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

Proof:
 Extended Uncurrying Processor:
  application symbol: a
  symbol table:
   g ==> g0/0 g1/1
   h ==> h0/0 h1/1
   f ==> f0/0 f1/1
   
  uncurry-rules:
   a(f0(),x1) -> f1(x1)
   a(h0(),x3) -> h1(x3)
   a(g0(),x5) -> g1(x5)
  eta-rules:
   
  problem:
   f1(f1(x)) -> a(x,x)
   h1(x) -> f1(g1(f1(x)))
   a(f0(),x1) -> f1(x1)
   a(h0(),x3) -> h1(x3)
   a(g0(),x5) -> g1(x5)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
           [1]
    [f0] = [0]
           [1],
    
           [1]
    [g0] = [0]
           [1],
    
                  [1 0 1]     [1 1 1]  
    [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [1 0 0]     [1 1 1]  ,
    
               [1 0 1]  
    [f1](x0) = [0 0 0]x0
               [1 1 1]  ,
    
               [1 0 1]  
    [h1](x0) = [0 0 0]x0
               [1 1 1]  ,
    
               [1 1 0]  
    [g1](x0) = [0 0 0]x0
               [0 1 0]  ,
    
           [0]
    [h0] = [0]
           [1]
   orientation:
                [2 1 2]     [2 1 2]          
    f1(f1(x)) = [0 0 0]x >= [0 0 0]x = a(x,x)
                [2 1 2]     [2 1 1]          
    
            [1 0 1]     [1 0 1]                 
    h1(x) = [0 0 0]x >= [0 0 0]x = f1(g1(f1(x)))
            [1 1 1]     [1 0 1]                 
    
                 [1 1 1]     [2]    [1 0 1]           
    a(f0(),x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = f1(x1)
                 [1 1 1]     [1]    [1 1 1]           
    
                 [1 1 1]     [1]    [1 0 1]           
    a(h0(),x3) = [0 0 0]x3 + [0] >= [0 0 0]x3 = h1(x3)
                 [1 1 1]     [0]    [1 1 1]           
    
                 [1 1 1]     [2]    [1 1 0]           
    a(g0(),x5) = [0 0 0]x5 + [0] >= [0 0 0]x5 = g1(x5)
                 [1 1 1]     [1]    [0 1 0]           
   problem:
    f1(f1(x)) -> a(x,x)
    h1(x) -> f1(g1(f1(x)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 1 0]  
     [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [1 1 1]     [1 1 1]  ,
     
                [1 0 1]  
     [f1](x0) = [0 1 0]x0
                [1 1 1]  ,
     
                [1 1 1]     [1]
     [h1](x0) = [1 1 0]x0 + [1]
                [1 0 1]     [1],
     
                [1 0 0]     [0]
     [g1](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0]
    orientation:
                 [2 1 2]     [2 1 0]          
     f1(f1(x)) = [0 1 0]x >= [0 0 0]x = a(x,x)
                 [2 2 2]     [2 2 2]          
     
             [1 1 1]    [1]    [1 0 1]    [0]                
     h1(x) = [1 1 0]x + [1] >= [0 0 0]x + [1] = f1(g1(f1(x)))
             [1 0 1]    [1]    [1 0 1]    [1]                
    problem:
     f1(f1(x)) -> a(x,x)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                    [1 1 0]     [1 0 0]     [0]
      [a](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1]
                    [0 0 0]     [0 0 0]     [0],
      
                 [1 1 1]     [0]
      [f1](x0) = [1 0 0]x0 + [1]
                 [0 0 0]     [1]
     orientation:
                  [2 1 1]    [2]    [2 1 0]    [0]         
      f1(f1(x)) = [1 1 1]x + [1] >= [0 1 0]x + [1] = a(x,x)
                  [0 0 0]    [1]    [0 0 0]    [0]         
     problem:
      
     Qed