169.96/43.24	YES
169.96/43.24	
169.96/43.24	Problem:
169.96/43.24	 a(x1) -> x1
169.96/43.24	 a(b(x1)) -> c(b(b(a(a(x1)))))
169.96/43.24	 b(x1) -> c(x1)
169.96/43.24	 c(c(x1)) -> x1
169.96/43.24	
169.96/43.24	Proof:
169.96/43.24	 DP Processor:
169.96/43.24	  DPs:
169.96/43.24	   a#(b(x1)) -> a#(x1)
169.96/43.24	   a#(b(x1)) -> a#(a(x1))
169.96/43.24	   a#(b(x1)) -> b#(a(a(x1)))
169.96/43.24	   a#(b(x1)) -> b#(b(a(a(x1))))
169.96/43.24	   a#(b(x1)) -> c#(b(b(a(a(x1)))))
169.96/43.24	   b#(x1) -> c#(x1)
169.96/43.24	  TRS:
169.96/43.24	   a(x1) -> x1
169.96/43.24	   a(b(x1)) -> c(b(b(a(a(x1)))))
169.96/43.24	   b(x1) -> c(x1)
169.96/43.24	   c(c(x1)) -> x1
169.96/43.24	  TDG Processor:
169.96/43.24	   DPs:
169.96/43.24	    a#(b(x1)) -> a#(x1)
169.96/43.24	    a#(b(x1)) -> a#(a(x1))
169.96/43.24	    a#(b(x1)) -> b#(a(a(x1)))
169.96/43.24	    a#(b(x1)) -> b#(b(a(a(x1))))
169.96/43.24	    a#(b(x1)) -> c#(b(b(a(a(x1)))))
169.96/43.24	    b#(x1) -> c#(x1)
169.96/43.24	   TRS:
169.96/43.24	    a(x1) -> x1
169.96/43.24	    a(b(x1)) -> c(b(b(a(a(x1)))))
169.96/43.24	    b(x1) -> c(x1)
169.96/43.24	    c(c(x1)) -> x1
169.96/43.24	   graph:
169.96/43.24	    a#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) -> c#(x1)
169.96/43.24	    a#(b(x1)) -> b#(a(a(x1))) -> b#(x1) -> c#(x1)
169.96/43.24	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(b(a(a(x1)))))
169.96/43.24	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(b(a(a(x1))))
169.96/43.24	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
169.96/43.24	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
169.96/43.24	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
169.96/43.24	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(b(a(a(x1)))))
169.96/43.24	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(b(a(a(x1))))
169.96/43.24	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
169.96/43.24	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
169.96/43.24	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
169.96/43.24	   SCC Processor:
169.96/43.24	    #sccs: 1
169.96/43.24	    #rules: 2
169.96/43.24	    #arcs: 12/36
169.96/43.24	    DPs:
169.96/43.24	     a#(b(x1)) -> a#(a(x1))
169.96/43.24	     a#(b(x1)) -> a#(x1)
169.96/43.24	    TRS:
169.96/43.24	     a(x1) -> x1
169.96/43.24	     a(b(x1)) -> c(b(b(a(a(x1)))))
169.96/43.24	     b(x1) -> c(x1)
169.96/43.24	     c(c(x1)) -> x1
169.96/43.24	    Arctic Interpretation Processor:
169.96/43.24	     dimension: 2
169.96/43.24	     usable rules:
169.96/43.24	      a(x1) -> x1
169.96/43.24	      a(b(x1)) -> c(b(b(a(a(x1)))))
169.96/43.24	      b(x1) -> c(x1)
169.96/43.24	      c(c(x1)) -> x1
169.96/43.24	     interpretation:
169.96/43.24	      [a#](x0) = [0 1]x0 + [0],
169.96/43.24	      
169.96/43.24	                [0  0 ]     [-&]
169.96/43.24	      [c](x0) = [0  -&]x0 + [0 ],
169.96/43.24	      
169.96/43.24	                [0 0]     [-&]
169.96/43.24	      [b](x0) = [0 2]x0 + [2 ],
169.96/43.24	      
169.96/43.24	                [0  2 ]     [0]
169.96/43.24	      [a](x0) = [-& 0 ]x0 + [0]
169.96/43.24	     orientation:
169.96/43.24	      a#(b(x1)) = [1 3]x1 + [3] >= [0 2]x1 + [1] = a#(a(x1))
169.96/43.24	      
169.96/43.24	      a#(b(x1)) = [1 3]x1 + [3] >= [0 1]x1 + [0] = a#(x1)
169.96/43.24	      
169.96/43.24	              [0  2 ]     [0]           
169.96/43.24	      a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
169.96/43.24	      
169.96/43.24	                 [2 4]     [4]    [2 4]     [4]                    
169.96/43.24	      a(b(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = c(b(b(a(a(x1)))))
169.96/43.24	      
169.96/43.24	              [0 0]     [-&]    [0  0 ]     [-&]        
169.96/43.24	      b(x1) = [0 2]x1 + [2 ] >= [0  -&]x1 + [0 ] = c(x1)
169.96/43.24	      
169.96/43.24	                 [0 0]     [0]           
169.96/43.24	      c(c(x1)) = [0 0]x1 + [0] >= x1 = x1
169.96/43.24	     problem:
169.96/43.24	      DPs:
169.96/43.24	       
169.96/43.24	      TRS:
169.96/43.24	       a(x1) -> x1
169.96/43.24	       a(b(x1)) -> c(b(b(a(a(x1)))))
169.96/43.24	       b(x1) -> c(x1)
169.96/43.24	       c(c(x1)) -> x1
169.96/43.24	     Qed
169.96/43.25	EOF