/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:
 f(f(X)) -> c(n__f(n__g(n__f(X))))
 c(X) -> d(activate(X))
 h(X) -> c(n__d(X))
 f(X) -> n__f(X)
 g(X) -> n__g(X)
 d(X) -> n__d(X)
 activate(n__f(X)) -> f(activate(X))
 activate(n__g(X)) -> g(X)
 activate(n__d(X)) -> d(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = x0,
   
   [n__d](x0) = x0,
   
   [h](x0) = x0 + 8,
   
   [d](x0) = x0,
   
   [activate](x0) = x0,
   
   [c](x0) = x0,
   
   [n__g](x0) = x0,
   
   [n__f](x0) = 4x0,
   
   [f](x0) = 4x0
  orientation:
   f(f(X)) = 16X >= 16X = c(n__f(n__g(n__f(X))))
   
   c(X) = X >= X = d(activate(X))
   
   h(X) = X + 8 >= X = c(n__d(X))
   
   f(X) = 4X >= 4X = n__f(X)
   
   g(X) = X >= X = n__g(X)
   
   d(X) = X >= X = n__d(X)
   
   activate(n__f(X)) = 4X >= 4X = f(activate(X))
   
   activate(n__g(X)) = X >= X = g(X)
   
   activate(n__d(X)) = X >= X = d(X)
   
   activate(X) = X >= X = X
  problem:
   f(f(X)) -> c(n__f(n__g(n__f(X))))
   c(X) -> d(activate(X))
   f(X) -> n__f(X)
   g(X) -> n__g(X)
   d(X) -> n__d(X)
   activate(n__f(X)) -> f(activate(X))
   activate(n__g(X)) -> g(X)
   activate(n__d(X)) -> d(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [g](x0) = [1 0 0]x0
              [0 0 0]  ,
    
                 [1 0 0]  
    [n__d](x0) = [0 0 0]x0
                 [0 0 0]  ,
    
              [1 0 0]  
    [d](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                     [1 1 0]     [0]
    [activate](x0) = [1 1 0]x0 + [0]
                     [0 0 1]     [1],
    
              [1 1 0]     [1]
    [c](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
                 [1 0 0]  
    [n__g](x0) = [0 0 0]x0
                 [0 0 0]  ,
    
                 [1 1 0]     [0]
    [n__f](x0) = [1 1 0]x0 + [1]
                 [0 0 0]     [0],
    
              [1 1 0]     [1]
    [f](x0) = [1 1 0]x0 + [1]
              [0 0 0]     [1]
   orientation:
              [2 2 0]    [3]    [2 2 0]    [2]                         
    f(f(X)) = [2 2 0]X + [3] >= [0 0 0]X + [0] = c(n__f(n__g(n__f(X))))
              [0 0 0]    [1]    [0 0 0]    [1]                         
    
           [1 1 0]    [1]    [1 1 0]                  
    c(X) = [0 0 0]X + [0] >= [0 0 0]X = d(activate(X))
           [0 0 0]    [1]    [0 0 0]                  
    
           [1 1 0]    [1]    [1 1 0]    [0]          
    f(X) = [1 1 0]X + [1] >= [1 1 0]X + [1] = n__f(X)
           [0 0 0]    [1]    [0 0 0]    [0]          
    
           [1 0 0]     [1 0 0]           
    g(X) = [1 0 0]X >= [0 0 0]X = n__g(X)
           [0 0 0]     [0 0 0]           
    
           [1 0 0]     [1 0 0]           
    d(X) = [0 0 0]X >= [0 0 0]X = n__d(X)
           [0 0 0]     [0 0 0]           
    
                        [2 2 0]    [1]    [2 2 0]    [1]                 
    activate(n__f(X)) = [2 2 0]X + [1] >= [2 2 0]X + [1] = f(activate(X))
                        [0 0 0]    [1]    [0 0 0]    [1]                 
    
                        [1 0 0]    [0]    [1 0 0]        
    activate(n__g(X)) = [1 0 0]X + [0] >= [1 0 0]X = g(X)
                        [0 0 0]    [1]    [0 0 0]        
    
                        [1 0 0]    [0]    [1 0 0]        
    activate(n__d(X)) = [1 0 0]X + [0] >= [0 0 0]X = d(X)
                        [0 0 0]    [1]    [0 0 0]        
    
                  [1 1 0]    [0]         
    activate(X) = [1 1 0]X + [0] >= X = X
                  [0 0 1]    [1]         
   problem:
    g(X) -> n__g(X)
    d(X) -> n__d(X)
    activate(n__f(X)) -> f(activate(X))
    activate(n__g(X)) -> g(X)
    activate(n__d(X)) -> d(X)
    activate(X) -> X
   String Reversal Processor:
    g(X) -> n__g(X)
    d(X) -> n__d(X)
    n__f(activate(X)) -> activate(f(X))
    n__g(activate(X)) -> g(X)
    n__d(activate(X)) -> d(X)
    activate(X) -> X
    KBO Processor:
     weight function:
      w0 = 1
      w(g) = w(n__d) = w(d) = w(activate) = w(n__f) = w(f) = 1
      w(n__g) = 0
     precedence:
      n__g > d ~ n__f > g ~ n__d ~ activate ~ f
     problem:
      
     Qed