167.23/42.68	YES
167.23/42.69	
167.23/42.69	Problem:
167.23/42.69	 a(x1) -> x1
167.23/42.69	 a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	 b(x1) -> a(a(x1))
167.23/42.69	 c(c(x1)) -> x1
167.23/42.69	
167.23/42.69	Proof:
167.23/42.69	 DP Processor:
167.23/42.69	  DPs:
167.23/42.69	   a#(b(x1)) -> c#(b(x1))
167.23/42.69	   a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	   a#(b(x1)) -> c#(b(c(b(x1))))
167.23/42.69	   b#(x1) -> a#(x1)
167.23/42.69	   b#(x1) -> a#(a(x1))
167.23/42.69	  TRS:
167.23/42.69	   a(x1) -> x1
167.23/42.69	   a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	   b(x1) -> a(a(x1))
167.23/42.69	   c(c(x1)) -> x1
167.23/42.69	  TDG Processor:
167.23/42.69	   DPs:
167.23/42.69	    a#(b(x1)) -> c#(b(x1))
167.23/42.69	    a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	    a#(b(x1)) -> c#(b(c(b(x1))))
167.23/42.69	    b#(x1) -> a#(x1)
167.23/42.69	    b#(x1) -> a#(a(x1))
167.23/42.69	   TRS:
167.23/42.69	    a(x1) -> x1
167.23/42.69	    a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	    b(x1) -> a(a(x1))
167.23/42.69	    c(c(x1)) -> x1
167.23/42.69	   graph:
167.23/42.69	    b#(x1) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(c(b(x1))))
167.23/42.69	    b#(x1) -> a#(a(x1)) -> a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	    b#(x1) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(x1))
167.23/42.69	    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(c(b(x1))))
167.23/42.69	    b#(x1) -> a#(x1) -> a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(x1))
167.23/42.69	    a#(b(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(a(x1))
167.23/42.69	    a#(b(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(x1)
167.23/42.69	   SCC Processor:
167.23/42.69	    #sccs: 1
167.23/42.69	    #rules: 3
167.23/42.69	    #arcs: 8/25
167.23/42.69	    DPs:
167.23/42.69	     b#(x1) -> a#(a(x1))
167.23/42.69	     a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	     b#(x1) -> a#(x1)
167.23/42.69	    TRS:
167.23/42.69	     a(x1) -> x1
167.23/42.69	     a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	     b(x1) -> a(a(x1))
167.23/42.69	     c(c(x1)) -> x1
167.23/42.69	    Arctic Interpretation Processor:
167.23/42.69	     dimension: 2
167.23/42.69	     usable rules:
167.23/42.69	      a(x1) -> x1
167.23/42.69	      a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	      b(x1) -> a(a(x1))
167.23/42.69	      c(c(x1)) -> x1
167.23/42.69	     interpretation:
167.23/42.69	      [b#](x0) = [1 3]x0 + [3],
167.23/42.69	      
167.23/42.69	      [a#](x0) = [0 2]x0 + [0],
167.23/42.69	      
167.23/42.69	                [-& 0 ]     [0]
167.23/42.69	      [c](x0) = [0  -&]x0 + [0],
167.23/42.69	      
167.23/42.69	                [0 1]     [1]
167.23/42.69	      [b](x0) = [1 2]x0 + [2],
167.23/42.69	      
167.23/42.69	                [0  1 ]     [0]
167.23/42.69	      [a](x0) = [-& 0 ]x0 + [0]
167.23/42.69	     orientation:
167.23/42.69	      b#(x1) = [1 3]x1 + [3] >= [0 2]x1 + [2] = a#(a(x1))
167.23/42.69	      
167.23/42.69	      a#(b(x1)) = [3 4]x1 + [4] >= [3 4]x1 + [4] = b#(c(b(x1)))
167.23/42.69	      
167.23/42.69	      b#(x1) = [1 3]x1 + [3] >= [0 2]x1 + [0] = a#(x1)
167.23/42.69	      
167.23/42.69	              [0  1 ]     [0]           
167.23/42.69	      a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
167.23/42.69	      
167.23/42.69	                 [2 3]     [3]    [2 3]     [3]                 
167.23/42.69	      a(b(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = c(b(c(b(x1))))
167.23/42.69	      
167.23/42.69	              [0 1]     [1]    [0  1 ]     [1]           
167.23/42.69	      b(x1) = [1 2]x1 + [2] >= [-& 0 ]x1 + [0] = a(a(x1))
167.23/42.69	      
167.23/42.69	                      [0]           
167.23/42.69	      c(c(x1)) = x1 + [0] >= x1 = x1
167.23/42.69	     problem:
167.23/42.69	      DPs:
167.23/42.69	       a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	      TRS:
167.23/42.69	       a(x1) -> x1
167.23/42.69	       a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	       b(x1) -> a(a(x1))
167.23/42.69	       c(c(x1)) -> x1
167.23/42.69	     Restore Modifier:
167.23/42.69	      DPs:
167.23/42.69	       a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	      TRS:
167.23/42.69	       a(x1) -> x1
167.23/42.69	       a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	       b(x1) -> a(a(x1))
167.23/42.69	       c(c(x1)) -> x1
167.23/42.69	      EDG Processor:
167.23/42.69	       DPs:
167.23/42.69	        a#(b(x1)) -> b#(c(b(x1)))
167.23/42.69	       TRS:
167.23/42.69	        a(x1) -> x1
167.23/42.69	        a(b(x1)) -> c(b(c(b(x1))))
167.23/42.69	        b(x1) -> a(a(x1))
167.23/42.69	        c(c(x1)) -> x1
167.23/42.69	       graph:
167.23/42.69	        
167.23/42.69	       SCC Processor:
167.23/42.69	        #sccs: 0
167.23/42.69	        #rules: 0
167.23/42.69	        #arcs: 0/1
167.23/42.69	        
167.23/42.69	EOF