/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /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=2
   
   interpretation:
               [1 0]  
    [g1](x0) = [0 0]x0,
    
           [0]
    [g0] = [0],
    
               [2 1]  
    [h1](x0) = [2 2]x0,
    
           [0]
    [h0] = [0],
    
               [1 1]  
    [f1](x0) = [2 0]x0,
    
           [1]
    [f0] = [0],
    
                  [1 0]     [2 1]  
    [a](x0, x1) = [0 0]x0 + [2 2]x1
   orientation:
                [3 1]     [3 1]          
    f1(f1(x)) = [2 2]x >= [2 2]x = a(x,x)
    
            [2 1]     [1 1]                 
    h1(x) = [2 2]x >= [2 2]x = f1(g1(f1(x)))
    
                 [2 1]     [1]    [1 1]           
    a(f0(),x1) = [2 2]x1 + [0] >= [2 0]x1 = f1(x1)
    
                 [2 1]      [2 1]           
    a(h0(),x3) = [2 2]x3 >= [2 2]x3 = h1(x3)
    
                 [2 1]      [1 0]           
    a(g0(),x5) = [2 2]x5 >= [0 0]x5 = g1(x5)
   problem:
    f1(f1(x)) -> a(x,x)
    h1(x) -> f1(g1(f1(x)))
    a(h0(),x3) -> h1(x3)
    a(g0(),x5) -> g1(x5)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                [1 0]  
     [g1](x0) = [0 0]x0,
     
            [0]
     [g0] = [1],
     
                [2 2]     [3]
     [h1](x0) = [1 2]x0 + [0],
     
            [1]
     [h0] = [2],
     
                [1 2]  
     [f1](x0) = [1 1]x0,
     
                   [1 1]     [2 2]  
     [a](x0, x1) = [1 0]x0 + [1 2]x1
    orientation:
                 [3 4]     [3 3]          
     f1(f1(x)) = [2 3]x >= [2 2]x = a(x,x)
     
             [2 2]    [3]    [1 2]                 
     h1(x) = [1 2]x + [0] >= [1 2]x = f1(g1(f1(x)))
     
                  [2 2]     [3]    [2 2]     [3]         
     a(h0(),x3) = [1 2]x3 + [1] >= [1 2]x3 + [0] = h1(x3)
     
                  [2 2]     [1]    [1 0]           
     a(g0(),x5) = [1 2]x5 + [0] >= [0 0]x5 = g1(x5)
    problem:
     f1(f1(x)) -> a(x,x)
     a(h0(),x3) -> h1(x3)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [h1](x0) = x0,
      
      [h0] = 4,
      
      [f1](x0) = 4x0 + 1,
      
      [a](x0, x1) = x0 + x1 + 5
     orientation:
      f1(f1(x)) = 16x + 5 >= 2x + 5 = a(x,x)
      
      a(h0(),x3) = x3 + 9 >= x3 = h1(x3)
     problem:
      f1(f1(x)) -> a(x,x)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [f1](x0) = 3x0 + 1,
       
       [a](x0, x1) = x0 + 6x1
      orientation:
       f1(f1(x)) = 9x + 4 >= 7x = a(x,x)
      problem:
       
      Qed