7.40/2.21	YES
7.40/2.22	
7.40/2.22	Problem:
7.40/2.22	 b(b(x1)) -> c(d(x1))
7.40/2.22	 c(c(x1)) -> d(d(d(x1)))
7.40/2.22	 c(x1) -> g(x1)
7.40/2.22	 d(d(x1)) -> c(f(x1))
7.40/2.22	 d(d(d(x1))) -> g(c(x1))
7.40/2.22	 f(x1) -> a(g(x1))
7.40/2.22	 g(x1) -> d(a(b(x1)))
7.40/2.22	 g(g(x1)) -> b(c(x1))
7.40/2.22	
7.40/2.22	Proof:
7.40/2.22	 Matrix Interpretation Processor: dim=2
7.40/2.22	  
7.40/2.22	  interpretation:
7.40/2.22	             [1 0]  
7.40/2.22	   [a](x0) = [0 0]x0,
7.40/2.22	   
7.40/2.22	             [1 2]     [1]
7.40/2.22	   [f](x0) = [0 0]x0 + [0],
7.40/2.22	   
7.40/2.22	             [1 2]     [1]
7.40/2.22	   [g](x0) = [0 0]x0 + [1],
7.40/2.22	   
7.40/2.22	             [1 2]     [1]
7.40/2.22	   [c](x0) = [0 0]x0 + [1],
7.40/2.22	   
7.40/2.22	             [1 2]     [0]
7.40/2.22	   [d](x0) = [0 0]x0 + [1],
7.40/2.22	   
7.40/2.22	             [1 2]     [1]
7.40/2.22	   [b](x0) = [0 0]x0 + [1]
7.40/2.22	  orientation:
7.40/2.22	              [1 2]     [4]    [1 2]     [3]           
7.40/2.22	   b(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(d(x1))
7.40/2.22	   
7.40/2.22	              [1 2]     [4]    [1 2]     [4]              
7.40/2.22	   c(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(d(d(x1)))
7.40/2.22	   
7.40/2.22	           [1 2]     [1]    [1 2]     [1]        
7.40/2.22	   c(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = g(x1)
7.40/2.22	   
7.40/2.22	              [1 2]     [2]    [1 2]     [2]           
7.40/2.22	   d(d(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(f(x1))
7.40/2.22	   
7.40/2.22	                 [1 2]     [4]    [1 2]     [4]           
7.40/2.22	   d(d(d(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = g(c(x1))
7.40/2.22	   
7.40/2.22	           [1 2]     [1]    [1 2]     [1]           
7.40/2.22	   f(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(g(x1))
7.40/2.22	   
7.40/2.22	           [1 2]     [1]    [1 2]     [1]              
7.40/2.22	   g(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(a(b(x1)))
7.40/2.22	   
7.40/2.22	              [1 2]     [4]    [1 2]     [4]           
7.40/2.22	   g(g(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(x1))
7.40/2.22	  problem:
7.40/2.22	   c(c(x1)) -> d(d(d(x1)))
7.40/2.22	   c(x1) -> g(x1)
7.40/2.22	   d(d(x1)) -> c(f(x1))
7.40/2.22	   d(d(d(x1))) -> g(c(x1))
7.40/2.22	   f(x1) -> a(g(x1))
7.40/2.22	   g(x1) -> d(a(b(x1)))
7.40/2.22	   g(g(x1)) -> b(c(x1))
7.40/2.22	  String Reversal Processor:
7.40/2.22	   c(c(x1)) -> d(d(d(x1)))
7.40/2.22	   c(x1) -> g(x1)
7.40/2.22	   d(d(x1)) -> f(c(x1))
7.40/2.22	   d(d(d(x1))) -> c(g(x1))
7.40/2.22	   f(x1) -> g(a(x1))
7.40/2.22	   g(x1) -> b(a(d(x1)))
7.40/2.22	   g(g(x1)) -> c(b(x1))
7.40/2.22	   Matrix Interpretation Processor: dim=3
7.40/2.22	    
7.40/2.22	    interpretation:
7.40/2.22	               [1 1 0]     [0]
7.40/2.22	     [a](x0) = [1 0 0]x0 + [1]
7.40/2.22	               [0 0 0]     [0],
7.40/2.22	     
7.40/2.22	               [1 1 0]     [0]
7.40/2.22	     [f](x0) = [0 0 0]x0 + [0]
7.40/2.22	               [0 0 0]     [1],
7.40/2.22	     
7.40/2.22	               [1 0 1]     [0]
7.40/2.22	     [g](x0) = [0 0 0]x0 + [0]
7.40/2.22	               [0 0 0]     [1],
7.40/2.22	     
7.40/2.22	               [1 0 1]     [1]
7.40/2.22	     [c](x0) = [0 0 0]x0 + [0]
7.40/2.22	               [0 0 0]     [1],
7.40/2.22	     
7.40/2.22	               [1 0 1]     [0]
7.40/2.22	     [d](x0) = [0 0 0]x0 + [0]
7.40/2.22	               [0 0 0]     [1],
7.40/2.22	     
7.40/2.22	               [1 0 0]  
7.40/2.22	     [b](x0) = [0 0 0]x0
7.40/2.22	               [0 0 0]  
