169.21/43.60	YES
170.85/43.61	
170.85/43.61	Problem:
170.85/43.61	 a(a(x1)) -> b(x1)
170.85/43.61	 b(c(x1)) -> a(x1)
170.85/43.61	 c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	
170.85/43.61	Proof:
170.85/43.61	 DP Processor:
170.85/43.61	  DPs:
170.85/43.61	   a#(a(x1)) -> b#(x1)
170.85/43.61	   b#(c(x1)) -> a#(x1)
170.85/43.61	   c#(b(x1)) -> c#(x1)
170.85/43.61	   c#(b(x1)) -> c#(c(x1))
170.85/43.61	   c#(b(x1)) -> b#(c(c(x1)))
170.85/43.61	   c#(b(x1)) -> a#(b(c(c(x1))))
170.85/43.61	  TRS:
170.85/43.61	   a(a(x1)) -> b(x1)
170.85/43.61	   b(c(x1)) -> a(x1)
170.85/43.61	   c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	  TDG Processor:
170.85/43.61	   DPs:
170.85/43.61	    a#(a(x1)) -> b#(x1)
170.85/43.61	    b#(c(x1)) -> a#(x1)
170.85/43.61	    c#(b(x1)) -> c#(x1)
170.85/43.61	    c#(b(x1)) -> c#(c(x1))
170.85/43.61	    c#(b(x1)) -> b#(c(c(x1)))
170.85/43.61	    c#(b(x1)) -> a#(b(c(c(x1))))
170.85/43.61	   TRS:
170.85/43.61	    a(a(x1)) -> b(x1)
170.85/43.61	    b(c(x1)) -> a(x1)
170.85/43.61	    c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	   graph:
170.85/43.61	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(b(c(c(x1))))
170.85/43.61	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> b#(c(c(x1)))
170.85/43.61	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1))
170.85/43.61	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(x1)
170.85/43.61	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(c(x1))))
170.85/43.61	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(c(x1)))
170.85/43.61	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(c(x1))
170.85/43.61	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
170.85/43.61	    c#(b(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> a#(x1)
170.85/43.61	    c#(b(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> b#(x1)
170.85/43.61	    b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
170.85/43.61	    a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
170.85/43.61	   SCC Processor:
170.85/43.61	    #sccs: 2
170.85/43.61	    #rules: 4
170.85/43.61	    #arcs: 12/36
170.85/43.61	    DPs:
170.85/43.61	     c#(b(x1)) -> c#(c(x1))
170.85/43.61	     c#(b(x1)) -> c#(x1)
170.85/43.61	    TRS:
170.85/43.61	     a(a(x1)) -> b(x1)
170.85/43.61	     b(c(x1)) -> a(x1)
170.85/43.61	     c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	    Arctic Interpretation Processor:
170.85/43.61	     dimension: 2
170.85/43.61	     usable rules:
170.85/43.61	      a(a(x1)) -> b(x1)
170.85/43.61	      b(c(x1)) -> a(x1)
170.85/43.61	      c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	     interpretation:
170.85/43.61	      [c#](x0) = [0 0]x0,
170.85/43.61	      
170.85/43.61	                [0  -&]     [-&]
170.85/43.61	      [c](x0) = [0  0 ]x0 + [0 ],
170.85/43.61	      
170.85/43.61	                [1  1 ]     [1 ]
170.85/43.61	      [b](x0) = [-& 0 ]x0 + [-&],
170.85/43.61	      
170.85/43.61	                [0 1]     [-&]
170.85/43.61	      [a](x0) = [0 0]x0 + [0 ]
170.85/43.61	     orientation:
170.85/43.61	      c#(b(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = c#(c(x1))
170.85/43.61	      
