3.42/1.22	YES
3.42/1.22	
3.42/1.22	Problem:
3.42/1.22	 a(a(x1)) -> b(b(b(x1)))
3.42/1.22	 b(b(x1)) -> c(c(c(x1)))
3.42/1.22	 c(c(x1)) -> d(d(d(x1)))
3.42/1.22	 b(x1) -> d(d(x1))
3.42/1.22	 c(d(d(x1))) -> a(x1)
3.42/1.22	
3.42/1.22	Proof:
3.42/1.22	 Matrix Interpretation Processor: dim=1
3.42/1.22	  
3.42/1.22	  interpretation:
3.42/1.22	   [d](x0) = x0 + 4,
3.42/1.22	   
3.42/1.22	   [c](x0) = x0 + 6,
3.42/1.22	   
3.42/1.22	   [b](x0) = x0 + 9,
3.42/1.22	   
3.42/1.22	   [a](x0) = x0 + 14
3.42/1.22	  orientation:
3.42/1.22	   a(a(x1)) = x1 + 28 >= x1 + 27 = b(b(b(x1)))
3.42/1.22	   
3.42/1.22	   b(b(x1)) = x1 + 18 >= x1 + 18 = c(c(c(x1)))
3.42/1.22	   
3.42/1.22	   c(c(x1)) = x1 + 12 >= x1 + 12 = d(d(d(x1)))
3.42/1.22	   
3.42/1.22	   b(x1) = x1 + 9 >= x1 + 8 = d(d(x1))
3.42/1.22	   
3.42/1.22	   c(d(d(x1))) = x1 + 14 >= x1 + 14 = a(x1)
3.42/1.22	  problem:
3.42/1.22	   b(b(x1)) -> c(c(c(x1)))
3.42/1.22	   c(c(x1)) -> d(d(d(x1)))
3.42/1.22	   c(d(d(x1))) -> a(x1)
3.42/1.22	  String Reversal Processor:
3.42/1.22	   b(b(x1)) -> c(c(c(x1)))
3.42/1.22	   c(c(x1)) -> d(d(d(x1)))
3.42/1.22	   d(d(c(x1))) -> a(x1)
3.42/1.22	   Bounds Processor:
3.42/1.22	    bound: 2
3.42/1.22	    enrichment: match
3.42/1.22	    automaton:
3.42/1.22	     final states: {5}
3.42/1.22	     transitions:
3.42/1.22	      a1(52) -> 53*
3.42/1.22	      a1(22) -> 23*
3.42/1.22	      d1(15) -> 16*
3.42/1.22	      d1(34) -> 35*
3.42/1.22	      d1(14) -> 15*
3.42/1.22	      d1(16) -> 17*
3.42/1.22	      c1(10) -> 11*
3.42/1.22	      c1(12) -> 13*
3.42/1.22	      c1(11) -> 12*
3.42/1.22	      a2(80) -> 81*
3.42/1.22	      a2(76) -> 77*
3.42/1.22	      a2(68) -> 69*
3.42/1.22	      d2(45) -> 46*
3.42/1.22	      d2(25) -> 26*
3.42/1.22	      d2(37) -> 38*
3.42/1.22	      d2(44) -> 45*
3.42/1.22	      d2(24) -> 25*
3.42/1.22	      d2(46) -> 47*
3.42/1.22	      d2(36) -> 37*
3.42/1.22	      d2(26) -> 27*
3.42/1.22	      d2(38) -> 39*
3.42/1.22	      b0(5) -> 5*
3.42/1.22	      c0(5) -> 5*
3.42/1.22	      d0(5) -> 5*
3.42/1.22	      a0(5) -> 5*
3.42/1.22	      5 -> 22,14,10
3.42/1.22	      10 -> 76,36
3.42/1.22	      11 -> 80,24
3.42/1.22	      12 -> 68,52,44,34
3.42/1.22	      13 -> 5*
3.42/1.22	      17 -> 11,5
3.42/1.22	      23 -> 38,37,16,15,5
3.42/1.22	      27 -> 13*
3.42/1.22	      35 -> 15*
3.42/1.22	      39 -> 12*
3.42/1.22	      47 -> 11*
3.42/1.22	      53 -> 37,5,14,10,22,15
3.42/1.22	      69 -> 38,16
3.42/1.22	      77 -> 26*
3.42/1.22	      81 -> 46,16
3.42/1.22	    problem:
3.42/1.22	     
3.42/1.22	    Qed
3.42/1.22	EOF