168.35/42.96	YES
168.35/42.97	
168.35/42.97	Problem:
168.35/42.97	 a(x1) -> x1
168.35/42.97	 a(b(x1)) -> c(b(b(x1)))
168.35/42.97	 b(x1) -> a(a(c(x1)))
168.35/42.97	 c(c(x1)) -> x1
168.35/42.97	
168.35/42.97	Proof:
168.35/42.97	 DP Processor:
168.35/42.97	  DPs:
168.35/42.97	   a#(b(x1)) -> b#(b(x1))
168.35/42.97	   a#(b(x1)) -> c#(b(b(x1)))
168.35/42.97	   b#(x1) -> c#(x1)
168.35/42.97	   b#(x1) -> a#(c(x1))
168.35/42.97	   b#(x1) -> a#(a(c(x1)))
168.35/42.97	  TRS:
168.35/42.97	   a(x1) -> x1
168.35/42.97	   a(b(x1)) -> c(b(b(x1)))
168.35/42.97	   b(x1) -> a(a(c(x1)))
168.35/42.97	   c(c(x1)) -> x1
168.35/42.97	  TDG Processor:
168.35/42.97	   DPs:
168.35/42.97	    a#(b(x1)) -> b#(b(x1))
168.35/42.97	    a#(b(x1)) -> c#(b(b(x1)))
168.35/42.97	    b#(x1) -> c#(x1)
168.35/42.97	    b#(x1) -> a#(c(x1))
168.35/42.97	    b#(x1) -> a#(a(c(x1)))
168.35/42.97	   TRS:
168.35/42.97	    a(x1) -> x1
168.35/42.97	    a(b(x1)) -> c(b(b(x1)))
168.35/42.97	    b(x1) -> a(a(c(x1)))
168.35/42.97	    c(c(x1)) -> x1
168.35/42.97	   graph:
168.35/42.97	    b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> c#(b(b(x1)))
168.35/42.97	    b#(x1) -> a#(c(x1)) -> a#(b(x1)) -> b#(b(x1))
168.35/42.97	    b#(x1) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(b(b(x1)))
168.35/42.97	    b#(x1) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(b(x1))
168.35/42.97	    a#(b(x1)) -> b#(b(x1)) -> b#(x1) -> a#(a(c(x1)))
168.35/42.97	    a#(b(x1)) -> b#(b(x1)) -> b#(x1) -> a#(c(x1))
168.35/42.97	    a#(b(x1)) -> b#(b(x1)) -> b#(x1) -> c#(x1)
168.35/42.97	   SCC Processor:
168.35/42.97	    #sccs: 1
168.35/42.97	    #rules: 3
168.35/42.97	    #arcs: 7/25
168.35/42.97	    DPs:
168.35/42.97	     b#(x1) -> a#(c(x1))
168.35/42.97	     a#(b(x1)) -> b#(b(x1))
168.35/42.97	     b#(x1) -> a#(a(c(x1)))
168.35/42.97	    TRS:
168.35/42.97	     a(x1) -> x1
168.35/42.97	     a(b(x1)) -> c(b(b(x1)))
168.35/42.97	     b(x1) -> a(a(c(x1)))
168.35/42.97	     c(c(x1)) -> x1
168.35/42.97	    Arctic Interpretation Processor:
168.35/42.97	     dimension: 2
168.35/42.97	     usable rules:
168.35/42.97	      a(x1) -> x1
168.35/42.97	      a(b(x1)) -> c(b(b(x1)))
168.35/42.97	      b(x1) -> a(a(c(x1)))
168.35/42.97	      c(c(x1)) -> x1
168.35/42.97	     interpretation:
168.35/42.97	      [b#](x0) = [0 1]x0 + [1],
168.35/42.97	      
168.35/42.97	      [a#](x0) = [0  -&]x0 + [0],
168.35/42.97	      
168.35/42.97	                [-& 0 ]     [0]
168.35/42.97	      [c](x0) = [0  0 ]x0 + [2],
168.35/42.97	      
168.35/42.97	                [1 2]     [3]
168.35/42.97	      [b](x0) = [0 1]x0 + [2],
168.35/42.97	      
168.35/42.97	                [0  -&]     [0]
168.35/42.97	      [a](x0) = [1  0 ]x0 + [0]
168.35/42.97	     orientation:
168.35/42.97	      b#(x1) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(c(x1))
168.35/42.97	      
168.35/42.97	      a#(b(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = b#(b(x1))
168.35/42.97	      
168.35/42.97	      b#(x1) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(a(c(x1)))
168.35/42.97	      
168.35/42.97	              [0  -&]     [0]           
168.35/42.97	      a(x1) = [1  0 ]x1 + [0] >= x1 = x1
168.35/42.97	      
168.35/42.97	                 [1 2]     [3]    [1 2]     [3]              
168.35/42.97	      a(b(x1)) = [2 3]x1 + [4] >= [2 3]x1 + [4] = c(b(b(x1)))
168.35/42.97	      
168.35/42.97	              [1 2]     [3]    [-& 0 ]     [0]              
168.35/42.97	      b(x1) = [0 1]x1 + [2] >= [0  1 ]x1 + [2] = a(a(c(x1)))
168.35/42.97	      
168.35/42.97	                 [0 0]     [2]           
168.35/42.97	      c(c(x1)) = [0 0]x1 + [2] >= x1 = x1
168.35/42.97	     problem:
168.35/42.97	      DPs:
168.35/42.97	       a#(b(x1)) -> b#(b(x1))
168.35/42.97	      TRS:
168.35/42.97	       a(x1) -> x1
168.35/42.97	       a(b(x1)) -> c(b(b(x1)))
168.35/42.97	       b(x1) -> a(a(c(x1)))
168.35/42.97	       c(c(x1)) -> x1
168.35/42.97	     Restore Modifier:
168.35/42.97	      DPs:
168.35/42.97	       a#(b(x1)) -> b#(b(x1))
168.35/42.97	      TRS:
168.35/42.97	       a(x1) -> x1
168.35/42.97	       a(b(x1)) -> c(b(b(x1)))
168.35/42.97	       b(x1) -> a(a(c(x1)))
168.35/42.97	       c(c(x1)) -> x1
168.35/42.97	      EDG Processor:
168.35/42.97	       DPs:
168.35/42.97	        a#(b(x1)) -> b#(b(x1))
168.35/42.97	       TRS:
168.35/42.97	        a(x1) -> x1
168.35/42.97	        a(b(x1)) -> c(b(b(x1)))
168.35/42.97	        b(x1) -> a(a(c(x1)))
168.35/42.97	        c(c(x1)) -> x1
168.35/42.97	       graph:
168.35/42.97	        
168.35/42.97	       SCC Processor:
168.35/42.97	        #sccs: 0
168.35/42.97	        #rules: 0
168.35/42.97	        #arcs: 0/1
168.35/42.97	        
168.35/42.97	EOF