/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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YES

Problem:
 rev(nil()) -> nil()
 rev(rev(x)) -> x
 rev(++(x,y)) -> ++(rev(y),rev(x))
 ++(nil(),y) -> y
 ++(x,nil()) -> x
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(x,++(y,z)) -> ++(++(x,y),z)
 make(x) -> .(x,nil())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [make](x0) = 2x0 + 6,
   
   [.](x0, x1) = x0 + x1,
   
   [++](x0, x1) = x0 + x1,
   
   [rev](x0) = 5x0,
   
   [nil] = 4
  orientation:
   rev(nil()) = 20 >= 4 = nil()
   
   rev(rev(x)) = 25x >= x = x
   
   rev(++(x,y)) = 5x + 5y >= 5x + 5y = ++(rev(y),rev(x))
   
   ++(nil(),y) = y + 4 >= y = y
   
   ++(x,nil()) = x + 4 >= x = x
   
   ++(.(x,y),z) = x + y + z >= x + y + z = .(x,++(y,z))
   
   ++(x,++(y,z)) = x + y + z >= x + y + z = ++(++(x,y),z)
   
   make(x) = 2x + 6 >= x + 4 = .(x,nil())
  problem:
   rev(rev(x)) -> x
   rev(++(x,y)) -> ++(rev(y),rev(x))
   ++(.(x,y),z) -> .(x,++(y,z))
   ++(x,++(y,z)) -> ++(++(x,y),z)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [.](x0, x1) = x0 + x1 + 4,
    
    [++](x0, x1) = x0 + x1 + 4,
    
    [rev](x0) = 4x0 + 4
   orientation:
    rev(rev(x)) = 16x + 20 >= x = x
    
    rev(++(x,y)) = 4x + 4y + 20 >= 4x + 4y + 12 = ++(rev(y),rev(x))
    
    ++(.(x,y),z) = x + y + z + 8 >= x + y + z + 8 = .(x,++(y,z))
    
    ++(x,++(y,z)) = x + y + z + 8 >= x + y + z + 8 = ++(++(x,y),z)
   problem:
    ++(.(x,y),z) -> .(x,++(y,z))
    ++(x,++(y,z)) -> ++(++(x,y),z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [.](x0, x1) = x0 + x1 + 6,
     
     [++](x0, x1) = x0 + 2x1 + 5
    orientation:
     ++(.(x,y),z) = x + y + 2z + 11 >= x + y + 2z + 11 = .(x,++(y,z))
     
     ++(x,++(y,z)) = x + 2y + 4z + 15 >= x + 2y + 2z + 10 = ++(++(x,y),z)
    problem:
     ++(.(x,y),z) -> .(x,++(y,z))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 0 0]          [0]
      [.](x0, x1) = [0 0 0]x0 + x1 + [1]
                    [0 0 0]          [1],
      
                     [1 1 0]     [1 0 1]  
      [++](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                     [0 1 0]     [0 0 1]  
     orientation:
                     [1 0 0]    [1 1 0]    [1 0 1]    [1]    [1 0 0]    [1 1 0]    [1 0 1]    [0]               
      ++(.(x,y),z) = [0 0 0]x + [0 1 0]y + [0 0 0]z + [1] >= [0 0 0]x + [0 1 0]y + [0 0 0]z + [1] = .(x,++(y,z))
                     [0 0 0]    [0 1 0]    [0 0 1]    [1]    [0 0 0]    [0 1 0]    [0 0 1]    [1]               
     problem:
      
     Qed