/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /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:
   [+](x0, x1) = x0 + x1 + 2,
   
   [*](x0, x1) = 4x0 + 2x1 + 4,
   
   [u] = 2
  orientation:
   +(*(x,y),*(x,z)) = 8x + 2y + 2z + 10 >= 4x + 2y + 2z + 8 = *(x,+(y,z))
   
   +(+(x,y),z) = x + y + z + 4 >= x + y + z + 4 = +(x,+(y,z))
   
   +(*(x,y),+(*(x,z),u())) = 8x + 2y + 2z + 14 >= 4x + 2y + 2z + 12 = +(*(x,+(y,z)),u())
  problem:
   +(+(x,y),z) -> +(x,+(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = 2x0 + x1 + 2
   orientation:
    +(+(x,y),z) = 4x + 2y + z + 6 >= 2x + 2y + z + 4 = +(x,+(y,z))
   problem:
    
   Qed