/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:
 +(*(x,y),*(x,z)) -> *(x,+(y,z))
 +(+(x,y),z) -> +(x,+(y,z))
 +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [u] = 2,
   
   [+](x0, x1) = x0 + x1 + 2,
   
   [*](x0, x1) = 2x0 + x1 + 3
  orientation:
   +(*(x,y),*(x,z)) = 4x + y + z + 8 >= 2x + y + z + 5 = *(x,+(y,z))
   
   +(+(x,y),z) = x + y + z + 4 >= x + y + z + 4 = +(x,+(y,z))
   
   +(*(x,y),+(*(x,z),u())) = 4x + y + z + 12 >= 2x + y + z + 9 = +(*(x,+(y,z)),u())
  problem:
   +(+(x,y),z) -> +(x,+(y,z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 1 0]          [0]
    [+](x0, x1) = [0 0 1]x0 + x1 + [1]
                  [0 0 1]          [1]
   orientation:
                  [1 1 1]    [1 1 0]        [1]    [1 1 0]    [1 1 0]        [0]              
    +(+(x,y),z) = [0 0 1]x + [0 0 1]y + z + [2] >= [0 0 1]x + [0 0 1]y + z + [2] = +(x,+(y,z))
                  [0 0 1]    [0 0 1]        [2]    [0 0 1]    [0 0 1]        [2]              
   problem:
    
   Qed