170.85/43.61	      c#(b(x1)) = [1 1]x1 + [1] >= [0 0]x1 = c#(x1)
170.85/43.61	      
170.85/43.61	                 [1 1]     [1]    [1  1 ]     [1 ]        
170.85/43.61	      a(a(x1)) = [0 1]x1 + [0] >= [-& 0 ]x1 + [-&] = b(x1)
170.85/43.61	      
170.85/43.61	                 [1 1]     [1]    [0 1]     [-&]        
170.85/43.61	      b(c(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0 ] = a(x1)
170.85/43.61	      
170.85/43.61	                 [1 1]     [1]    [1 1]     [1]                 
170.85/43.61	      c(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(c(c(x1))))
170.85/43.61	     problem:
170.85/43.61	      DPs:
170.85/43.61	       
170.85/43.61	      TRS:
170.85/43.61	       a(a(x1)) -> b(x1)
170.85/43.61	       b(c(x1)) -> a(x1)
170.85/43.61	       c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	     Qed
170.85/43.61	    
170.85/43.61	    DPs:
170.85/43.61	     b#(c(x1)) -> a#(x1)
170.85/43.61	     a#(a(x1)) -> b#(x1)
170.85/43.61	    TRS:
170.85/43.61	     a(a(x1)) -> b(x1)
170.85/43.61	     b(c(x1)) -> a(x1)
170.85/43.61	     c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	    Usable Rule Processor:
170.85/43.61	     DPs:
170.85/43.61	      b#(c(x1)) -> a#(x1)
170.85/43.61	      a#(a(x1)) -> b#(x1)
170.85/43.61	     TRS:
170.85/43.61	      
170.85/43.61	     Arctic Interpretation Processor:
170.85/43.61	      dimension: 4
170.85/43.61	      usable rules:
170.85/43.61	       
170.85/43.61	      interpretation:
170.85/43.61	       [b#](x0) = [1 0 1 0]x0,
170.85/43.61	       
170.85/43.61	       [a#](x0) = [0 0 0 0]x0 + [0],
170.85/43.61	       
170.85/43.61	                 [0  -& -& 0 ]     [-&]
170.85/43.61	                 [1  -& 0  1 ]     [0 ]
170.85/43.61	       [c](x0) = [-& -& 0  0 ]x0 + [0 ]
170.85/43.61	                 [0  1  1  0 ]     [-&],
170.85/43.61	       
170.85/43.61	                 [1  0  -& 0 ]     [0]
170.85/43.61	                 [0  1  0  -&]     [0]
170.85/43.61	       [a](x0) = [0  0  0  1 ]x0 + [0]
170.85/43.61	                 [1  0  1  0 ]     [1]
170.85/43.61	      orientation:
170.85/43.61	       b#(c(x1)) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = a#(x1)
170.85/43.61	       
170.85/43.61	       a#(a(x1)) = [1 1 1 1]x1 + [1] >= [1 0 1 0]x1 = b#(x1)
170.85/43.61	      problem:
170.85/43.61	       DPs:
170.85/43.61	        a#(a(x1)) -> b#(x1)
170.85/43.61	       TRS:
170.85/43.61	        
170.85/43.61	      Restore Modifier:
170.85/43.61	       DPs:
170.85/43.61	        a#(a(x1)) -> b#(x1)
170.85/43.61	       TRS:
170.85/43.61	        a(a(x1)) -> b(x1)
170.85/43.61	        b(c(x1)) -> a(x1)
170.85/43.61	        c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	       EDG Processor:
170.85/43.61	        DPs:
170.85/43.61	         a#(a(x1)) -> b#(x1)
170.85/43.61	        TRS:
170.85/43.61	         a(a(x1)) -> b(x1)
170.85/43.61	         b(c(x1)) -> a(x1)
170.85/43.61	         c(b(x1)) -> a(b(c(c(x1))))
170.85/43.61	        graph:
170.85/43.61	         
170.85/43.61	        SCC Processor:
170.85/43.61	         #sccs: 0
170.85/43.61	         #rules: 0
170.85/43.61	         #arcs: 0/1
170.85/43.61	         
170.85/43.61	EOF