YES

Problem:
 a__zeros() -> cons(0(),zeros())
 a__U11(tt(),L) -> s(a__length(mark(L)))
 a__and(tt(),X) -> mark(X)
 a__isNat(0()) -> tt()
 a__isNat(length(V1)) -> a__isNatList(V1)
 a__isNat(s(V1)) -> a__isNat(V1)
 a__isNatIList(V) -> a__isNatList(V)
 a__isNatIList(zeros()) -> tt()
 a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
 a__isNatList(nil()) -> tt()
 a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
 a__length(nil()) -> 0()
 a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
 mark(zeros()) -> a__zeros()
 mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
 mark(length(X)) -> a__length(mark(X))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNat(X)) -> a__isNat(X)
 mark(isNatList(X)) -> a__isNatList(X)
 mark(isNatIList(X)) -> a__isNatIList(X)
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(tt()) -> tt()
 mark(s(X)) -> s(mark(X))
 mark(nil()) -> nil()
 a__zeros() -> zeros()
 a__U11(X1,X2) -> U11(X1,X2)
 a__length(X) -> length(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNat(X) -> isNat(X)
 a__isNatList(X) -> isNatList(X)
 a__isNatIList(X) -> isNatIList(X)

Proof:
 DP Processor:
  DPs:
   a__U11#(tt(),L) -> mark#(L)
   a__U11#(tt(),L) -> a__length#(mark(L))
   a__and#(tt(),X) -> mark#(X)
   a__isNat#(length(V1)) -> a__isNatList#(V1)
   a__isNat#(s(V1)) -> a__isNat#(V1)
   a__isNatIList#(V) -> a__isNatList#(V)
   a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1)
   a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2))
   a__isNatList#(cons(V1,V2)) -> a__isNat#(V1)
   a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2))
   a__length#(cons(N,L)) -> a__isNatList#(L)
   a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N))
   a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L)
   mark#(zeros()) -> a__zeros#()
   mark#(U11(X1,X2)) -> mark#(X1)
   mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
   mark#(length(X)) -> mark#(X)
   mark#(length(X)) -> a__length#(mark(X))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   mark#(isNat(X)) -> a__isNat#(X)
   mark#(isNatList(X)) -> a__isNatList#(X)
   mark#(isNatIList(X)) -> a__isNatIList#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__zeros() -> cons(0(),zeros())
   a__U11(tt(),L) -> s(a__length(mark(L)))
   a__and(tt(),X) -> mark(X)
   a__isNat(0()) -> tt()
   a__isNat(length(V1)) -> a__isNatList(V1)
   a__isNat(s(V1)) -> a__isNat(V1)
   a__isNatIList(V) -> a__isNatList(V)
   a__isNatIList(zeros()) -> tt()
   a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
   a__isNatList(nil()) -> tt()
   a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
   a__length(nil()) -> 0()
   a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
   mark(zeros()) -> a__zeros()
   mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
   mark(length(X)) -> a__length(mark(X))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(isNatList(X)) -> a__isNatList(X)
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(0()) -> 0()
   mark(tt()) -> tt()
   mark(s(X)) -> s(mark(X))
   mark(nil()) -> nil()
   a__zeros() -> zeros()
   a__U11(X1,X2) -> U11(X1,X2)
   a__length(X) -> length(X)
   a__and(X1,X2) -> and(X1,X2)
   a__isNat(X) -> isNat(X)
   a__isNatList(X) -> isNatList(X)
   a__isNatIList(X) -> isNatIList(X)
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    a__zeros() -> cons(0(),zeros())
    a__U11(tt(),L) -> s(a__length(mark(L)))
    a__and(tt(),X) -> mark(X)
    a__isNat(0()) -> tt()
    a__isNat(length(V1)) -> a__isNatList(V1)
    a__isNat(s(V1)) -> a__isNat(V1)
    a__isNatIList(V) -> a__isNatList(V)
    a__isNatIList(zeros()) -> tt()
    a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
    a__isNatList(nil()) -> tt()
    a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
    a__length(nil()) -> 0()
    a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
    mark(zeros()) -> a__zeros()
    mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    mark(length(X)) -> a__length(mark(X))
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(isNat(X)) -> a__isNat(X)
    mark(isNatList(X)) -> a__isNatList(X)
    mark(isNatIList(X)) -> a__isNatIList(X)
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(0()) -> 0()
    mark(tt()) -> tt()
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    a__zeros() -> zeros()
    a__U11(X1,X2) -> U11(X1,X2)
    a__length(X) -> length(X)
    a__and(X1,X2) -> and(X1,X2)
    a__isNat(X) -> isNat(X)
    a__isNatList(X) -> isNatList(X)
    a__isNatIList(X) -> isNatIList(X)
   interpretation:
    [a__isNatIList#](x0) = 5x0 + 7,
    
