167.13/42.68	YES
167.13/42.69	
167.13/42.69	Problem:
167.13/42.69	 a(x1) -> x1
167.13/42.69	 a(x1) -> b(x1)
167.13/42.69	 a(b(x1)) -> b(c(x1))
167.13/42.69	 c(c(x1)) -> a(c(a(x1)))
167.13/42.69	
167.13/42.69	Proof:
167.13/42.69	 String Reversal Processor:
167.13/42.69	  a(x1) -> x1
167.13/42.69	  a(x1) -> b(x1)
167.13/42.69	  b(a(x1)) -> c(b(x1))
167.13/42.69	  c(c(x1)) -> a(c(a(x1)))
167.13/42.69	  DP Processor:
167.13/42.69	   DPs:
167.13/42.69	    a#(x1) -> b#(x1)
167.13/42.69	    b#(a(x1)) -> b#(x1)
167.13/42.69	    b#(a(x1)) -> c#(b(x1))
167.13/42.69	    c#(c(x1)) -> a#(x1)
167.13/42.69	    c#(c(x1)) -> c#(a(x1))
167.13/42.69	    c#(c(x1)) -> a#(c(a(x1)))
167.13/42.69	   TRS:
167.13/42.69	    a(x1) -> x1
167.13/42.69	    a(x1) -> b(x1)
167.13/42.69	    b(a(x1)) -> c(b(x1))
167.13/42.69	    c(c(x1)) -> a(c(a(x1)))
167.13/42.69	   TDG Processor:
167.13/42.69	    DPs:
167.13/42.69	     a#(x1) -> b#(x1)
167.13/42.69	     b#(a(x1)) -> b#(x1)
167.13/42.69	     b#(a(x1)) -> c#(b(x1))
167.13/42.69	     c#(c(x1)) -> a#(x1)
167.13/42.69	     c#(c(x1)) -> c#(a(x1))
167.13/42.69	     c#(c(x1)) -> a#(c(a(x1)))
167.13/42.69	    TRS:
167.13/42.69	     a(x1) -> x1
167.13/42.69	     a(x1) -> b(x1)
167.13/42.69	     b(a(x1)) -> c(b(x1))
167.13/42.69	     c(c(x1)) -> a(c(a(x1)))
167.13/42.69	    graph:
167.13/42.69	     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(c(a(x1)))
167.13/42.69	     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1))
167.13/42.69	     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
167.13/42.69	     c#(c(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(x1)
167.13/42.69	     c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
167.13/42.69	     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(c(a(x1)))
167.13/42.69	     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(a(x1))
167.13/42.69	     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
167.13/42.69	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
167.13/42.69	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
167.13/42.69	     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
167.13/42.69	     a#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1)
167.13/42.69	    Arctic Interpretation Processor:
167.13/42.69	     dimension: 2
167.13/42.69	     usable rules:
167.13/42.69	      a(x1) -> x1
167.13/42.69	      a(x1) -> b(x1)
167.13/42.69	      b(a(x1)) -> c(b(x1))
167.13/42.69	      c(c(x1)) -> a(c(a(x1)))
167.13/42.69	     interpretation:
167.13/42.69	      [c#](x0) = [-& 3 ]x0 + [0],
167.13/42.69	      
167.13/42.69	      [b#](x0) = [1 0]x0,
167.13/42.69	      
167.13/42.69	      [a#](x0) = [2 0]x0,
167.13/42.69	      
167.13/42.69	                [-& 2 ]     [0]
167.13/42.69	      [c](x0) = [2  2 ]x0 + [3],
167.13/42.69	      
167.13/42.69	                [0  -&]     [0 ]
167.13/42.69	      [b](x0) = [0  -&]x0 + [-&],
167.13/42.69	      
167.13/42.69	                [2 0]     [3]
167.13/42.69	      [a](x0) = [0 0]x0 + [0]
167.13/42.69	     orientation:
167.13/42.69	      a#(x1) = [2 0]x1 >= [1 0]x1 = b#(x1)
167.13/42.69	      
167.13/42.69	      b#(a(x1)) = [3 1]x1 + [4] >= [1 0]x1 = b#(x1)
167.13/42.69	      
167.13/42.69	      b#(a(x1)) = [3 1]x1 + [4] >= [3  -&]x1 + [0] = c#(b(x1))
167.13/42.69	      
167.13/42.69	      c#(c(x1)) = [5 5]x1 + [6] >= [2 0]x1 = a#(x1)
167.13/42.69	      
167.13/42.69	      c#(c(x1)) = [5 5]x1 + [6] >= [3 3]x1 + [3] = c#(a(x1))
167.13/42.69	      
167.13/42.69	      c#(c(x1)) = [5 5]x1 + [6] >= [4 4]x1 + [5] = a#(c(a(x1)))
167.13/42.69	      
167.13/42.69	              [2 0]     [3]           
167.13/42.69	      a(x1) = [0 0]x1 + [0] >= x1 = x1
167.13/42.69	      
167.13/42.69	              [2 0]     [3]    [0  -&]     [0 ]        
167.13/42.69	      a(x1) = [0 0]x1 + [0] >= [0  -&]x1 + [-&] = b(x1)
167.13/42.69	      
167.13/42.69	                 [2 0]     [3]    [2  -&]     [0]           
167.13/42.69	      b(a(x1)) = [2 0]x1 + [3] >= [2  -&]x1 + [3] = c(b(x1))
167.13/42.69	      
167.13/42.69	                 [4 4]     [5]    [4 4]     [5]              
167.13/42.69	      c(c(x1)) = [4 4]x1 + [5] >= [4 2]x1 + [5] = a(c(a(x1)))
167.13/42.69	     problem:
167.13/42.69	      DPs:
167.13/42.69	       a#(x1) -> b#(x1)
167.13/42.69	       b#(a(x1)) -> c#(b(x1))
167.13/42.69	      TRS:
167.13/42.69	       a(x1) -> x1
167.13/42.69	       a(x1) -> b(x1)
167.13/42.69	       b(a(x1)) -> c(b(x1))
167.13/42.69	       c(c(x1)) -> a(c(a(x1)))
167.13/42.69	     Restore Modifier:
167.13/42.69	      DPs:
167.13/42.69	       a#(x1) -> b#(x1)
167.13/42.69	       b#(a(x1)) -> c#(b(x1))
167.13/42.69	      TRS:
167.13/42.69	       a(x1) -> x1
167.13/42.69	       a(x1) -> b(x1)
167.13/42.69	       b(a(x1)) -> c(b(x1))
167.13/42.69	       c(c(x1)) -> a(c(a(x1)))
167.13/42.69	      EDG Processor:
167.13/42.69	       DPs:
167.13/42.69	        a#(x1) -> b#(x1)
167.13/42.69	        b#(a(x1)) -> c#(b(x1))
167.13/42.69	       TRS:
167.13/42.69	        a(x1) -> x1
167.13/42.69	        a(x1) -> b(x1)
167.13/42.69	        b(a(x1)) -> c(b(x1))
167.13/42.69	        c(c(x1)) -> a(c(a(x1)))
167.13/42.69	       graph:
167.13/42.69	        a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
167.13/42.69	       SCC Processor:
167.13/42.69	        #sccs: 0
167.13/42.69	        #rules: 0
167.13/42.69	        #arcs: 1/4
167.13/42.69	        
167.13/42.70	EOF