X + 3 = isPal(X)
   
   isPal(active(X)) = 3X + 3 >= 3X + 3 = isPal(X)
  problem:
   active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2)))
   active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2)))
   active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2)))
   active(isQid(o())) -> mark(tt())
   active(isQid(u())) -> mark(tt())
   mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
   mark(nil()) -> active(nil())
   mark(and(X1,X2)) -> active(and(mark(X1),X2))
   mark(tt()) -> active(tt())
   mark(isList(X)) -> active(isList(X))
   mark(isNeList(X)) -> active(isNeList(X))
   mark(isQid(X)) -> active(isQid(X))
   mark(isNePal(X)) -> active(isNePal(X))
   mark(isPal(X)) -> active(isPal(X))
   mark(a()) -> active(a())
   mark(e()) -> active(e())
   mark(i()) -> active(i())
   mark(o()) -> active(o())
   mark(u()) -> active(u())
   __(mark(X1),X2) -> __(X1,X2)
   __(X1,mark(X2)) -> __(X1,X2)
   __(active(X1),X2) -> __(X1,X2)
   __(X1,active(X2)) -> __(X1,X2)
   and(mark(X1),X2) -> and(X1,X2)
   and(X1,mark(X2)) -> and(X1,X2)
   and(active(X1),X2) -> and(X1,X2)
   and(X1,active(X2)) -> and(X1,X2)
   isList(mark(X)) -> isList(X)
   isList(active(X)) -> isList(X)
   isNeList(mark(X)) -> isNeList(X)
   isNeList(active(X)) -> isNeList(X)
   isQid(mark(X)) -> isQid(X)
   isQid(active(X)) -> isQid(X)
   isNePal(mark(X)) -> isNePal(X)
   isNePal(active(X)) -> isNePal(X)
   isPal(mark(X)) -> isPal(X)
   isPal(active(X)) -> isPal(X)
  LPO Processor:
   precedence:
    isNeList > isList > o ~ isQid > mark > u > i ~ e ~ a ~ isPal ~ isNePal ~ 
    and ~ tt ~ nil ~ active ~ __
   problem:
    
   Qed