/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:
 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:
   [i](x0) = x0,
   
   [0] = 1,
   
   [+](x0, x1) = x0 + 4x1 + 1
  orientation:
   i(0()) = 1 >= 1 = 0()
   
   +(0(),y) = 4y + 2 >= y = y
   
   +(x,0()) = x + 5 >= x = x
   
   i(i(x)) = x >= x = x
   
   +(i(x),x) = 5x + 1 >= 1 = 0()
   
   +(x,i(x)) = 5x + 1 >= 1 = 0()
   
   i(+(x,y)) = x + 4y + 1 >= x + 4y + 1 = +(i(x),i(y))
   
   +(x,+(y,z)) = x + 4y + 16z + 5 >= x + 4y + 4z + 2 = +(+(x,y),z)
   
   +(+(x,i(y)),y) = x + 8y + 2 >= x = x
   
   +(+(x,y),i(y)) = x + 8y + 2 >= x = x
  problem:
   i(0()) -> 0()
   i(i(x)) -> x
   +(i(x),x) -> 0()
   +(x,i(x)) -> 0()
   i(+(x,y)) -> +(i(x),i(y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [i](x0) = [0 1 1]x0
              [0 1 0]  ,
    
          [0]
    [0] = [0]
          [0],
    
                  [1 0 0]     [1 0 0]     [1]
    [+](x0, x1) = [1 0 0]x0 + [1 0 0]x1 + [0]
                  [0 0 0]     [1 0 0]     [0]
   orientation:
             [0]    [0]      
    i(0()) = [0] >= [0] = 0()
             [0]    [0]      
    
              [1 0 0]          
    i(i(x)) = [0 2 1]x >= x = x
              [0 1 1]          
    
                [2 0 0]    [1]    [0]      
    +(i(x),x) = [2 0 0]x + [0] >= [0] = 0()
                [1 0 0]    [0]    [0]      
    
                [2 0 0]    [1]    [0]      
    +(x,i(x)) = [2 0 0]x + [0] >= [0] = 0()
                [1 0 0]    [0]    [0]      
    
                [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]               
    i(+(x,y)) = [1 0 0]x + [2 0 0]y + [0] >= [1 0 0]x + [1 0 0]y + [0] = +(i(x),i(y))
                [1 0 0]    [1 0 0]    [0]    [0 0 0]    [1 0 0]    [0]               
   problem:
    i(0()) -> 0()
    i(i(x)) -> x
    i(+(x,y)) -> +(i(x),i(y))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 1]  
     [i](x0) = [0 0 1]x0
               [0 1 0]  ,
     
           [0]
     [0] = [1]
           [1],
     
                        [1 0 1]     [0]
     [+](x0, x1) = x0 + [0 0 1]x1 + [1]
                        [0 1 0]     [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 1 1]    [1]    [1 0 1]    [1 1 1]    [0]               
     i(+(x,y)) = [0 0 1]x + [0 1 0]y + [1] >= [0 0 1]x + [0 1 0]y + [1] = +(i(x),i(y))
                 [0 1 0]    [0 0 1]    [1]    [0 1 0]    [0 0 1]    [1]               
    problem:
     i(i(x)) -> x
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 1]     [0]
      [i](x0) = [0 0 1]x0 + [0]
                [0 1 0]     [1]
     orientation:
                [1 1 1]    [1]         
      i(i(x)) = [0 1 0]x + [1] >= x = x
                [0 0 1]    [1]         
     problem:
      
     Qed