167.73/42.89	YES
167.73/42.90	
167.73/42.90	Problem:
167.73/42.90	 a(x1) -> x1
167.73/42.90	 a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	 b(b(x1)) -> x1
167.73/42.90	 c(c(x1)) -> x1
167.73/42.90	
167.73/42.90	Proof:
167.73/42.90	 DP Processor:
167.73/42.90	  DPs:
167.73/42.90	   a#(b(x1)) -> c#(x1)
167.73/42.90	   a#(b(x1)) -> a#(c(x1))
167.73/42.90	   a#(b(x1)) -> a#(a(c(x1)))
167.73/42.90	   a#(b(x1)) -> b#(a(a(c(x1))))
167.73/42.90	   a#(b(x1)) -> b#(b(a(a(c(x1)))))
167.73/42.90	  TRS:
167.73/42.90	   a(x1) -> x1
167.73/42.90	   a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	   b(b(x1)) -> x1
167.73/42.90	   c(c(x1)) -> x1
167.73/42.90	  TDG Processor:
167.73/42.90	   DPs:
167.73/42.90	    a#(b(x1)) -> c#(x1)
167.73/42.90	    a#(b(x1)) -> a#(c(x1))
167.73/42.90	    a#(b(x1)) -> a#(a(c(x1)))
167.73/42.90	    a#(b(x1)) -> b#(a(a(c(x1))))
167.73/42.90	    a#(b(x1)) -> b#(b(a(a(c(x1)))))
167.73/42.90	   TRS:
167.73/42.90	    a(x1) -> x1
167.73/42.90	    a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	    b(b(x1)) -> x1
167.73/42.90	    c(c(x1)) -> x1
167.73/42.90	   graph:
167.73/42.90	    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(b(a(a(c(x1)))))
167.73/42.90	    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(a(a(c(x1))))
167.73/42.90	    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(a(c(x1)))
167.73/42.90	    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(c(x1))
167.73/42.90	    a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> c#(x1)
167.73/42.90	    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(b(a(a(c(x1)))))
167.73/42.90	    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> b#(a(a(c(x1))))
167.73/42.90	    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> a#(a(c(x1)))
167.73/42.90	    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> a#(c(x1))
167.73/42.90	    a#(b(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(x1)
167.73/42.90	   SCC Processor:
167.73/42.90	    #sccs: 1
167.73/42.90	    #rules: 2
167.73/42.90	    #arcs: 10/25
167.73/42.90	    DPs:
167.73/42.90	     a#(b(x1)) -> a#(c(x1))
167.73/42.90	     a#(b(x1)) -> a#(a(c(x1)))
167.73/42.90	    TRS:
167.73/42.90	     a(x1) -> x1
167.73/42.90	     a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	     b(b(x1)) -> x1
167.73/42.90	     c(c(x1)) -> x1
167.73/42.90	    Bounds Processor:
167.73/42.90	     bound: 1
167.73/42.90	     enrichment: match-dp
167.73/42.90	     automaton:
167.73/42.90	      final states: {4}
167.73/42.90	      transitions:
167.73/42.90	       a{#,0}(7) -> 4*
167.73/42.90	       a{#,0}(26) -> 27*
167.73/42.90	       c0(5) -> 6*
167.73/42.90	       a0(30) -> 31*
167.73/42.90	       a0(11) -> 12*
167.73/42.90	       a0(6) -> 7*
167.73/42.90	       b0(12) -> 13*
167.73/42.90	       b0(13) -> 14*
167.73/42.90	       a{#,1}(24) -> 25*
167.73/42.90	       c1(22) -> 23*
167.73/42.90	       a1(23) -> 24*
167.73/42.90	       f60() -> 5*
167.73/42.90	       4 -> 27*
167.73/42.90	       5 -> 23,26,24,31,13,22,6,7
167.73/42.90	       6 -> 7*
167.73/42.90	       7 -> 11*
167.73/42.90	       11 -> 12*
167.73/42.90	       12 -> 14,7,11
167.73/42.90	       13 -> 22*
167.73/42.90	       14 -> 24,30,7
167.73/42.90	       23 -> 24,26
167.73/42.90	       24 -> 30*
167.73/42.90	       25 -> 4*
167.73/42.90	       27 -> 4*
167.73/42.90	       30 -> 31*
167.73/42.90	       31 -> 12*
167.73/42.90	     problem:
167.73/42.90	      DPs:
167.73/42.90	       a#(b(x1)) -> a#(c(x1))
167.73/42.90	      TRS:
167.73/42.90	       a(x1) -> x1
167.73/42.90	       a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	       b(b(x1)) -> x1
167.73/42.90	       c(c(x1)) -> x1
167.73/42.90	     Restore Modifier:
167.73/42.90	      DPs:
167.73/42.90	       a#(b(x1)) -> a#(c(x1))
167.73/42.90	      TRS:
167.73/42.90	       a(x1) -> x1
167.73/42.90	       a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	       b(b(x1)) -> x1
167.73/42.90	       c(c(x1)) -> x1
167.73/42.90	      EDG Processor:
167.73/42.90	       DPs:
167.73/42.90	        a#(b(x1)) -> a#(c(x1))
167.73/42.90	       TRS:
167.73/42.90	        a(x1) -> x1
167.73/42.90	        a(b(x1)) -> b(b(a(a(c(x1)))))
167.73/42.90	        b(b(x1)) -> x1
167.73/42.90	        c(c(x1)) -> x1
167.73/42.90	       graph:
167.73/42.90	        a#(b(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(c(x1))
167.73/42.90	       Usable Rule Processor:
167.73/42.90	        DPs:
167.73/42.90	         a#(b(x1)) -> a#(c(x1))
167.73/42.90	        TRS:
167.73/42.90	         c(c(x1)) -> x1
167.73/42.90	        Arctic Interpretation Processor:
167.73/42.90	         dimension: 1
167.73/42.90	         usable rules:
167.73/42.90	          c(c(x1)) -> x1
167.73/42.90	         interpretation:
167.73/42.90	          [a#](x0) = 15x0 + 0,
167.73/42.90	          
167.73/42.90	          [c](x0) = x0 + 9,
167.73/42.90	          
167.73/42.90	          [b](x0) = 1x0 + 12
167.73/42.90	         orientation:
167.73/42.90	          a#(b(x1)) = 16x1 + 27 >= 15x1 + 24 = a#(c(x1))
167.73/42.90	          
167.73/42.90	          c(c(x1)) = x1 + 9 >= x1 = x1
167.73/42.90	         problem:
167.73/42.90	          DPs:
167.73/42.90	           
167.73/42.90	          TRS:
167.73/42.90	           c(c(x1)) -> x1
167.73/42.90	         Qed
167.73/42.91	EOF