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