167.63/42.98	YES
167.63/42.98	
167.63/42.98	Problem:
167.63/42.98	 a(x1) -> x1
167.63/42.98	 a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	 b(x1) -> c(x1)
167.63/42.98	 c(c(x1)) -> b(x1)
167.63/42.98	
167.63/42.98	Proof:
167.63/42.98	 DP Processor:
167.63/42.98	  DPs:
167.63/42.98	   a#(b(x1)) -> a#(x1)
167.63/42.98	   a#(b(x1)) -> a#(a(x1))
167.63/42.98	   a#(b(x1)) -> b#(a(a(x1)))
167.63/42.98	   a#(b(x1)) -> c#(b(a(a(x1))))
167.63/42.98	   b#(x1) -> c#(x1)
167.63/42.98	   c#(c(x1)) -> b#(x1)
167.63/42.98	  TRS:
167.63/42.98	   a(x1) -> x1
167.63/42.98	   a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	   b(x1) -> c(x1)
167.63/42.98	   c(c(x1)) -> b(x1)
167.63/42.98	  TDG Processor:
167.63/42.98	   DPs:
167.63/42.98	    a#(b(x1)) -> a#(x1)
167.63/42.98	    a#(b(x1)) -> a#(a(x1))
167.63/42.98	    a#(b(x1)) -> b#(a(a(x1)))
167.63/42.98	    a#(b(x1)) -> c#(b(a(a(x1))))
167.63/42.98	    b#(x1) -> c#(x1)
167.63/42.98	    c#(c(x1)) -> b#(x1)
167.63/42.98	   TRS:
167.63/42.98	    a(x1) -> x1
167.63/42.98	    a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	    b(x1) -> c(x1)
167.63/42.98	    c(c(x1)) -> b(x1)
167.63/42.98	   graph:
167.63/42.98	    c#(c(x1)) -> b#(x1) -> b#(x1) -> c#(x1)
167.63/42.98	    b#(x1) -> c#(x1) -> c#(c(x1)) -> b#(x1)
167.63/42.98	    a#(b(x1)) -> c#(b(a(a(x1)))) -> c#(c(x1)) -> b#(x1)
167.63/42.98	    a#(b(x1)) -> b#(a(a(x1))) -> b#(x1) -> c#(x1)
167.63/42.98	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(a(a(x1))))
167.63/42.98	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
167.63/42.98	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
167.63/42.98	    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
167.63/42.98	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(a(a(x1))))
167.63/42.98	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
167.63/42.98	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
167.63/42.98	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
167.63/42.98	   SCC Processor:
167.63/42.98	    #sccs: 2
167.63/42.98	    #rules: 4
167.63/42.98	    #arcs: 12/36
167.63/42.98	    DPs:
167.63/42.98	     a#(b(x1)) -> a#(a(x1))
167.63/42.98	     a#(b(x1)) -> a#(x1)
167.63/42.98	    TRS:
167.63/42.98	     a(x1) -> x1
167.63/42.98	     a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	     b(x1) -> c(x1)
167.63/42.98	     c(c(x1)) -> b(x1)
167.63/42.98	    Arctic Interpretation Processor:
167.63/42.98	     dimension: 2
167.63/42.98	     usable rules:
167.63/42.98	      a(x1) -> x1
167.63/42.98	      a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	      b(x1) -> c(x1)
167.63/42.98	      c(c(x1)) -> b(x1)
167.63/42.98	     interpretation:
167.63/42.98	      [a#](x0) = [0 1]x0,
167.63/42.98	      
167.63/42.98	                [-& 1 ]     [1]
167.63/42.98	      [c](x0) = [0  0 ]x0 + [3],
167.63/42.98	      
167.63/42.98	                [-& 1 ]     [1]
167.63/42.98	      [b](x0) = [0  1 ]x0 + [3],
167.63/42.98	      
167.63/42.98	                [0  1 ]     [0]
167.63/42.98	      [a](x0) = [-& 0 ]x0 + [1]
167.63/42.98	     orientation:
167.63/42.98	      a#(b(x1)) = [1 2]x1 + [4] >= [0 1]x1 + [2] = a#(a(x1))