    [a__isNatList#](x0) = 4x0 + 1,
    
    [a__isNat#](x0) = 2x0 + 2,
    
    [a__and#](x0, x1) = x0 + 4x1 + 4,
    
    [a__length#](x0) = 2x0 + 5,
    
    [mark#](x0) = 4x0 + 3,
    
    [a__U11#](x0, x1) = 2x0 + 4x1 + 2,
    
    [a__zeros#] = 0,
    
    [and](x0, x1) = x0 + 2x1 + 1,
    
    [U11](x0, x1) = 2x0 + 2x1 + 4,
    
    [isNat](x0) = x0 + 1,
    
    [isNatList](x0) = 4x0,
    
    [nil] = 2,
    
    [isNatIList](x0) = 2x0 + 2,
    
    [a__isNatIList](x0) = 4x0 + 6,
    
    [a__isNatList](x0) = 4x0,
    
    [length](x0) = 2x0 + 6,
    
    [a__isNat](x0) = 2x0 + 4,
    
    [a__and](x0, x1) = x0 + 2x1 + 1,
    
    [s](x0) = x0 + 1,
    
    [a__length](x0) = 2x0 + 7,
    
    [mark](x0) = 2x0 + 2,
    
    [a__U11](x0, x1) = 2x0 + 4x1 + 4,
    
    [tt] = 4,
    
    [cons](x0, x1) = 2x0 + 6x1 + 2,
    
    [zeros] = 0,
    
    [0] = 0,
    
    [a__zeros] = 2
   orientation:
    a__U11#(tt(),L) = 4L + 10 >= 4L + 3 = mark#(L)
    
    a__U11#(tt(),L) = 4L + 10 >= 4L + 9 = a__length#(mark(L))
    
    a__and#(tt(),X) = 4X + 8 >= 4X + 3 = mark#(X)
    
    a__isNat#(length(V1)) = 4V1 + 14 >= 4V1 + 1 = a__isNatList#(V1)
    
    a__isNat#(s(V1)) = 2V1 + 4 >= 2V1 + 2 = a__isNat#(V1)
    
    a__isNatIList#(V) = 5V + 7 >= 4V + 1 = a__isNatList#(V)
    
    a__isNatIList#(cons(V1,V2)) = 10V1 + 30V2 + 17 >= 2V1 + 2 = a__isNat#(V1)
    
    a__isNatIList#(cons(V1,V2)) = 10V1 + 30V2 + 17 >= 2V1 + 8V2 + 16 = a__and#(a__isNat(V1),isNatIList(V2))
    
    a__isNatList#(cons(V1,V2)) = 8V1 + 24V2 + 9 >= 2V1 + 2 = a__isNat#(V1)
    
    a__isNatList#(cons(V1,V2)) = 8V1 + 24V2 + 9 >= 2V1 + 16V2 + 8 = a__and#(a__isNat(V1),isNatList(V2))
    
    a__length#(cons(N,L)) = 12L + 4N + 9 >= 4L + 1 = a__isNatList#(L)
    
    a__length#(cons(N,L)) = 12L + 4N + 9 >= 4L + 4N + 8 = a__and#(a__isNatList(L),isNat(N))
    
    a__length#(cons(N,L)) = 12L + 4N + 9 >= 12L + 4N + 8 = a__U11#(a__and(a__isNatList(L),isNat(N)),L)
    
    mark#(zeros()) = 3 >= 0 = a__zeros#()
    
    mark#(U11(X1,X2)) = 8X1 + 8X2 + 19 >= 4X1 + 3 = mark#(X1)
    
    mark#(U11(X1,X2)) = 8X1 + 8X2 + 19 >= 4X1 + 4X2 + 6 = a__U11#(mark(X1),X2)
    
    mark#(length(X)) = 8X + 27 >= 4X + 3 = mark#(X)
    
    mark#(length(X)) = 8X + 27 >= 4X + 9 = a__length#(mark(X))
    
    mark#(and(X1,X2)) = 4X1 + 8X2 + 7 >= 4X1 + 3 = mark#(X1)
    
    mark#(and(X1,X2)) = 4X1 + 8X2 + 7 >= 2X1 + 4X2 + 6 = a__and#(mark(X1),X2)
    
    mark#(isNat(X)) = 4X + 7 >= 2X + 2 = a__isNat#(X)
    
    mark#(isNatList(X)) = 16X + 3 >= 4X + 1 = a__isNatList#(X)
    
    mark#(isNatIList(X)) = 8X + 11 >= 5X + 7 = a__isNatIList#(X)
    