7.40/2.22	    orientation:
7.40/2.22	                [1 0 1]     [3]    [1 0 1]     [2]              
7.40/2.22	     c(c(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(d(d(x1)))
7.40/2.22	                [0 0 0]     [1]    [0 0 0]     [1]              
7.40/2.22	     
7.40/2.22	             [1 0 1]     [1]    [1 0 1]     [0]        
7.40/2.22	     c(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = g(x1)
7.40/2.22	             [0 0 0]     [1]    [0 0 0]     [1]        
7.40/2.22	     
7.40/2.22	                [1 0 1]     [1]    [1 0 1]     [1]           
7.40/2.22	     d(d(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = f(c(x1))
7.40/2.22	                [0 0 0]     [1]    [0 0 0]     [1]           
7.40/2.22	     
7.40/2.22	                   [1 0 1]     [2]    [1 0 1]     [2]           
7.40/2.22	     d(d(d(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(g(x1))
7.40/2.22	                   [0 0 0]     [1]    [0 0 0]     [1]           
7.40/2.22	     
7.40/2.22	             [1 1 0]     [0]    [1 1 0]     [0]           
7.40/2.22	     f(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = g(a(x1))
7.40/2.22	             [0 0 0]     [1]    [0 0 0]     [1]           
7.40/2.22	     
7.40/2.22	             [1 0 1]     [0]    [1 0 1]                
7.40/2.22	     g(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(d(x1)))
7.40/2.22	             [0 0 0]     [1]    [0 0 0]                
7.40/2.22	     
7.40/2.22	                [1 0 1]     [1]    [1 0 0]     [1]           
7.40/2.22	     g(g(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b(x1))
7.40/2.22	                [0 0 0]     [1]    [0 0 0]     [1]           
7.40/2.22	    problem:
7.40/2.22	     d(d(x1)) -> f(c(x1))
7.40/2.22	     d(d(d(x1))) -> c(g(x1))
7.40/2.22	     f(x1) -> g(a(x1))
7.40/2.22	     g(x1) -> b(a(d(x1)))
7.40/2.22	     g(g(x1)) -> c(b(x1))
7.40/2.22	    Bounds Processor:
7.40/2.22	     bound: 3
7.40/2.22	     enrichment: match
7.40/2.22	     automaton:
7.40/2.22	      final states: {7}
7.40/2.22	      transitions:
7.40/2.22	       a3(77) -> 78*
7.40/2.22	       c1(15) -> 16*
7.40/2.22	       c1(11) -> 12*
7.40/2.22	       d3(76) -> 77*
7.40/2.22	       b1(32) -> 33*
7.40/2.22	       b1(86) -> 87*
7.40/2.22	       b1(26) -> 27*
7.40/2.22	       b1(58) -> 59*
7.40/2.22	       a1(25) -> 26*
7.40/2.22	       a1(21) -> 22*
7.40/2.22	       d1(24) -> 25*
7.40/2.22	       g1(22) -> 23*
7.40/2.22	       g1(14) -> 15*
7.40/2.22	       f1(12) -> 13*
7.40/2.22	       c2(66) -> 67*
7.40/2.22	       d0(7) -> 7*
7.40/2.22	       b2(65) -> 66*
7.40/2.22	       b2(92) -> 93*
7.40/2.22	       b2(56) -> 57*
7.40/2.22	       b2(48) -> 49*
7.40/2.22	       f0(7) -> 7*
7.40/2.22	       a2(55) -> 56*
7.40/2.22	       a2(47) -> 48*
7.40/2.22	       a2(39) -> 40*
7.40/2.22	       c0(7) -> 7*
7.40/2.22	       d2(54) -> 55*
7.40/2.22	       d2(46) -> 47*
7.40/2.22	       g0(7) -> 7*
7.40/2.22	       g2(40) -> 41*
7.40/2.22	       a0(7) -> 7*
7.40/2.22	       b3(78) -> 79*
7.40/2.22	       b0(7) -> 7*
7.40/2.22	       7 -> 32,24,21,14,11
7.40/2.22	       12 -> 39*
7.40/2.22	       13 -> 55,25,7
7.40/2.22	       14 -> 54*
7.40/2.22	       16 -> 55,15,25,7
7.40/2.22	       22 -> 65,58,46
7.40/2.22	       23 -> 7*
7.40/2.22	       27 -> 7*
7.40/2.22	       33 -> 15*
7.40/2.22	       40 -> 92,86,76
7.40/2.22	       41 -> 13,7
7.40/2.22	       49 -> 23*
7.40/2.22	       57 -> 15*
7.40/2.22	       59 -> 15*
7.40/2.22	       67 -> 15*
7.40/2.22	       79 -> 41,7,25
7.40/2.22	       87 -> 15*
7.40/2.22	       93 -> 66*
7.40/2.22	     problem:
7.40/2.22	      
7.40/2.22	     Qed
7.40/2.23	EOF