167.63/42.98	      
167.63/42.98	      a#(b(x1)) = [1 2]x1 + [4] >= [0 1]x1 = a#(x1)
167.63/42.98	      
167.63/42.98	              [0  1 ]     [0]           
167.63/42.98	      a(x1) = [-& 0 ]x1 + [1] >= x1 = x1
167.63/42.98	      
167.63/42.98	                 [1 2]     [4]    [1 2]     [4]                 
167.63/42.98	      a(b(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = c(b(a(a(x1))))
167.63/42.98	      
167.63/42.98	              [-& 1 ]     [1]    [-& 1 ]     [1]        
167.63/42.98	      b(x1) = [0  1 ]x1 + [3] >= [0  0 ]x1 + [3] = c(x1)
167.63/42.98	      
167.63/42.98	                 [1 1]     [4]    [-& 1 ]     [1]        
167.63/42.98	      c(c(x1)) = [0 1]x1 + [3] >= [0  1 ]x1 + [3] = b(x1)
167.63/42.98	     problem:
167.63/42.98	      DPs:
167.63/42.98	       
167.63/42.98	      TRS:
167.63/42.98	       a(x1) -> x1
167.63/42.98	       a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	       b(x1) -> c(x1)
167.63/42.98	       c(c(x1)) -> b(x1)
167.63/42.98	     Qed
167.63/42.98	    
167.63/42.98	    DPs:
167.63/42.98	     c#(c(x1)) -> b#(x1)
167.63/42.98	     b#(x1) -> c#(x1)
167.63/42.98	    TRS:
167.63/42.98	     a(x1) -> x1
167.63/42.98	     a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	     b(x1) -> c(x1)
167.63/42.98	     c(c(x1)) -> b(x1)
167.63/42.98	    Usable Rule Processor:
167.63/42.98	     DPs:
167.63/42.98	      c#(c(x1)) -> b#(x1)
167.63/42.98	      b#(x1) -> c#(x1)
167.63/42.98	     TRS:
167.63/42.98	      
167.63/42.98	     Arctic Interpretation Processor:
167.63/42.98	      dimension: 4
167.63/42.98	      usable rules:
167.63/42.98	       
167.63/42.98	      interpretation:
167.63/42.98	       [c#](x0) = [0  -& -& -&]x0,
167.63/42.98	       
167.63/42.98	       [b#](x0) = [1 0 0 0]x0,
167.63/42.98	       
167.63/42.98	                 [1 0 0 0]     [0]
167.63/42.98	                 [0 0 0 0]     [0]
167.63/42.98	       [c](x0) = [0 0 0 0]x0 + [0]
167.63/42.98	                 [0 0 0 0]     [0]
167.63/42.98	      orientation:
167.63/42.98	       c#(c(x1)) = [1 0 0 0]x1 + [0] >= [1 0 0 0]x1 = b#(x1)
167.63/42.98	       
167.63/42.98	       b#(x1) = [1 0 0 0]x1 >= [0  -& -& -&]x1 = c#(x1)
167.63/42.98	      problem:
167.63/42.98	       DPs:
167.63/42.98	        c#(c(x1)) -> b#(x1)
167.63/42.98	       TRS:
167.63/42.98	        
167.63/42.98	      Restore Modifier:
167.63/42.98	       DPs:
167.63/42.98	        c#(c(x1)) -> b#(x1)
167.63/42.98	       TRS:
167.63/42.98	        a(x1) -> x1
167.63/42.98	        a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	        b(x1) -> c(x1)
167.63/42.98	        c(c(x1)) -> b(x1)
167.63/42.98	       EDG Processor:
167.63/42.98	        DPs:
167.63/42.98	         c#(c(x1)) -> b#(x1)
167.63/42.98	        TRS:
167.63/42.98	         a(x1) -> x1
167.63/42.98	         a(b(x1)) -> c(b(a(a(x1))))
167.63/42.98	         b(x1) -> c(x1)
167.63/42.98	         c(c(x1)) -> b(x1)
167.63/42.98	        graph:
167.63/42.98	         
167.63/42.98	        SCC Processor:
167.63/42.98	         #sccs: 0
167.63/42.98	         #rules: 0
167.63/42.98	         #arcs: 0/1
167.63/42.98	         
167.63/42.99	EOF