/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:
 strict:
  f(s(x),y,y) -> f(y,x,s(x))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [1 1]     [1]
   [rand](x0) = [0 2]x0 + [0],
   
                     [3 3]     [2 2]     [1 1]     [0]
   [f](x0, x1, x2) = [0 2]x0 + [0 2]x1 + [0 0]x2 + [2],
   
               
   [s](x0) = x0
  orientation:
                 [3 3]    [3 3]    [0]    [3 3]    [3 3]    [0]              
   f(s(x),y,y) = [0 2]x + [0 2]y + [2] >= [0 2]x + [0 2]y + [2] = f(y,x,s(x))
   
             [1 1]    [1]         
   rand(x) = [0 2]x + [0] >= x = x
   
             [1 1]    [1]    [1 1]    [1]             
   rand(x) = [0 2]x + [0] >= [0 2]x + [0] = rand(s(x))
  problem:
   strict:
    f(s(x),y,y) -> f(y,x,s(x))
   weak:
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=5
   
   interpretation:
                 [1 0 0 0 0]     [1]
                 [0 0 0 0 0]     [0]
    [rand](x0) = [0 0 0 0 0]x0 + [0]
                 [1 0 0 0 0]     [0]
                 [0 0 0 0 0]     [0],
    
                      [1 1 1 0 1]     [1 1 0 0 1]     [1 0 1 0 0]     [0]
                      [0 0 1 0 1]     [0 0 0 0 1]     [0 0 1 0 0]     [1]
    [f](x0, x1, x2) = [1 0 0 1 0]x0 + [0 0 0 0 0]x1 + [1 0 0 1 0]x2 + [1]
                      [0 0 1 0 0]     [0 0 0 0 0]     [0 0 1 0 0]     [0]
                      [1 0 1 0 0]     [1 0 0 0 0]     [0 0 1 0 0]     [0],
    
              [1 0 0 0 0]     [0]
              [1 1 0 0 0]     [0]
    [s](x0) = [1 0 0 0 1]x0 + [0]
              [0 1 0 0 0]     [0]
              [0 0 0 0 1]     [1]
   orientation:
                  [3 1 0 0 2]    [2 1 1 0 1]    [1]    [3 1 0 0 2]    [1 1 1 0 1]    [0]              
                  [1 0 0 0 2]    [0 0 1 0 1]    [2]    [1 0 0 0 2]    [0 0 1 0 1]    [1]              
    f(s(x),y,y) = [1 1 0 0 0]x + [1 0 0 1 0]y + [1] >= [1 1 0 0 0]x + [1 0 0 1 0]y + [1] = f(y,x,s(x))
                  [1 0 0 0 1]    [0 0 1 0 0]    [0]    [1 0 0 0 1]    [0 0 1 0 0]    [0]              
                  [2 0 0 0 1]    [1 0 1 0 0]    [0]    [2 0 0 0 1]    [1 0 1 0 0]    [0]              
    
              [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]             
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
    rand(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = rand(s(x))
              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]             
              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
   problem:
    strict:
     
    weak:
     rand(x) -> rand(s(x))
   Qed