/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:
 minus(minus(x)) -> x
 minux(+(x,y)) -> +(minus(y),minus(x))
 +(minus(x),+(x,y)) -> y
 +(+(x,y),minus(y)) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [minux](x0) = 6x0 + 2,
   
   [+](x0, x1) = x0 + x1,
   
   [minus](x0) = 4x0 + 1
  orientation:
   minus(minus(x)) = 16x + 5 >= x = x
   
   minux(+(x,y)) = 6x + 6y + 2 >= 4x + 4y + 2 = +(minus(y),minus(x))
   
   +(minus(x),+(x,y)) = 5x + y + 1 >= y = y
   
   +(+(x,y),minus(y)) = x + 5y + 1 >= x = x
  problem:
   minux(+(x,y)) -> +(minus(y),minus(x))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1]
    [minux](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0],
    
                  [1 0 0]     [1 0 0]  
    [+](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
                  [1 0 0]  
    [minus](x0) = [0 0 0]x0
                  [0 0 0]  
   orientation:
                    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]                        
    minux(+(x,y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = +(minus(y),minus(x))
                    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                        
   problem:
    
   Qed