/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:
 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:
   [+](x0, x1) = x0 + x1 + 4,
   
   [minus](x0) = 2x0 + 5,
   
   [minux](x0) = 2x0 + 6
  orientation:
   minus(minus(x)) = 4x + 15 >= x = x
   
   minux(+(x,y)) = 2x + 2y + 14 >= 2x + 2y + 14 = +(minus(y),minus(x))
   
   +(minus(x),+(x,y)) = 3x + y + 13 >= y = y
   
   +(+(x,y),minus(y)) = x + 3y + 13 >= x = x
  problem:
   minux(+(x,y)) -> +(minus(y),minus(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = x0 + x1 + 6,
    
    [minus](x0) = x0 + 2,
    
    [minux](x0) = x0 + 5
   orientation:
    minux(+(x,y)) = x + y + 11 >= x + y + 10 = +(minus(y),minus(x))
   problem:
    
   Qed