    mark#(cons(X1,X2)) = 8X1 + 24X2 + 11 >= 4X1 + 3 = mark#(X1)
    
    mark#(s(X)) = 4X + 7 >= 4X + 3 = mark#(X)
    
    a__zeros() = 2 >= 2 = cons(0(),zeros())
    
    a__U11(tt(),L) = 4L + 12 >= 4L + 12 = s(a__length(mark(L)))
    
    a__and(tt(),X) = 2X + 5 >= 2X + 2 = mark(X)
    
    a__isNat(0()) = 4 >= 4 = tt()
    
    a__isNat(length(V1)) = 4V1 + 16 >= 4V1 = a__isNatList(V1)
    
    a__isNat(s(V1)) = 2V1 + 6 >= 2V1 + 4 = a__isNat(V1)
    
    a__isNatIList(V) = 4V + 6 >= 4V = a__isNatList(V)
    
    a__isNatIList(zeros()) = 6 >= 4 = tt()
    
    a__isNatIList(cons(V1,V2)) = 8V1 + 24V2 + 14 >= 2V1 + 4V2 + 9 = a__and(a__isNat(V1),isNatIList(V2))
    
    a__isNatList(nil()) = 8 >= 4 = tt()
    
    a__isNatList(cons(V1,V2)) = 8V1 + 24V2 + 8 >= 2V1 + 8V2 + 5 = a__and(a__isNat(V1),isNatList(V2))
    
    a__length(nil()) = 11 >= 0 = 0()
    
    a__length(cons(N,L)) = 12L + 4N + 11 >= 12L + 4N + 10 = a__U11(a__and(a__isNatList(L),isNat(N)),L)
    
    mark(zeros()) = 2 >= 2 = a__zeros()
    
    mark(U11(X1,X2)) = 4X1 + 4X2 + 10 >= 4X1 + 4X2 + 8 = a__U11(mark(X1),X2)
    
    mark(length(X)) = 4X + 14 >= 4X + 11 = a__length(mark(X))
    
    mark(and(X1,X2)) = 2X1 + 4X2 + 4 >= 2X1 + 2X2 + 3 = a__and(mark(X1),X2)
    
    mark(isNat(X)) = 2X + 4 >= 2X + 4 = a__isNat(X)
    
    mark(isNatList(X)) = 8X + 2 >= 4X = a__isNatList(X)
    
    mark(isNatIList(X)) = 4X + 6 >= 4X + 6 = a__isNatIList(X)
    
    mark(cons(X1,X2)) = 4X1 + 12X2 + 6 >= 4X1 + 6X2 + 6 = cons(mark(X1),X2)
    
    mark(0()) = 2 >= 0 = 0()
    
    mark(tt()) = 10 >= 4 = tt()
    
    mark(s(X)) = 2X + 4 >= 2X + 3 = s(mark(X))
    
    mark(nil()) = 6 >= 2 = nil()
    
    a__zeros() = 2 >= 0 = zeros()
    
    a__U11(X1,X2) = 2X1 + 4X2 + 4 >= 2X1 + 2X2 + 4 = U11(X1,X2)
    
    a__length(X) = 2X + 7 >= 2X + 6 = length(X)
    
    a__and(X1,X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = and(X1,X2)
    
    a__isNat(X) = 2X + 4 >= X + 1 = isNat(X)
    
    a__isNatList(X) = 4X >= 4X = isNatList(X)
    
    a__isNatIList(X) = 4X + 6 >= 2X + 2 = isNatIList(X)
   problem:
    DPs:
     
    TRS:
     a__zeros() -> cons(0(),zeros())
     a__U11(tt(),L) -> s(a__length(mark(L)))
     a__and(tt(),X) -> mark(X)
     a__isNat(0()) -> tt()
     a__isNat(length(V1)) -> a__isNatList(V1)
     a__isNat(s(V1)) -> a__isNat(V1)
     a__isNatIList(V) -> a__isNatList(V)
     a__isNatIList(zeros()) -> tt()
     a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
     a__isNatList(nil()) -> tt()
     a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
     a__length(nil()) -> 0()
     a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
     mark(zeros()) -> a__zeros()
     mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
     mark(length(X)) -> a__length(mark(X))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(isNat(X)) -> a__isNat(X)
     mark(isNatList(X)) -> a__isNatList(X)
     mark(isNatIList(X)) -> a__isNatIList(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(0()) -> 0()
     mark(tt()) -> tt()
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     a__zeros() -> zeros()
     a__U11(X1,X2) -> U11(X1,X2)
     a__length(X) -> length(X)
     a__and(X1,X2) -> and(X1,X2)
     a__isNat(X) -> isNat(X)
     a__isNatList(X) -> isNatList(X)
     a__isNatIList(X) -> isNatIList(X)
   Qed