/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:
 a__zeros() -> cons(0(),zeros())
 a__and(tt(),X) -> mark(X)
 a__length(nil()) -> 0()
 a__length(cons(N,L)) -> s(a__length(mark(L)))
 mark(zeros()) -> a__zeros()
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(length(X)) -> a__length(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(tt()) -> tt()
 mark(nil()) -> nil()
 mark(s(X)) -> s(mark(X))
 a__zeros() -> zeros()
 a__and(X1,X2) -> and(X1,X2)
 a__length(X) -> length(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [length](x0) = 2x0 + 1,
   
   [and](x0, x1) = 2x0 + x1 + 1,
   
   [s](x0) = x0,
   
   [a__length](x0) = 2x0 + 1,
   
   [nil] = 0,
   
   [mark](x0) = 4x0,
   
   [a__and](x0, x1) = 2x0 + 4x1 + 2,
   
   [tt] = 0,
   
   [cons](x0, x1) = 3x0 + 4x1,
   
   [zeros] = 0,
   
   [0] = 0,
   
   [a__zeros] = 0
  orientation:
   a__zeros() = 0 >= 0 = cons(0(),zeros())
   
   a__and(tt(),X) = 4X + 2 >= 4X = mark(X)
   
   a__length(nil()) = 1 >= 0 = 0()
   
   a__length(cons(N,L)) = 8L + 6N + 1 >= 8L + 1 = s(a__length(mark(L)))
   
   mark(zeros()) = 0 >= 0 = a__zeros()
   
   mark(and(X1,X2)) = 8X1 + 4X2 + 4 >= 8X1 + 4X2 + 2 = a__and(mark(X1),X2)
   
   mark(length(X)) = 8X + 4 >= 8X + 1 = a__length(mark(X))
   
   mark(cons(X1,X2)) = 12X1 + 16X2 >= 12X1 + 4X2 = cons(mark(X1),X2)
   
   mark(0()) = 0 >= 0 = 0()
   
   mark(tt()) = 0 >= 0 = tt()
   
   mark(nil()) = 0 >= 0 = nil()
   
   mark(s(X)) = 4X >= 4X = s(mark(X))
   
   a__zeros() = 0 >= 0 = zeros()
   
   a__and(X1,X2) = 2X1 + 4X2 + 2 >= 2X1 + X2 + 1 = and(X1,X2)
   
   a__length(X) = 2X + 1 >= 2X + 1 = length(X)
  problem:
   a__zeros() -> cons(0(),zeros())
   a__length(cons(N,L)) -> s(a__length(mark(L)))
   mark(zeros()) -> a__zeros()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(0()) -> 0()
   mark(tt()) -> tt()
   mark(nil()) -> nil()
   mark(s(X)) -> s(mark(X))
   a__zeros() -> zeros()
   a__length(X) -> length(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [length](x0) = x0,
    
    [s](x0) = x0,
    
    [a__length](x0) = x0 + 7,
    
    [nil] = 0,
    
    [mark](x0) = 4x0 + 2,
    
    [tt] = 4,
    
    [cons](x0, x1) = 2x0 + 4x1 + 2,
    
    [zeros] = 0,
    
    [0] = 0,
    
    [a__zeros] = 2
   orientation:
    a__zeros() = 2 >= 2 = cons(0(),zeros())
    
    a__length(cons(N,L)) = 4L + 2N + 9 >= 4L + 9 = s(a__length(mark(L)))
    
    mark(zeros()) = 2 >= 2 = a__zeros()
    
    mark(cons(X1,X2)) = 8X1 + 16X2 + 10 >= 8X1 + 4X2 + 6 = cons(mark(X1),X2)
    
    mark(0()) = 2 >= 0 = 0()
    
    mark(tt()) = 18 >= 4 = tt()
    
    mark(nil()) = 2 >= 0 = nil()
    
    mark(s(X)) = 4X + 2 >= 4X + 2 = s(mark(X))
    
    a__zeros() = 2 >= 0 = zeros()
    
    a__length(X) = X + 7 >= X = length(X)
   problem:
    a__zeros() -> cons(0(),zeros())
    a__length(cons(N,L)) -> s(a__length(mark(L)))
    mark(zeros()) -> a__zeros()
    mark(s(X)) -> s(mark(X))
   Unfolding Processor:
    loop length: 3
    terms:
     a__length(cons(N,zeros()))
     s(a__length(mark(zeros())))
     s(a__length(a__zeros()))
    context: s([])
    substitution:
     N -> 0()
    Qed