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


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YES

Problem:
 s(a()) -> a()
 s(s(x)) -> x
 s(f(x,y)) -> f(s(y),s(x))
 s(g(x,y)) -> g(s(x),s(y))
 f(x,a()) -> x
 f(a(),y) -> y
 f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
 g(a(),a()) -> a()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [s](x0) = 4x0,
   
   [g](x0, x1) = 4x0 + 2x1 + 4,
   
   [a] = 0,
   
   [f](x0, x1) = x0 + x1
  orientation:
   s(a()) = 0 >= 0 = a()
   
   s(s(x)) = 16x >= x = x
   
   s(f(x,y)) = 4x + 4y >= 4x + 4y = f(s(y),s(x))
   
   s(g(x,y)) = 16x + 8y + 16 >= 16x + 8y + 4 = g(s(x),s(y))
   
   f(x,a()) = x >= x = x
   
   f(a(),y) = y >= y = y
   
   f(g(x,y),g(u,v)) = 4u + 2v + 4x + 2y + 8 >= 4u + 2v + 4x + 2y + 4 = g(f(x,u),f(y,v))
   
   g(a(),a()) = 4 >= 0 = a()
  problem:
   s(a()) -> a()
   s(s(x)) -> x
   s(f(x,y)) -> f(s(y),s(x))
   f(x,a()) -> x
   f(a(),y) -> y
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 1]  
    [s](x0) = [0 0 1]x0
              [0 1 0]  ,
    
          [0]
    [a] = [1]
          [1],
    
                         
    [f](x0, x1) = x0 + x1
                         
   orientation:
             [1]    [0]      
    s(a()) = [1] >= [1] = a()
             [1]    [1]      
    
              [1 1 1]          
    s(s(x)) = [0 1 0]x >= x = x
              [0 0 1]          
    
                [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                
    s(f(x,y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = f(s(y),s(x))
                [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                
    
                   [0]         
    f(x,a()) = x + [1] >= x = x
                   [1]         
    
                   [0]         
    f(a(),y) = y + [1] >= y = y
                   [1]         
   problem:
    s(s(x)) -> x
    s(f(x,y)) -> f(s(y),s(x))
    f(x,a()) -> x
    f(a(),y) -> y
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 1]  
     [s](x0) = [0 0 1]x0
               [0 1 0]  ,
     
           [0]
     [a] = [0]
           [0],
     
                   [1 0 0]     [1 0 0]     [0]
     [f](x0, x1) = [0 1 1]x0 + [0 1 0]x1 + [1]
                   [0 0 1]     [0 1 1]     [1]
    orientation:
               [1 1 1]          
     s(s(x)) = [0 1 0]x >= x = x
               [0 0 1]          
     
                 [1 0 1]    [1 1 1]    [1]    [1 0 1]    [1 0 1]    [0]               
     s(f(x,y)) = [0 0 1]x + [0 1 1]y + [1] >= [0 0 1]x + [0 1 1]y + [1] = f(s(y),s(x))
                 [0 1 1]    [0 1 0]    [1]    [0 1 1]    [0 1 0]    [1]               
     
                [1 0 0]    [0]         
     f(x,a()) = [0 1 1]x + [1] >= x = x
                [0 0 1]    [1]         
     
                [1 0 0]    [0]         
     f(a(),y) = [0 1 0]y + [1] >= y = y
                [0 1 1]    [1]         
    problem:
     s(s(x)) -> x
     f(x,a()) -> x
     f(a(),y) -> y
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 1 0]     [0]
      [s](x0) = [0 0 1]x0 + [1]
                [0 1 0]     [0],
      
            [0]
      [a] = [1]
            [0],
      
                           
      [f](x0, x1) = x0 + x1
                           
     orientation:
                [1 1 1]    [1]         
      s(s(x)) = [0 1 0]x + [1] >= x = x
                [0 0 1]    [1]         
      
                     [0]         
      f(x,a()) = x + [1] >= x = x
                     [0]         
      
                     [0]         
      f(a(),y) = y + [1] >= y = y
                     [0]         
     problem:
      f(x,a()) -> x
      f(a(),y) -> y
     Matrix Interpretation Processor: dim=3
      
      interpretation:
             [1]
       [a] = [0]
             [0],
       
                          [1 0 0]  
       [f](x0, x1) = x0 + [1 1 0]x1
                          [0 0 1]  
      orientation:
                      [1]         
       f(x,a()) = x + [1] >= x = x
                      [0]         
       
                  [1 0 0]    [1]         
       f(a(),y) = [1 1 0]y + [0] >= y = y
                  [0 0 1]    [0]         
      problem:
       
      Qed