179.43/45.45	YES
179.43/45.45	
179.43/45.45	Problem:
179.43/45.45	 a(x1) -> x1
179.43/45.45	 a(a(b(x1))) -> c(c(b(a(x1))))
179.43/45.45	 b(c(x1)) -> a(b(x1))
179.43/45.45	
179.43/45.45	Proof:
179.43/45.45	 String Reversal Processor:
179.43/45.45	  a(x1) -> x1
179.43/45.45	  b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	  c(b(x1)) -> b(a(x1))
179.43/45.45	  DP Processor:
179.43/45.45	   DPs:
179.43/45.45	    b#(a(a(x1))) -> c#(x1)
179.43/45.45	    b#(a(a(x1))) -> c#(c(x1))
179.43/45.45	    b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	    b#(a(a(x1))) -> a#(b(c(c(x1))))
179.43/45.45	    c#(b(x1)) -> a#(x1)
179.43/45.45	    c#(b(x1)) -> b#(a(x1))
179.43/45.45	   TRS:
179.43/45.45	    a(x1) -> x1
179.43/45.45	    b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	    c(b(x1)) -> b(a(x1))
179.43/45.45	   TDG Processor:
179.43/45.45	    DPs:
179.43/45.45	     b#(a(a(x1))) -> c#(x1)
179.43/45.45	     b#(a(a(x1))) -> c#(c(x1))
179.43/45.45	     b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	     b#(a(a(x1))) -> a#(b(c(c(x1))))
179.43/45.45	     c#(b(x1)) -> a#(x1)
179.43/45.45	     c#(b(x1)) -> b#(a(x1))
179.43/45.45	    TRS:
179.43/45.45	     a(x1) -> x1
179.43/45.45	     b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	     c(b(x1)) -> b(a(x1))
179.43/45.45	    graph:
179.43/45.45	     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(c(x1))))
179.43/45.45	     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(c(x1))
179.43/45.45	     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
179.43/45.45	     b#(a(a(x1))) -> c#(c(x1)) -> c#(b(x1)) -> b#(a(x1))
179.43/45.45	     b#(a(a(x1))) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
179.43/45.45	     b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
179.43/45.45	     b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> a#(x1)
179.43/45.45	     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> a#(b(c(c(x1))))
179.43/45.45	     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> c#(c(x1))
179.43/45.45	     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> c#(x1)
179.43/45.45	    SCC Processor:
179.43/45.45	     #sccs: 1
179.43/45.45	     #rules: 4
179.43/45.45	     #arcs: 12/36
179.43/45.45	     DPs:
179.43/45.45	      c#(b(x1)) -> b#(a(x1))
179.43/45.45	      b#(a(a(x1))) -> c#(x1)
179.43/45.45	      b#(a(a(x1))) -> c#(c(x1))
179.43/45.45	      b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	     TRS:
179.43/45.45	      a(x1) -> x1
179.43/45.45	      b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	      c(b(x1)) -> b(a(x1))
179.43/45.45	     Arctic Interpretation Processor:
179.43/45.45	      dimension: 1
179.43/45.45	      usable rules:
179.43/45.45	       a(x1) -> x1
179.43/45.45	       b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	       c(b(x1)) -> b(a(x1))
179.43/45.45	      interpretation:
179.43/45.45	       [c#](x0) = x0 + 0,
179.43/45.45	       
179.43/45.45	       [b#](x0) = 1x0,
179.43/45.45	       
179.43/45.45	       [c](x0) = x0,
179.43/45.45	       
179.43/45.45	       [b](x0) = 1x0 + 1,
179.43/45.45	       
179.43/45.45	       [a](x0) = x0 + 0
179.43/45.45	      orientation:
179.43/45.45	       c#(b(x1)) = 1x1 + 1 >= 1x1 + 1 = b#(a(x1))
179.43/45.45	       
179.43/45.45	       b#(a(a(x1))) = 1x1 + 1 >= x1 + 0 = c#(x1)
179.43/45.45	       
179.43/45.45	       b#(a(a(x1))) = 1x1 + 1 >= x1 + 0 = c#(c(x1))
179.43/45.45	       
179.43/45.45	       b#(a(a(x1))) = 1x1 + 1 >= 1x1 = b#(c(c(x1)))
179.43/45.45	       
179.43/45.45	       a(x1) = x1 + 0 >= x1 = x1
179.43/45.45	       
179.43/45.45	       b(a(a(x1))) = 1x1 + 1 >= 1x1 + 1 = a(b(c(c(x1))))
179.43/45.45	       
179.43/45.45	       c(b(x1)) = 1x1 + 1 >= 1x1 + 1 = b(a(x1))
179.43/45.45	      problem:
179.43/45.45	       DPs:
179.43/45.45	        c#(b(x1)) -> b#(a(x1))
179.43/45.45	        b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	       TRS:
