7.81/2.33	YES
7.81/2.33	
7.81/2.33	Problem:
7.81/2.33	 a(c(a(x1))) -> c(a(c(x1)))
7.81/2.33	 a(a(b(x1))) -> a(d(b(x1)))
7.81/2.33	 a(b(x1)) -> b(a(a(x1)))
7.81/2.33	 d(d(x1)) -> a(d(b(x1)))
7.81/2.33	 b(b(x1)) -> b(c(x1))
7.81/2.33	 a(d(c(x1))) -> c(a(x1))
7.81/2.33	 b(c(x1)) -> a(a(a(x1)))
7.81/2.33	
7.81/2.33	Proof:
7.81/2.33	 Matrix Interpretation Processor: dim=3
7.81/2.33	  
7.81/2.33	  interpretation:
7.81/2.33	             [1 0 1]     [0]
7.81/2.33	   [d](x0) = [1 0 1]x0 + [1]
7.81/2.33	             [1 1 1]     [0],
7.81/2.33	   
7.81/2.33	             [1 1 0]     [0]
7.81/2.33	   [b](x0) = [1 1 0]x0 + [1]
7.81/2.33	             [0 0 0]     [0],
7.81/2.33	   
7.81/2.33	             [1 1 0]  
7.81/2.33	   [c](x0) = [0 0 0]x0
7.81/2.33	             [0 0 0]  ,
7.81/2.33	   
7.81/2.33	             [1 0 0]  
7.81/2.33	   [a](x0) = [0 1 0]x0
7.81/2.33	             [0 0 0]  
7.81/2.33	  orientation:
7.81/2.33	                 [1 1 0]      [1 1 0]                
7.81/2.33	   a(c(a(x1))) = [0 0 0]x1 >= [0 0 0]x1 = c(a(c(x1)))
7.81/2.33	                 [0 0 0]      [0 0 0]                
7.81/2.33	   
7.81/2.33	                 [1 1 0]     [0]    [1 1 0]     [0]              
7.81/2.33	   a(a(b(x1))) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = a(d(b(x1)))
7.81/2.33	                 [0 0 0]     [0]    [0 0 0]     [0]              
7.81/2.33	   
7.81/2.33	              [1 1 0]     [0]    [1 1 0]     [0]              
7.81/2.33	   a(b(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = b(a(a(x1)))
7.81/2.33	              [0 0 0]     [0]    [0 0 0]     [0]              
7.81/2.33	   
7.81/2.33	              [2 1 2]     [0]    [1 1 0]     [0]              
7.81/2.33	   d(d(x1)) = [2 1 2]x1 + [1] >= [1 1 0]x1 + [1] = a(d(b(x1)))
7.81/2.33	              [3 1 3]     [1]    [0 0 0]     [0]              
7.81/2.33	   
7.81/2.33	              [2 2 0]     [1]    [1 1 0]     [0]           
7.81/2.33	   b(b(x1)) = [2 2 0]x1 + [2] >= [1 1 0]x1 + [1] = b(c(x1))
7.81/2.33	              [0 0 0]     [0]    [0 0 0]     [0]           
7.81/2.33	   
7.81/2.33	                 [1 1 0]     [0]    [1 1 0]             
7.81/2.33	   a(d(c(x1))) = [1 1 0]x1 + [1] >= [0 0 0]x1 = c(a(x1))
7.81/2.33	                 [0 0 0]     [0]    [0 0 0]             
7.81/2.33	   
7.81/2.33	              [1 1 0]     [0]    [1 0 0]                
7.81/2.33	   b(c(x1)) = [1 1 0]x1 + [1] >= [0 1 0]x1 = a(a(a(x1)))
7.81/2.33	              [0 0 0]     [0]    [0 0 0]                
7.81/2.33	  problem:
7.81/2.33	   a(c(a(x1))) -> c(a(c(x1)))
7.81/2.33	   a(a(b(x1))) -> a(d(b(x1)))
7.81/2.33	   a(b(x1)) -> b(a(a(x1)))
7.81/2.33	   d(d(x1)) -> a(d(b(x1)))
7.81/2.33	   a(d(c(x1))) -> c(a(x1))
7.81/2.33	   b(c(x1)) -> a(a(a(x1)))
7.81/2.33	  String Reversal Processor:
7.81/2.33	   a(c(a(x1))) -> c(a(c(x1)))
7.81/2.33	   b(a(a(x1))) -> b(d(a(x1)))
7.81/2.33	   b(a(x1)) -> a(a(b(x1)))
7.81/2.33	   d(d(x1)) -> b(d(a(x1)))
7.81/2.33	   c(d(a(x1))) -> a(c(x1))
7.81/2.33	   c(b(x1)) -> a(a(a(x1)))
7.81/2.33	   Bounds Processor:
7.81/2.33	    bound: 2
7.81/2.33	    enrichment: match
7.81/2.33	    automaton:
7.81/2.33	     final states: {11,4,8,5,1}
7.81/2.33	     transitions:
7.81/2.33	      c1(25) -> 26*
7.81/2.33	      c1(15) -> 16*
7.81/2.33	      c1(27) -> 28*
7.81/2.33	      c1(39) -> 40*
7.81/2.33	      c1(29) -> 30*
7.81/2.33	      c1(41) -> 42*
7.81/2.33	      c1(33) -> 34*
7.81/2.33	      c1(13) -> 14*
7.81/2.33	      a1(14) -> 15*
7.81/2.33	      a1(26) -> 27*
7.81/2.33	      c2(55) -> 56*
7.81/2.33	      c2(45) -> 46*
7.81/2.33	      c2(47) -> 48*
7.81/2.33	      a2(46) -> 47*
7.81/2.33	      f40() -> 2*
7.81/2.33	      c0(2) -> 3*
7.81/2.33	      c0(4) -> 1*
7.81/2.33	      a0(10) -> 8*
7.81/2.33	      a0(12) -> 11*
7.81/2.33	      a0(2) -> 6*
7.81/2.33	      a0(9) -> 10*
7.81/2.33	      a0(6) -> 12*
7.81/2.33	      a0(3) -> 4*
7.81/2.33	      b0(7) -> 5*
7.81/2.33	      b0(2) -> 9*
7.81/2.33	      d0(6) -> 7*
7.81/2.33	      1 -> 6,4
7.81/2.33	      2 -> 41*
7.81/2.33	      3 -> 13*
7.81/2.33	      4 -> 42,14,25,3
7.81/2.33	      5 -> 9*
7.81/2.33	      6 -> 39*
7.81/2.33	      8 -> 9*
7.81/2.33	      11 -> 42,14,25,3
7.81/2.33	      12 -> 33*
7.81/2.33	      14 -> 45,25
7.81/2.33	      16 -> 47,27,15,4,12
7.81/2.33	      26 -> 55,29
7.81/2.33	      28 -> 4,11
7.81/2.33	      30 -> 14*
7.81/2.33	      34 -> 14*
7.81/2.33	      40 -> 14*
7.81/2.33	      42 -> 14*
7.81/2.33	      48 -> 15*
7.81/2.33	      56 -> 46*
7.81/2.33	    problem:
7.81/2.33	     
7.81/2.33	    Qed
7.81/2.34	EOF