/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 f(nil()) -> nil()
 f(.(nil(),y)) -> .(nil(),f(y))
 f(.(.(x,y),z)) -> f(.(x,.(y,z)))
 g(nil()) -> nil()
 g(.(x,nil())) -> .(g(x),nil())
 g(.(x,.(y,z))) -> g(.(.(x,y),z))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 4x0 + 4,
   
   [.](x0, x1) = x0 + x1,
   
   [f](x0) = x0,
   
   [nil] = 6
  orientation:
   f(nil()) = 6 >= 6 = nil()
   
   f(.(nil(),y)) = y + 6 >= y + 6 = .(nil(),f(y))
   
   f(.(.(x,y),z)) = x + y + z >= x + y + z = f(.(x,.(y,z)))
   
   g(nil()) = 28 >= 6 = nil()
   
   g(.(x,nil())) = 4x + 28 >= 4x + 10 = .(g(x),nil())
   
   g(.(x,.(y,z))) = 4x + 4y + 4z + 4 >= 4x + 4y + 4z + 4 = g(.(.(x,y),z))
  problem:
   f(nil()) -> nil()
   f(.(nil(),y)) -> .(nil(),f(y))
   f(.(.(x,y),z)) -> f(.(x,.(y,z)))
   g(.(x,.(y,z))) -> g(.(.(x,y),z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0) = x0 + 1,
    
    [.](x0, x1) = x0 + x1,
    
    [f](x0) = 4x0,
    
    [nil] = 2
   orientation:
    f(nil()) = 8 >= 2 = nil()
    
    f(.(nil(),y)) = 4y + 8 >= 4y + 2 = .(nil(),f(y))
    
    f(.(.(x,y),z)) = 4x + 4y + 4z >= 4x + 4y + 4z = f(.(x,.(y,z)))
    
    g(.(x,.(y,z))) = x + y + z + 1 >= x + y + z + 1 = g(.(.(x,y),z))
   problem:
    f(.(.(x,y),z)) -> f(.(x,.(y,z)))
    g(.(x,.(y,z))) -> g(.(.(x,y),z))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]  
     [g](x0) = [0 1 0]x0
               [0 0 0]  ,
     
                   [1 0 0]     [1 0 0]     [0]
     [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                   [0 1 1]     [0 0 0]     [0],
     
               [1 0 1]  
     [f](x0) = [0 0 0]x0
               [0 1 0]  
    orientation:
                      [1 1 1]    [1 0 0]    [1 0 0]    [1]    [1 1 1]    [1 0 0]    [1 0 0]    [0]                 
     f(.(.(x,y),z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] = f(.(x,.(y,z)))
                      [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                 
     
                      [1 0 0]    [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [1 0 0]    [0]                 
     g(.(x,.(y,z))) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] = g(.(.(x,y),z))
                      [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                 
    problem:
     g(.(x,.(y,z))) -> g(.(.(x,y),z))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [g](x0) = x0 + 6,
      
      [.](x0, x1) = x0 + 4x1 + 5
     orientation:
      g(.(x,.(y,z))) = x + 4y + 16z + 31 >= x + 4y + 4z + 16 = g(.(.(x,y),z))
     problem:
      
     Qed