/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 strict:
  t(f(x),g(y),f(z)) -> t(z,g(x),g(y))
  t(g(x),g(y),f(z)) -> t(f(y),f(z),x)
 weak:
  f(g(x)) -> g(f(x))
  g(f(x)) -> f(g(x))
  f(f(x)) -> g(g(x))
  g(g(x)) -> f(f(x))

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