/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:
 i(0()) -> 0()
 +(0(),y) -> y
 +(x,0()) -> x
 i(i(x)) -> x
 +(i(x),x) -> 0()
 +(x,i(x)) -> 0()
 i(+(x,y)) -> +(i(x),i(y))
 +(x,+(y,z)) -> +(+(x,y),z)
 +(+(x,i(y)),y) -> x
 +(+(x,y),i(y)) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [+](x0, x1) = x0 + x1 + 1,
   
   [i](x0) = x0,
   
   [0] = 0
  orientation:
   i(0()) = 0 >= 0 = 0()
   
   +(0(),y) = y + 1 >= y = y
   
   +(x,0()) = x + 1 >= x = x
   
   i(i(x)) = x >= x = x
   
   +(i(x),x) = 2x + 1 >= 0 = 0()
   
   +(x,i(x)) = 2x + 1 >= 0 = 0()
   
   i(+(x,y)) = x + y + 1 >= x + y + 1 = +(i(x),i(y))
   
   +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
   
   +(+(x,i(y)),y) = x + 2y + 2 >= x = x
   
   +(+(x,y),i(y)) = x + 2y + 2 >= x = x
  problem:
   i(0()) -> 0()
   i(i(x)) -> x
   i(+(x,y)) -> +(i(x),i(y))
   +(x,+(y,z)) -> +(+(x,y),z)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                         
    [+](x0, x1) = x0 + x1
                         ,
    
              [1 0 1]  
    [i](x0) = [0 0 1]x0
              [0 1 0]  ,
    
          [0]
    [0] = [1]
          [1]
   orientation:
             [1]    [0]      
    i(0()) = [1] >= [1] = 0()
             [1]    [1]      
    
              [1 1 1]          
    i(i(x)) = [0 1 0]x >= x = x
              [0 0 1]          
    
                [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                
    i(+(x,y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = +(i(x),i(y))
                [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                
    
                                                      
    +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
                                                      
   problem:
    i(i(x)) -> x
    i(+(x,y)) -> +(i(x),i(y))
    +(x,+(y,z)) -> +(+(x,y),z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = x0 + 4x1 + 4,
     
     [i](x0) = 4x0 + 3
    orientation:
     i(i(x)) = 16x + 15 >= x = x
     
     i(+(x,y)) = 4x + 16y + 19 >= 4x + 16y + 19 = +(i(x),i(y))
     
     +(x,+(y,z)) = x + 4y + 16z + 20 >= x + 4y + 4z + 8 = +(+(x,y),z)
    problem:
     i(+(x,y)) -> +(i(x),i(y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 0 0]          [0]
      [+](x0, x1) = [0 0 0]x0 + x1 + [0]
                    [0 0 1]          [1],
      
                [1 0 1]     [0]
      [i](x0) = [0 0 0]x0 + [1]
                [0 0 1]     [0]
     orientation:
                  [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 1]    [0]               
      i(+(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = +(i(x),i(y))
                  [0 0 1]    [0 0 1]    [1]    [0 0 1]    [0 0 1]    [1]               
     problem:
      
     Qed