/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem:
 f(c(s(x),y)) -> f(c(x,s(y)))
 g(c(x,s(y))) -> g(c(s(x),y))
 g(s(f(x))) -> g(f(x))

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