/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

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