/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:
 a(f(),a(g(),a(f(),x))) -> a(f(),a(g(),a(g(),a(f(),x))))
 a(g(),a(f(),a(g(),x))) -> a(g(),a(f(),a(f(),a(g(),x))))

Proof:
 Extended Uncurrying Processor:
  application symbol: a
  symbol table:
   g ==> g0/0 g1/1
   f ==> f0/0 f1/1
   
  uncurry-rules:
   a(f0(),x1) -> f1(x1)
   a(g0(),x3) -> g1(x3)
  eta-rules:
   
  problem:
   f1(g1(f1(x))) -> f1(g1(g1(f1(x))))
   g1(f1(g1(x))) -> g1(f1(f1(g1(x))))
   a(f0(),x1) -> f1(x1)
   a(g0(),x3) -> g1(x3)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]  
    [g1](x0) = [0 0 0]x0
               [0 1 0]  ,
    
           [0]
    [g0] = [0]
           [0],
    
               [1 0 1]     [0]
    [f1](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
    
           [0]
    [f0] = [0]
           [1],
    
                  [1 0 0]     [1 0 1]  
    [a](x0, x1) = [0 0 1]x0 + [0 1 0]x1
                  [0 0 0]     [0 1 0]  
   orientation:
                    [1 0 1]    [1]    [1 0 1]    [0]                    
    f1(g1(f1(x))) = [0 0 0]x + [1] >= [0 0 0]x + [1] = f1(g1(g1(f1(x))))
                    [0 0 0]    [0]    [0 0 0]    [0]                    
    
                    [1 1 0]    [0]    [1 1 0]    [0]                    
    g1(f1(g1(x))) = [0 0 0]x + [0] >= [0 0 0]x + [0] = g1(f1(f1(g1(x))))
                    [0 0 0]    [1]    [0 0 0]    [1]                    
    
                 [1 0 1]     [0]    [1 0 1]     [0]         
    a(f0(),x1) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [1] = f1(x1)
                 [0 1 0]     [0]    [0 0 0]     [0]         
    
                 [1 0 1]      [1 0 0]           
    a(g0(),x3) = [0 1 0]x3 >= [0 0 0]x3 = g1(x3)
                 [0 1 0]      [0 1 0]           
   problem:
    g1(f1(g1(x))) -> g1(f1(f1(g1(x))))
    a(f0(),x1) -> f1(x1)
    a(g0(),x3) -> g1(x3)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 0 1]     [0]
     [g1](x0) = [0 0 0]x0 + [1]
                [1 0 0]     [0],
     
            [0]
     [g0] = [0]
            [0],
     
                [1 0 0]  
     [f1](x0) = [0 0 0]x0
                [0 1 0]  ,
     
            [0]
     [f0] = [0]
            [0],
     
                   [1 0 0]     [1 0 1]     [0]
     [a](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1]
                   [0 0 0]     [1 1 1]     [0]
    orientation:
                     [1 0 1]    [1]    [1 0 1]    [0]                    
     g1(f1(g1(x))) = [0 0 0]x + [1] >= [0 0 0]x + [1] = g1(f1(f1(g1(x))))
                     [1 0 1]    [0]    [1 0 1]    [0]                    
     
                  [1 0 1]     [0]    [1 0 0]           
     a(f0(),x1) = [0 1 0]x1 + [1] >= [0 0 0]x1 = f1(x1)
                  [1 1 1]     [0]    [0 1 0]           
     
                  [1 0 1]     [0]    [1 0 1]     [0]         
     a(g0(),x3) = [0 1 0]x3 + [1] >= [0 0 0]x3 + [1] = g1(x3)
                  [1 1 1]     [0]    [1 0 0]     [0]         
    problem:
     a(f0(),x1) -> f1(x1)
     a(g0(),x3) -> g1(x3)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                 [1 0 0]  
      [g1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
             [0]
      [g0] = [0]
             [0],
      
                 [1 0 0]  
      [f1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
             [0]
      [f0] = [0]
             [0],
      
                    [1 0 0]     [1 0 0]     [1]
      [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [0]
     orientation:
                   [1 0 0]     [1]    [1 0 0]           
      a(f0(),x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = f1(x1)
                   [0 0 0]     [0]    [0 0 0]           
      
                   [1 0 0]     [1]    [1 0 0]           
      a(g0(),x3) = [0 0 0]x3 + [0] >= [0 0 0]x3 = g1(x3)
                   [0 0 0]     [0]    [0 0 0]           
     problem:
      
     Qed