/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [n__take](x0, x1) = x0 + 2x1,
   
   [take](x0, x1) = x0 + 2x1,
   
   [s](x0) = x0,
   
   [length](x0) = x0 + 4,
   
   [nil] = 0,
   
   [activate](x0) = x0,
   
   [and](x0, x1) = x0 + x1 + 4,
   
   [tt] = 0,
   
   [cons](x0, x1) = 4x0 + x1,
   
   [n__zeros] = 0,
   
   [0] = 0,
   
   [zeros] = 0
  orientation:
   zeros() = 0 >= 0 = cons(0(),n__zeros())
   
   and(tt(),X) = X + 4 >= X = activate(X)
   
   length(nil()) = 4 >= 0 = 0()
   
   length(cons(N,L)) = L + 4N + 4 >= L + 4 = s(length(activate(L)))
   
   take(0(),IL) = 2IL >= 0 = nil()
   
   take(s(M),cons(N,IL)) = 2IL + M + 8N >= 2IL + M + 4N = cons(N,n__take(M,activate(IL)))
   
   zeros() = 0 >= 0 = n__zeros()
   
   take(X1,X2) = X1 + 2X2 >= X1 + 2X2 = n__take(X1,X2)
   
   activate(n__zeros()) = 0 >= 0 = zeros()
   
   activate(n__take(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = take(activate(X1),activate(X2))
   
   activate(X) = X >= X = X
  problem:
   zeros() -> cons(0(),n__zeros())
   length(cons(N,L)) -> s(length(activate(L)))
   take(0(),IL) -> nil()
   take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
   zeros() -> n__zeros()
   take(X1,X2) -> n__take(X1,X2)
   activate(n__zeros()) -> zeros()
   activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [n__take](x0, x1) = x0 + 2x1 + 4,
    
    [take](x0, x1) = x0 + 2x1 + 4,
    
    [s](x0) = x0,
    
    [length](x0) = x0 + 4,
    
    [nil] = 0,
    
    [activate](x0) = x0,
    
    [cons](x0, x1) = 4x0 + x1,
    
    [n__zeros] = 0,
    
    [0] = 0,
    
    [zeros] = 0
   orientation:
    zeros() = 0 >= 0 = cons(0(),n__zeros())
    
    length(cons(N,L)) = L + 4N + 4 >= L + 4 = s(length(activate(L)))
    
    take(0(),IL) = 2IL + 4 >= 0 = nil()
    
    take(s(M),cons(N,IL)) = 2IL + M + 8N + 4 >= 2IL + M + 4N + 4 = cons(N,n__take(M,activate(IL)))
    
    zeros() = 0 >= 0 = n__zeros()
    
    take(X1,X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = n__take(X1,X2)
    
    activate(n__zeros()) = 0 >= 0 = zeros()
    
    activate(n__take(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = take(activate(X1),activate(X2))
    
    activate(X) = X >= X = X
   problem:
    zeros() -> cons(0(),n__zeros())
    length(cons(N,L)) -> s(length(activate(L)))
    take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
    zeros() -> n__zeros()
    take(X1,X2) -> n__take(X1,X2)
    activate(n__zeros()) -> zeros()
    activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
    activate(X) -> X
   Unfolding Processor:
    loop length: 3
    terms:
     length(cons(N,n__zeros()))
     s(length(activate(n__zeros())))
     s(length(zeros()))
    context: s([])
    substitution:
     N -> 0()
    Qed