NO

Problem:
 zeros() -> cons(0(),n__zeros())
 U11(tt(),L) -> U12(tt(),activate(L))
 U12(tt(),L) -> s(length(activate(L)))
 length(nil()) -> 0()
 length(cons(N,L)) -> U11(tt(),activate(L))
 zeros() -> n__zeros()
 activate(n__zeros()) -> zeros()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
          [0]
   [tt] = [0]
          [0],
   
                  [1 1 1]  
   [length](x0) = [0 0 0]x0
                  [1 0 0]  ,
   
         [0]
   [0] = [0]
         [0],
   
                    [1 0 0]     [1 0 0]  
   [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1
                    [0 0 0]     [0 1 0]  ,
   
                   [1 0 0]     [1 1 1]  
   [U11](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
   
           [1]
   [nil] = [0]
           [0],
   
             [1]
   [zeros] = [1]
             [1],
   
                   [1 0 0]     [1 1 1]  
   [U12](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                      
   [activate](x0) = x0
                      ,
   
                [1]
   [n__zeros] = [1]
                [1]
  orientation:
             [1]    [1]                       
   zeros() = [1] >= [1] = cons(0(),n__zeros())
             [1]    [1]                       
   
                 [1 1 1]     [1 1 1]                         
   U11(tt(),L) = [0 0 0]L >= [0 0 0]L = U12(tt(),activate(L))
                 [0 0 0]     [0 0 0]                         
   
                 [1 1 1]     [1 1 1]                          
   U12(tt(),L) = [0 0 0]L >= [0 0 0]L = s(length(activate(L)))
                 [0 0 0]     [0 0 0]                          
   
                   [1]    [0]      
   length(nil()) = [0] >= [0] = 0()
                   [1]    [0]      
   
                       [1 1 1]    [1 0 0]     [1 1 1]                         
   length(cons(N,L)) = [0 0 0]L + [0 0 0]N >= [0 0 0]L = U11(tt(),activate(L))
                       [1 0 0]    [1 0 0]     [0 0 0]                         
   
             [1]    [1]             
   zeros() = [1] >= [1] = n__zeros()
             [1]    [1]             
   
                          [1]    [1]          
   activate(n__zeros()) = [1] >= [1] = zeros()
                          [1]    [1]          
   
                           
   activate(X) = X >= X = X
                           
  problem:
   zeros() -> cons(0(),n__zeros())
   U11(tt(),L) -> U12(tt(),activate(L))
   U12(tt(),L) -> s(length(activate(L)))
   length(cons(N,L)) -> U11(tt(),activate(L))
   zeros() -> n__zeros()
   activate(n__zeros()) -> zeros()
   activate(X) -> X
  Unfolding Processor:
   loop length: 7
   terms:
    U11(tt(),n__zeros())
    U12(tt(),activate(n__zeros()))
    s(length(activate(activate(n__zeros()))))
    s(length(activate(n__zeros())))
    s(length(zeros()))
    s(length(cons(0(),n__zeros())))
    s(U11(tt(),activate(n__zeros())))
   context: s([])
   substitution:
    
   Qed