NO

Problem:
 zeros() -> cons(0(),n__zeros())
 U11(tt(),L) -> U12(tt(),activate(L))
 U12(tt(),L) -> s(length(activate(L)))
 U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N))
 U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N))
 U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
 length(nil()) -> 0()
 length(cons(N,L)) -> U11(tt(),activate(L))
 take(0(),IL) -> nil()
 take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N)
 zeros() -> n__zeros()
 take(X1,X2) -> n__take(X1,X2)
 activate(n__zeros()) -> zeros()
 activate(n__take(X1,X2)) -> take(X1,X2)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [tt] = 0,
   
   [take](x0, x1) = x0 + x1 + 4,
   
   [length](x0) = x0,
   
   [0] = 0,
   
   [cons](x0, x1) = x0 + x1,
   
   [U11](x0, x1) = x0 + x1,
   
   [U21](x0, x1, x2, x3) = 2x0 + x1 + x2 + x3 + 4,
   
   [zeros] = 2,
   
   [U12](x0, x1) = x0 + x1,
   
   [nil] = 4,
   
   [U23](x0, x1, x2, x3) = 4x0 + x1 + x2 + x3 + 4,
   
   [U22](x0, x1, x2, x3) = 2x0 + x1 + x2 + x3 + 4,
   
   [s](x0) = x0,
   
   [n__take](x0, x1) = x0 + x1 + 4,
   
   [activate](x0) = x0,
   
   [n__zeros] = 2
  orientation:
   zeros() = 2 >= 2 = cons(0(),n__zeros())
   
   U11(tt(),L) = L >= L = U12(tt(),activate(L))
   
   U12(tt(),L) = L >= L = s(length(activate(L)))
   
   U21(tt(),IL,M,N) = IL + M + N + 4 >= IL + M + N + 4 = U22(tt(),activate(IL),activate(M),activate(N))
   
   U22(tt(),IL,M,N) = IL + M + N + 4 >= IL + M + N + 4 = U23(tt(),activate(IL),activate(M),activate(N))
   
   U23(tt(),IL,M,N) = IL + M + N + 4 >= IL + M + N + 4 = cons(activate(N),n__take(activate(M),activate(IL)))
   
   length(nil()) = 4 >= 0 = 0()
   
   length(cons(N,L)) = L + N >= L = U11(tt(),activate(L))
   
   take(0(),IL) = IL + 4 >= 4 = nil()
   
   take(s(M),cons(N,IL)) = IL + M + N + 4 >= IL + M + N + 4 = U21(tt(),activate(IL),M,N)
   
   zeros() = 2 >= 2 = n__zeros()
   
   take(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 4 = n__take(X1,X2)
   
   activate(n__zeros()) = 2 >= 2 = zeros()
   
   activate(n__take(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = take(X1,X2)
   
   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)))
   U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N))
   U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N))
   U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
   length(cons(N,L)) -> U11(tt(),activate(L))
   take(0(),IL) -> nil()
   take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N)
   zeros() -> n__zeros()
   take(X1,X2) -> n__take(X1,X2)
   activate(n__zeros()) -> zeros()
   activate(n__take(X1,X2)) -> take(X1,X2)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [tt] = 0,
    
    [take](x0, x1) = x0 + x1 + 1,
    
    [length](x0) = 4x0,
    
    [0] = 0,
    
    [cons](x0, x1) = 2x0 + x1,
    
    [U11](x0, x1) = x0 + 4x1,
    
    [U21](x0, x1, x2, x3) = 2x0 + x1 + x2 + 2x3 + 1,
    
    [zeros] = 0,
    
    [U12](x0, x1) = 2x0 + 4x1,
    
    [nil] = 0,
    
    [U23](x0, x1, x2, x3) = x0 + x1 + x2 + 2x3 + 1,
    
    [U22](x0, x1, x2, x3) = 4x0 + x1 + x2 + 2x3 + 1,
    
    [s](x0) = x0,
    
    [n__take](x0, x1) = x0 + x1 + 1,
    
    [activate](x0) = x0,
    
    [n__zeros] = 0
   orientation:
    zeros() = 0 >= 0 = cons(0(),n__zeros())
    
    U11(tt(),L) = 4L >= 4L = U12(tt(),activate(L))
    
    U12(tt(),L) = 4L >= 4L = s(length(activate(L)))
    
    U21(tt(),IL,M,N) = IL + M + 2N + 1 >= IL + M + 2N + 1 = U22(tt(),activate(IL),activate(M),activate(N))
    
    U22(tt(),IL,M,N) = IL + M + 2N + 1 >= IL + M + 2N + 1 = U23(tt(),activate(IL),activate(M),activate(N))
    
    U23(tt(),IL,M,N) = IL + M + 2N + 1 >= IL + M + 2N + 1 = cons(activate(N),n__take(activate(M),activate(IL)))
    
    length(cons(N,L)) = 4L + 8N >= 4L = U11(tt(),activate(L))
    
    take(0(),IL) = IL + 1 >= 0 = nil()
    
    take(s(M),cons(N,IL)) = IL + M + 2N + 1 >= IL + M + 2N + 1 = U21(tt(),activate(IL),M,N)
    
    zeros() = 0 >= 0 = n__zeros()
    
    take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = n__take(X1,X2)
    
    activate(n__zeros()) = 0 >= 0 = zeros()
    
    activate(n__take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2)
    
    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)))
    U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N))
    U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N))
    U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
    length(cons(N,L)) -> U11(tt(),activate(L))
    take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N)
    zeros() -> n__zeros()
    take(X1,X2) -> n__take(X1,X2)
    activate(n__zeros()) -> zeros()
    activate(n__take(X1,X2)) -> take(X1,X2)
    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