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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [*](x0, x1) = 2x0 + x1 + 4,
   
   [+](x0, x1) = x0 + x1
  orientation:
   +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
   
   +(*(x,y),+(x,z)) = 3x + y + z + 4 >= 2x + y + z + 4 = *(x,+(y,z))
   
   +(*(x,y),+(*(x,z),u)) = u + 4x + y + z + 8 >= u + 2x + y + z + 4 = +(*(x,+(y,z)),u)
  problem:
   +(x,+(y,z)) -> +(+(x,y),z)
   +(*(x,y),+(x,z)) -> *(x,+(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [*](x0, x1) = 4x0 + x1,
    
    [+](x0, x1) = x0 + x1 + 4
   orientation:
    +(x,+(y,z)) = x + y + z + 8 >= x + y + z + 8 = +(+(x,y),z)
    
    +(*(x,y),+(x,z)) = 5x + y + z + 8 >= 4x + y + z + 4 = *(x,+(y,z))
   problem:
    +(x,+(y,z)) -> +(+(x,y),z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [+](x0, x1) = x0 + 4x1 + 3
    orientation:
     +(x,+(y,z)) = x + 4y + 16z + 15 >= x + 4y + 4z + 6 = +(+(x,y),z)
    problem:
     
    Qed