/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:
 f(s(x),y) -> f(x,s(x))
 f(x,s(y)) -> f(y,x)
 f(c(x),y) -> f(x,s(x))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 1 1]     [1 1 0]  
   [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
             [1 1 0]     [1]
   [s](x0) = [1 1 1]x0 + [1]
             [1 1 1]     [0],
   
             [1 1 1]     [0]
   [c](x0) = [1 1 1]x0 + [1]
             [1 1 0]     [1]
  orientation:
               [3 3 2]    [1 1 0]    [2]    [3 3 2]    [2]            
   f(s(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0] = f(x,s(x))
               [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0]            
   
               [1 1 1]    [2 2 1]    [2]    [1 1 0]    [1 1 1]          
   f(x,s(y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = f(y,x)
               [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]          
   
               [3 3 2]    [1 1 0]    [2]    [3 3 2]    [2]            
   f(c(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0] = f(x,s(x))
               [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0]            
  problem:
   f(s(x),y) -> f(x,s(x))
   f(c(x),y) -> f(x,s(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0, x1) = 3x0 + 2x1 + 1,
    
    [s](x0) = 3x0 + 7,
    
    [c](x0) = 3x0 + 7
   orientation:
    f(s(x),y) = 9x + 2y + 22 >= 9x + 15 = f(x,s(x))
    
    f(c(x),y) = 9x + 2y + 22 >= 9x + 15 = f(x,s(x))
   problem:
    
   Qed