168.34/43.02	YES
168.34/43.03	
168.34/43.03	Problem:
168.34/43.03	 a(b(x1)) -> x1
168.34/43.03	 a(c(x1)) -> b(c(a(a(x1))))
168.34/43.03	 c(b(x1)) -> a(c(x1))
168.34/43.03	
168.34/43.03	Proof:
168.34/43.03	 String Reversal Processor:
168.34/43.03	  b(a(x1)) -> x1
168.34/43.03	  c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	  b(c(x1)) -> c(a(x1))
168.34/43.03	  DP Processor:
168.34/43.03	   DPs:
168.34/43.03	    c#(a(x1)) -> b#(x1)
168.34/43.03	    c#(a(x1)) -> c#(b(x1))
168.34/43.03	    b#(c(x1)) -> c#(a(x1))
168.34/43.03	   TRS:
168.34/43.03	    b(a(x1)) -> x1
168.34/43.03	    c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	    b(c(x1)) -> c(a(x1))
168.34/43.03	   TDG Processor:
168.34/43.03	    DPs:
168.34/43.03	     c#(a(x1)) -> b#(x1)
168.34/43.03	     c#(a(x1)) -> c#(b(x1))
168.34/43.03	     b#(c(x1)) -> c#(a(x1))
168.34/43.03	    TRS:
168.34/43.03	     b(a(x1)) -> x1
168.34/43.03	     c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	     b(c(x1)) -> c(a(x1))
168.34/43.03	    graph:
168.34/43.03	     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
168.34/43.03	     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
168.34/43.03	     c#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(a(x1))
168.34/43.03	     b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> c#(b(x1))
168.34/43.03	     b#(c(x1)) -> c#(a(x1)) -> c#(a(x1)) -> b#(x1)
168.34/43.03	    Arctic Interpretation Processor:
168.34/43.03	     dimension: 1
168.34/43.03	     usable rules:
168.34/43.03	      b(a(x1)) -> x1
168.34/43.03	      c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	      b(c(x1)) -> c(a(x1))
168.34/43.03	     interpretation:
168.34/43.03	      [c#](x0) = x0 + 0,
168.34/43.03	      
168.34/43.03	      [b#](x0) = x0 + 0,
168.34/43.03	      
168.34/43.03	      [c](x0) = 1x0 + 2,
168.34/43.03	      
168.34/43.03	      [a](x0) = x0 + 0,
168.34/43.03	      
168.34/43.03	      [b](x0) = x0 + 0
168.34/43.03	     orientation:
168.34/43.03	      c#(a(x1)) = x1 + 0 >= x1 + 0 = b#(x1)
168.34/43.03	      
168.34/43.03	      c#(a(x1)) = x1 + 0 >= x1 + 0 = c#(b(x1))
168.34/43.03	      
168.34/43.03	      b#(c(x1)) = 1x1 + 2 >= x1 + 0 = c#(a(x1))
168.34/43.03	      
168.34/43.03	      b(a(x1)) = x1 + 0 >= x1 = x1
168.34/43.03	      
168.34/43.03	      c(a(x1)) = 1x1 + 2 >= 1x1 + 2 = a(a(c(b(x1))))
168.34/43.03	      
168.34/43.03	      b(c(x1)) = 1x1 + 2 >= 1x1 + 2 = c(a(x1))
168.34/43.03	     problem:
168.34/43.03	      DPs:
168.34/43.03	       c#(a(x1)) -> b#(x1)
168.34/43.03	       c#(a(x1)) -> c#(b(x1))
168.34/43.03	      TRS:
168.34/43.03	       b(a(x1)) -> x1
168.34/43.03	       c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	       b(c(x1)) -> c(a(x1))
168.34/43.03	     Restore Modifier:
168.34/43.03	      DPs:
168.34/43.03	       c#(a(x1)) -> b#(x1)
168.34/43.03	       c#(a(x1)) -> c#(b(x1))
168.34/43.03	      TRS:
168.34/43.03	       b(a(x1)) -> x1
168.34/43.03	       c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	       b(c(x1)) -> c(a(x1))
168.34/43.03	      EDG Processor:
168.34/43.03	       DPs:
168.34/43.03	        c#(a(x1)) -> b#(x1)
168.34/43.03	        c#(a(x1)) -> c#(b(x1))
168.34/43.03	       TRS:
168.34/43.03	        b(a(x1)) -> x1
168.34/43.03	        c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	        b(c(x1)) -> c(a(x1))
168.34/43.03	       graph:
168.34/43.03	        c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
168.34/43.03	        c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
168.34/43.03	       SCC Processor:
168.34/43.03	        #sccs: 1
168.34/43.03	        #rules: 1
168.34/43.03	        #arcs: 2/4
168.34/43.03	        DPs:
168.34/43.03	         c#(a(x1)) -> c#(b(x1))
168.34/43.03	        TRS:
168.34/43.03	         b(a(x1)) -> x1
168.34/43.03	         c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	         b(c(x1)) -> c(a(x1))
168.34/43.03	        Bounds Processor:
168.34/43.03	         bound: 1
168.34/43.03	         enrichment: match-dp
168.34/43.03	         automaton:
168.34/43.03	          final states: {1}
168.34/43.03	          transitions:
168.34/43.03	           b1(36) -> 37*
168.34/43.03	           b1(23) -> 24*
168.34/43.03	           f50() -> 2*
168.34/43.03	           c{#,0}(3) -> 1*
168.34/43.03	           b0(10) -> 11*
168.34/43.03	           b0(2) -> 3*
168.34/43.03	           c0(26) -> 27*
168.34/43.03	           c0(11) -> 12*
168.34/43.03	           c0(8) -> 9*
168.34/43.03	           a0(27) -> 28*
168.34/43.03	           a0(12) -> 13*
168.34/43.03	           a0(7) -> 8*
168.34/43.03	           a0(28) -> 29*
168.34/43.03	           a0(13) -> 14*
168.34/43.03	           c{#,1}(24) -> 25*
168.34/43.03	           2 -> 11,7,3
168.34/43.03	           7 -> 10*
168.34/43.03	           9 -> 11,3
168.34/43.03	           12 -> 24*
168.34/43.03	           13 -> 23*
168.34/43.03	           14 -> 12,24,26,9,3
168.34/43.03	           24 -> 26*
168.34/43.03	           25 -> 1*
168.34/43.03	           27 -> 37,24
168.34/43.03	           28 -> 36*
168.34/43.03	           29 -> 27,12,24
168.34/43.03	           37 -> 24*
168.34/43.03	         problem:
168.34/43.03	          DPs:
168.34/43.03	           
168.34/43.03	          TRS:
168.34/43.03	           b(a(x1)) -> x1
168.34/43.03	           c(a(x1)) -> a(a(c(b(x1))))
168.34/43.03	           b(c(x1)) -> c(a(x1))
168.34/43.03	         Qed
168.34/43.03	EOF