/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))
 +(f(x),f(y)) -> f(+(x,y))
 +(f(x),+(f(y),z)) -> +(f(+(x,y)),z)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0) = x0 + 2,
   
   [+](x0, x1) = x0 + x1
  orientation:
   +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z))
   
   +(f(x),f(y)) = x + y + 4 >= x + y + 2 = f(+(x,y))
   
   +(f(x),+(f(y),z)) = x + y + z + 4 >= x + y + z + 2 = +(f(+(x,y)),z)
  problem:
   +(+(x,y),z) -> +(x,+(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = 2x0 + x1 + 1
   orientation:
    +(+(x,y),z) = 4x + 2y + z + 3 >= 2x + 2y + z + 2 = +(x,+(y,z))
   problem:
    
   Qed