167.36/42.81	YES
167.36/42.81	
167.36/42.81	Problem:
167.36/42.81	 a(x1) -> b(x1)
167.36/42.81	 a(c(x1)) -> c(c(a(b(x1))))
167.36/42.81	 b(b(x1)) -> a(x1)
167.36/42.81	
167.36/42.81	Proof:
167.36/42.81	 String Reversal Processor:
167.36/42.81	  a(x1) -> b(x1)
167.36/42.81	  c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	  b(b(x1)) -> a(x1)
167.36/42.81	  DP Processor:
167.36/42.81	   DPs:
167.36/42.81	    a#(x1) -> b#(x1)
167.36/42.81	    c#(a(x1)) -> c#(x1)
167.36/42.81	    c#(a(x1)) -> c#(c(x1))
167.36/42.81	    c#(a(x1)) -> a#(c(c(x1)))
167.36/42.81	    c#(a(x1)) -> b#(a(c(c(x1))))
167.36/42.81	    b#(b(x1)) -> a#(x1)
167.36/42.81	   TRS:
167.36/42.81	    a(x1) -> b(x1)
167.36/42.81	    c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	    b(b(x1)) -> a(x1)
167.36/42.81	   TDG Processor:
167.36/42.81	    DPs:
167.36/42.81	     a#(x1) -> b#(x1)
167.36/42.81	     c#(a(x1)) -> c#(x1)
167.36/42.81	     c#(a(x1)) -> c#(c(x1))
167.36/42.81	     c#(a(x1)) -> a#(c(c(x1)))
167.36/42.81	     c#(a(x1)) -> b#(a(c(c(x1))))
167.36/42.81	     b#(b(x1)) -> a#(x1)
167.36/42.81	    TRS:
167.36/42.81	     a(x1) -> b(x1)
167.36/42.81	     c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	     b(b(x1)) -> a(x1)
167.36/42.81	    graph:
167.36/42.81	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(a(c(c(x1))))
167.36/42.81	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(c(c(x1)))
167.36/42.81	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
167.36/42.81	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1)
167.36/42.81	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(c(x1))))
167.36/42.81	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(c(x1)))
167.36/42.81	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1))
167.36/42.81	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
167.36/42.81	     c#(a(x1)) -> b#(a(c(c(x1)))) -> b#(b(x1)) -> a#(x1)
167.36/42.81	     c#(a(x1)) -> a#(c(c(x1))) -> a#(x1) -> b#(x1)
167.36/42.81	     b#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
167.36/42.81	     a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(x1)
167.36/42.81	    SCC Processor:
167.36/42.81	     #sccs: 2
167.36/42.81	     #rules: 4
167.36/42.81	     #arcs: 12/36
167.36/42.81	     DPs:
167.36/42.81	      c#(a(x1)) -> c#(c(x1))
167.36/42.81	      c#(a(x1)) -> c#(x1)
167.36/42.81	     TRS:
167.36/42.81	      a(x1) -> b(x1)
167.36/42.81	      c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	      b(b(x1)) -> a(x1)
167.36/42.81	     Arctic Interpretation Processor:
167.36/42.81	      dimension: 2
167.36/42.81	      usable rules:
167.36/42.81	       a(x1) -> b(x1)
167.36/42.81	       c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	       b(b(x1)) -> a(x1)
167.36/42.81	      interpretation:
167.36/42.81	       [c#](x0) = [0 0]x0 + [0],
167.36/42.81	       
167.36/42.81	                 [0 0]     [-&]
167.36/42.81	       [c](x0) = [0 0]x0 + [2 ],
167.36/42.81	       
167.36/42.81	                 [0  1 ]     [0]
167.36/42.81	       [b](x0) = [0  -&]x0 + [2],
167.36/42.81	       
167.36/42.81	                 [1  1 ]     [3]