179.43/45.45	        a(x1) -> x1
179.43/45.45	        b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	        c(b(x1)) -> b(a(x1))
179.43/45.45	      Restore Modifier:
179.43/45.45	       DPs:
179.43/45.45	        c#(b(x1)) -> b#(a(x1))
179.43/45.45	        b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	       TRS:
179.43/45.45	        a(x1) -> x1
179.43/45.45	        b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	        c(b(x1)) -> b(a(x1))
179.43/45.45	       EDG Processor:
179.43/45.45	        DPs:
179.43/45.45	         c#(b(x1)) -> b#(a(x1))
179.43/45.45	         b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	        TRS:
179.43/45.45	         a(x1) -> x1
179.43/45.45	         b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	         c(b(x1)) -> b(a(x1))
179.43/45.45	        graph:
179.43/45.45	         c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	         b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	        SCC Processor:
179.43/45.45	         #sccs: 1
179.43/45.45	         #rules: 1
179.43/45.45	         #arcs: 2/4
179.43/45.45	         DPs:
179.43/45.45	          b#(a(a(x1))) -> b#(c(c(x1)))
179.43/45.45	         TRS:
179.43/45.45	          a(x1) -> x1
179.43/45.45	          b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.45	          c(b(x1)) -> b(a(x1))
179.43/45.45	         Bounds Processor:
179.43/45.45	          bound: 1
179.43/45.45	          enrichment: match-dp
179.43/45.45	          automaton:
179.43/45.45	           final states: {5}
179.43/45.45	           transitions:
179.43/45.45	            b{#,0}(7) -> 5*
179.43/45.45	            a0(2) -> 2*
179.43/45.45	            a0(1) -> 2*
179.43/45.45	            a0(3) -> 2*
179.43/45.45	            c0(2) -> 1*
179.43/45.45	            c0(4) -> 6*
179.43/45.45	            c0(6) -> 7*
179.43/45.45	            c0(1) -> 1*
179.43/45.45	            c0(3) -> 1*
179.43/45.45	            b0(2) -> 3*
179.43/45.45	            b0(1) -> 3*
179.43/45.45	            b0(3) -> 3*
179.43/45.45	            b{#,1}(14) -> 15*
179.43/45.45	            c1(50) -> 51*
179.43/45.45	            c1(35) -> 36*
179.43/45.45	            c1(12) -> 13*
179.43/45.45	            c1(34) -> 35*
179.43/45.45	            c1(13) -> 14*
179.43/45.46	            b1(22) -> 23*
179.43/45.46	            b1(17) -> 18*
179.43/45.46	            b1(29) -> 30*
179.43/45.46	            b1(36) -> 37*
179.43/45.46	            a1(55) -> 56*
179.43/45.46	            a1(37) -> 38*
179.43/45.46	            a1(61) -> 62*
179.43/45.46	            a1(46) -> 47*
179.43/45.46	            a1(16) -> 17*
179.43/45.46	            a1(28) -> 29*
179.43/45.46	            a1(23) -> 24*
179.43/45.46	            1 -> 2,4
179.43/45.46	            2 -> 16,12,3,4
179.43/45.46	            3 -> 7,6,1,2,4
179.43/45.46	            14 -> 22*
179.43/45.46	            15 -> 5*
179.43/45.46	            16 -> 34,17
179.43/45.46	            17 -> 28*
179.43/45.46	            18 -> 51,35,13
179.43/45.46	            22 -> 46*
179.43/45.46	            23 -> 24,13
179.43/45.46	            24 -> 18,13
179.43/45.46	            28 -> 29*
179.43/45.46	            29 -> 61,13,51
179.43/45.46	            30 -> 36,14
179.43/45.46	            36 -> 55*
179.43/45.46	            37 -> 50,38,14
179.43/45.46	            38 -> 30,14,22
179.43/45.46	            46 -> 47,29
179.43/45.46	            47 -> 29*
179.43/45.46	            51 -> 35*
179.43/45.46	            55 -> 56,17,28
179.43/45.46	            56 -> 17*
179.43/45.46	            61 -> 62,29,13,51
179.43/45.46	            62 -> 29*
179.43/45.46	          problem:
179.43/45.46	           DPs:
179.43/45.46	            
179.43/45.46	           TRS:
179.43/45.46	            a(x1) -> x1
179.43/45.46	            b(a(a(x1))) -> a(b(c(c(x1))))
179.43/45.46	            c(b(x1)) -> b(a(x1))
179.43/45.46	          Qed
179.43/45.46	EOF