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


--------------------------------------------------------------------------------


YES

Problem:
 g(h(g(x))) -> g(x)
 g(g(x)) -> g(h(g(x)))
 h(h(x)) -> h(f(h(x),x))

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