/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:
  s(a(x)) -> s(b(x))
  b(b(x)) -> a(x)
 weak:
  f(s(x),y) -> f(x,s(y))
  s(a(x)) -> a(s(x))
  s(b(x)) -> b(s(x))
  a(s(x)) -> s(a(x))
  b(s(x)) -> s(b(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                 [2 0]     [1 1]     [0]
   [f](x0, x1) = [0 0]x0 + [3 0]x1 + [2],
   
             [1 0]     [1]
   [b](x0) = [0 0]x0 + [0],
   
             [1 0]  
   [s](x0) = [0 0]x0,
   
             [1 0]     [1]
   [a](x0) = [0 0]x0 + [0]
  orientation:
             [1 0]    [1]    [1 0]    [1]          
   s(a(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(b(x))
   
             [1 0]    [2]    [1 0]    [1]       
   b(b(x)) = [0 0]x + [0] >= [0 0]x + [0] = a(x)
   
               [2 0]    [1 1]    [0]    [2 0]    [1 0]    [0]            
   f(s(x),y) = [0 0]x + [3 0]y + [2] >= [0 0]x + [3 0]y + [2] = f(x,s(y))
   
             [1 0]    [1]    [1 0]    [1]          
   s(a(x)) = [0 0]x + [0] >= [0 0]x + [0] = a(s(x))
   
             [1 0]    [1]    [1 0]    [1]          
   s(b(x)) = [0 0]x + [0] >= [0 0]x + [0] = b(s(x))
   
             [1 0]    [1]    [1 0]    [1]          
   a(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(a(x))
   
             [1 0]    [1]    [1 0]    [1]          
   b(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(b(x))
  problem:
   strict:
    s(a(x)) -> s(b(x))
   weak:
    f(s(x),y) -> f(x,s(y))
    s(a(x)) -> a(s(x))
    s(b(x)) -> b(s(x))
    a(s(x)) -> s(a(x))
    b(s(x)) -> s(b(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                  [2 2]     [2 1]     [1]
    [f](x0, x1) = [0 0]x0 + [0 0]x1 + [2],
    
                
    [b](x0) = x0,
    
                   [0]
    [s](x0) = x0 + [1],
    
                   [0]
    [a](x0) = x0 + [2]
   orientation:
                  [0]        [0]          
    s(a(x)) = x + [3] >= x + [1] = s(b(x))
    
                [2 2]    [2 1]    [3]    [2 2]    [2 1]    [2]            
    f(s(x),y) = [0 0]x + [0 0]y + [2] >= [0 0]x + [0 0]y + [2] = f(x,s(y))
    
                  [0]        [0]          
    s(a(x)) = x + [3] >= x + [3] = a(s(x))
    
                  [0]        [0]          
    s(b(x)) = x + [1] >= x + [1] = b(s(x))
    
                  [0]        [0]          
    a(s(x)) = x + [3] >= x + [3] = s(a(x))
    
                  [0]        [0]          
    b(s(x)) = x + [1] >= x + [1] = s(b(x))
   problem:
    strict:
     s(a(x)) -> s(b(x))
    weak:
     s(a(x)) -> a(s(x))
     s(b(x)) -> b(s(x))
     a(s(x)) -> s(a(x))
     b(s(x)) -> s(b(x))
   String Reversal Processor:
    strict:
     a(s(x)) -> b(s(x))
    weak:
     a(s(x)) -> s(a(x))
     b(s(x)) -> s(b(x))
     s(a(x)) -> a(s(x))
     s(b(x)) -> b(s(x))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b](x0) = 4x0,
      
      [s](x0) = 12x0,
      
      [a](x0) = 12x0
     orientation:
      a(s(x)) = 24x >= 16x = b(s(x))
      
      a(s(x)) = 24x >= 24x = s(a(x))
      
      b(s(x)) = 16x >= 16x = s(b(x))
      
      s(a(x)) = 24x >= 24x = a(s(x))
      
      s(b(x)) = 16x >= 16x = b(s(x))
     problem:
      strict:
       
      weak:
       a(s(x)) -> s(a(x))
       b(s(x)) -> s(b(x))
       s(a(x)) -> a(s(x))
       s(b(x)) -> b(s(x))
     Qed