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

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   a ==> a0/0 a1/1 a2/2
   
  uncurry-rules:
   f(a1(x2),x3) -> a2(x2,x3)
   f(a0(),x2) -> a1(x2)
  eta-rules:
   f(f(a(),f(f(a(),x),a())),x1) -> f(f(f(a(),f(a(),x)),a()),x1)
  problem:
   a1(a2(x,a0())) -> a2(a1(x),a0())
   a2(a2(x,a0()),x1) -> f(a2(a1(x),a0()),x1)
   f(a1(x2),x3) -> a2(x2,x3)
   f(a0(),x2) -> a1(x2)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a2](x0, x1) = x0 + 2x1 + 5,
    
    [f](x0, x1) = x0 + 2x1 + 2,
    
    [a1](x0) = x0 + 3,
    
    [a0] = 7
   orientation:
    a1(a2(x,a0())) = x + 22 >= x + 22 = a2(a1(x),a0())
    
    a2(a2(x,a0()),x1) = x + 2x1 + 24 >= x + 2x1 + 24 = f(a2(a1(x),a0()),x1)
    
    f(a1(x2),x3) = x2 + 2x3 + 5 >= x2 + 2x3 + 5 = a2(x2,x3)
    
    f(a0(),x2) = 2x2 + 9 >= x2 + 3 = a1(x2)
   problem:
    a1(a2(x,a0())) -> a2(a1(x),a0())
    a2(a2(x,a0()),x1) -> f(a2(a1(x),a0()),x1)
    f(a1(x2),x3) -> a2(x2,x3)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                    [1 0 0]     [1 0 0]     [0]
     [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [1 0 0]     [0 0 0]     [1],
     
                   [1 1 0]     [1 0 0]  
     [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [1 1 0]     [0 0 0]  ,
     
                [1 0 0]     [0]
     [a1](x0) = [0 0 0]x0 + [1]
                [1 0 0]     [1],
     
            [0]
     [a0] = [0]
            [0]
    orientation:
                      [1 0 0]    [0]    [1 0 0]    [0]                 
     a1(a2(x,a0())) = [0 0 0]x + [1] >= [0 0 0]x + [0] = a2(a1(x),a0())
                      [1 0 0]    [1]    [1 0 0]    [1]                 
     
                         [1 0 0]    [1 0 0]     [0]    [1 0 0]    [1 0 0]                         
     a2(a2(x,a0()),x1) = [0 0 0]x + [0 0 0]x1 + [0] >= [0 0 0]x + [0 0 0]x1 = f(a2(a1(x),a0()),x1)
                         [1 0 0]    [0 0 0]     [1]    [1 0 0]    [0 0 0]                         
     
                    [1 0 0]     [1 0 0]     [1]    [1 0 0]     [1 0 0]     [0]            
     f(a1(x2),x3) = [0 0 0]x2 + [0 0 0]x3 + [0] >= [0 0 0]x2 + [0 0 0]x3 + [0] = a2(x2,x3)
                    [1 0 0]     [0 0 0]     [1]    [1 0 0]     [0 0 0]     [1]            
    problem:
     a1(a2(x,a0())) -> a2(a1(x),a0())
     a2(a2(x,a0()),x1) -> f(a2(a1(x),a0()),x1)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                     [1 0 1]     [1 0 1]  
      [a2](x0, x1) = [0 1 0]x0 + [0 1 1]x1
                     [0 1 0]     [1 0 0]  ,
      
                    [1 0 0]     [1 0 0]  
      [f](x0, x1) = [0 1 0]x0 + [0 1 0]x1
                    [0 0 0]     [0 0 0]  ,
      
                 [1 1 0]  
      [a1](x0) = [0 1 0]x0
                 [0 0 1]  ,
      
             [0]
      [a0] = [1]
             [0]
     orientation:
                       [1 1 1]    [1]    [1 1 1]    [0]                 
      a1(a2(x,a0())) = [0 1 0]x + [1] >= [0 1 0]x + [1] = a2(a1(x),a0())
                       [0 1 0]    [0]    [0 1 0]    [0]                 
      
                          [1 1 1]    [1 0 1]     [0]    [1 1 1]    [1 0 0]     [0]                       
      a2(a2(x,a0()),x1) = [0 1 0]x + [0 1 1]x1 + [1] >= [0 1 0]x + [0 1 0]x1 + [1] = f(a2(a1(x),a0()),x1)
                          [0 1 0]    [1 0 0]     [1]    [0 0 0]    [0 0 0]     [0]                       
     problem:
      a2(a2(x,a0()),x1) -> f(a2(a1(x),a0()),x1)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                      [1 1 0]     [1 0 0]     [0]
       [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                      [1 0 0]     [0 0 0]     [0],
       
                     [1 0 0]     [1 0 0]  
       [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
       
                  [1 0 0]  
       [a1](x0) = [0 0 0]x0
                  [0 0 0]  ,
       
              [0]
       [a0] = [0]
              [0]
      orientation:
                           [1 1 0]    [1 0 0]     [1]    [1 0 0]    [1 0 0]                         
       a2(a2(x,a0()),x1) = [0 0 0]x + [0 0 0]x1 + [1] >= [0 0 0]x + [0 0 0]x1 = f(a2(a1(x),a0()),x1)
                           [1 1 0]    [0 0 0]     [0]    [0 0 0]    [0 0 0]                         
      problem:
       
      Qed