167.36/42.81	       [a](x0) = [0  -&]x0 + [2]
167.36/42.81	      orientation:
167.36/42.81	       c#(a(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [2] = c#(c(x1))
167.36/42.81	       
167.36/42.81	       c#(a(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [0] = c#(x1)
167.36/42.81	       
167.36/42.81	               [1  1 ]     [3]    [0  1 ]     [0]        
167.36/42.81	       a(x1) = [0  -&]x1 + [2] >= [0  -&]x1 + [2] = b(x1)
167.36/42.81	       
167.36/42.81	                  [1 1]     [3]    [1 1]     [3]                 
167.36/42.81	       c(a(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = b(a(c(c(x1))))
167.36/42.81	       
167.36/42.81	                  [1 1]     [3]    [1  1 ]     [3]        
167.36/42.81	       b(b(x1)) = [0 1]x1 + [2] >= [0  -&]x1 + [2] = a(x1)
167.36/42.81	      problem:
167.36/42.81	       DPs:
167.36/42.81	        
167.36/42.81	       TRS:
167.36/42.81	        a(x1) -> b(x1)
167.36/42.81	        c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	        b(b(x1)) -> a(x1)
167.36/42.81	      Qed
167.36/42.81	     
167.36/42.81	     DPs:
167.36/42.81	      a#(x1) -> b#(x1)
167.36/42.81	      b#(b(x1)) -> a#(x1)
167.36/42.81	     TRS:
167.36/42.81	      a(x1) -> b(x1)
167.36/42.81	      c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	      b(b(x1)) -> a(x1)
167.36/42.81	     Usable Rule Processor:
167.36/42.81	      DPs:
167.36/42.81	       a#(x1) -> b#(x1)
167.36/42.81	       b#(b(x1)) -> a#(x1)
167.36/42.81	      TRS:
167.36/42.81	       
167.36/42.81	      Arctic Interpretation Processor:
167.36/42.81	       dimension: 4
167.36/42.81	       usable rules:
167.36/42.81	        
167.36/42.81	       interpretation:
167.36/42.81	        [b#](x0) = [0  -& -& -&]x0,
167.36/42.81	        
167.36/42.81	        [a#](x0) = [0  -& -& -&]x0,
167.36/42.81	        
167.36/42.81	                  [1 0 0 1]     [0]
167.36/42.81	                  [0 0 0 0]     [0]
167.36/42.81	        [b](x0) = [0 0 0 0]x0 + [0]
167.36/42.81	                  [0 0 0 0]     [0]
167.36/42.81	       orientation:
167.36/42.81	        a#(x1) = [0  -& -& -&]x1 >= [0  -& -& -&]x1 = b#(x1)
167.36/42.81	        
167.36/42.81	        b#(b(x1)) = [1 0 0 1]x1 + [0] >= [0  -& -& -&]x1 = a#(x1)
167.36/42.81	       problem:
167.36/42.81	        DPs:
167.36/42.81	         a#(x1) -> b#(x1)
167.36/42.81	        TRS:
167.36/42.81	         
167.36/42.81	       Restore Modifier:
167.36/42.81	        DPs:
167.36/42.81	         a#(x1) -> b#(x1)
167.36/42.81	        TRS:
167.36/42.81	         a(x1) -> b(x1)
167.36/42.81	         c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	         b(b(x1)) -> a(x1)
167.36/42.81	        EDG Processor:
167.36/42.81	         DPs:
167.36/42.81	          a#(x1) -> b#(x1)
167.36/42.81	         TRS:
167.36/42.81	          a(x1) -> b(x1)
167.36/42.81	          c(a(x1)) -> b(a(c(c(x1))))
167.36/42.81	          b(b(x1)) -> a(x1)
167.36/42.81	         graph:
167.36/42.81	          
167.36/42.81	         SCC Processor:
167.36/42.81	          #sccs: 0
167.36/42.81	          #rules: 0
167.36/42.81	          #arcs: 0/1
167.36/42.81	          
167.36/42.82	EOF