12.67/3.62	YES
12.67/3.63	
12.67/3.63	Problem:
12.67/3.63	 g(h(x1)) -> g(f(s(x1)))
12.67/3.63	 f(s(s(s(x1)))) -> h(f(s(h(x1))))
12.67/3.63	 f(h(x1)) -> h(f(s(h(x1))))
12.67/3.63	 h(x1) -> x1
12.67/3.63	 f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
12.67/3.63	 b(a(x1)) -> a(b(x1))
12.67/3.63	 a(a(a(x1))) -> b(a(a(b(x1))))
12.67/3.63	 b(b(b(b(x1)))) -> a(x1)
12.67/3.63	
12.67/3.63	Proof:
12.67/3.63	 String Reversal Processor:
12.67/3.63	  h(g(x1)) -> s(f(g(x1)))
12.67/3.63	  s(s(s(f(x1)))) -> h(s(f(h(x1))))
12.67/3.63	  h(f(x1)) -> h(s(f(h(x1))))
12.67/3.63	  h(x1) -> x1
12.67/3.63	  s(s(f(f(x1)))) -> f(f(s(s(s(x1)))))
12.67/3.63	  a(b(x1)) -> b(a(x1))
12.67/3.63	  a(a(a(x1))) -> b(a(a(b(x1))))
12.67/3.63	  b(b(b(b(x1)))) -> a(x1)
12.67/3.63	  Matrix Interpretation Processor: dim=1
12.67/3.63	   
12.67/3.63	   interpretation:
12.67/3.63	    [b](x0) = x0 + 1,
12.67/3.63	    
12.67/3.63	    [a](x0) = x0 + 2,
12.67/3.63	    
12.67/3.63	    [f](x0) = x0,
12.67/3.63	    
12.67/3.63	    [s](x0) = x0,
12.67/3.63	    
12.67/3.63	    [g](x0) = 10x0 + 4,
12.67/3.63	    
12.67/3.63	    [h](x0) = x0
12.67/3.63	   orientation:
12.67/3.63	    h(g(x1)) = 10x1 + 4 >= 10x1 + 4 = s(f(g(x1)))
12.67/3.63	    
12.67/3.63	    s(s(s(f(x1)))) = x1 >= x1 = h(s(f(h(x1))))
12.67/3.63	    
12.67/3.63	    h(f(x1)) = x1 >= x1 = h(s(f(h(x1))))
12.67/3.63	    
12.67/3.63	    h(x1) = x1 >= x1 = x1
12.67/3.63	    
12.67/3.63	    s(s(f(f(x1)))) = x1 >= x1 = f(f(s(s(s(x1)))))
12.67/3.63	    
12.67/3.63	    a(b(x1)) = x1 + 3 >= x1 + 3 = b(a(x1))
12.67/3.63	    
12.67/3.63	    a(a(a(x1))) = x1 + 6 >= x1 + 6 = b(a(a(b(x1))))
12.67/3.63	    
12.67/3.63	    b(b(b(b(x1)))) = x1 + 4 >= x1 + 2 = a(x1)
12.67/3.63	   problem:
12.67/3.63	    h(g(x1)) -> s(f(g(x1)))
12.67/3.63	    s(s(s(f(x1)))) -> h(s(f(h(x1))))
12.67/3.63	    h(f(x1)) -> h(s(f(h(x1))))
12.67/3.63	    h(x1) -> x1
12.67/3.63	    s(s(f(f(x1)))) -> f(f(s(s(s(x1)))))
12.67/3.63	    a(b(x1)) -> b(a(x1))
12.67/3.63	    a(a(a(x1))) -> b(a(a(b(x1))))
12.67/3.63	   String Reversal Processor:
12.67/3.63	    g(h(x1)) -> g(f(s(x1)))
12.67/3.63	    f(s(s(s(x1)))) -> h(f(s(h(x1))))
12.67/3.63	    f(h(x1)) -> h(f(s(h(x1))))
12.67/3.63	    h(x1) -> x1
12.67/3.63	    f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
12.67/3.63	    b(a(x1)) -> a(b(x1))
12.67/3.63	    a(a(a(x1))) -> b(a(a(b(x1))))
12.67/3.63	    Matrix Interpretation Processor: dim=1
12.67/3.63	     
12.67/3.63	     interpretation:
12.67/3.63	      [b](x0) = x0 + 1,
12.67/3.63	      
12.67/3.63	      [a](x0) = x0 + 7,
12.67/3.63	      
12.67/3.63	      [f](x0) = x0,
12.67/3.63	      
12.67/3.63	      [s](x0) = x0,
12.67/3.63	      
12.67/3.63	      [g](x0) = 4x0 + 11,
12.67/3.63	      
12.67/3.63	      [h](x0) = x0
12.67/3.63	     orientation:
12.67/3.63	      g(h(x1)) = 4x1 + 11 >= 4x1 + 11 = g(f(s(x1)))
12.67/3.63	      
12.67/3.63	      f(s(s(s(x1)))) = x1 >= x1 = h(f(s(h(x1))))
12.67/3.63	      
12.67/3.63	      f(h(x1)) = x1 >= x1 = h(f(s(h(x1))))
12.67/3.63	      
12.67/3.63	      h(x1) = x1 >= x1 = x1
12.67/3.63	      
12.67/3.63	      f(f(s(s(x1)))) = x1 >= x1 = s(s(s(f(f(x1)))))
12.67/3.63	      
12.67/3.63	      b(a(x1)) = x1 + 8 >= x1 + 8 = a(b(x1))
12.67/3.63	      
12.67/3.63	      a(a(a(x1))) = x1 + 21 >= x1 + 16 = b(a(a(b(x1))))
12.67/3.63	     problem:
12.67/3.63	      g(h(x1)) -> g(f(s(x1)))
12.67/3.63	      f(s(s(s(x1)))) -> h(f(s(h(x1))))
12.67/3.63	      f(h(x1)) -> h(f(s(h(x1))))
12.67/3.63	      h(x1) -> x1
12.67/3.63	      f(f(s(s(x1)))) -> s(s(s(f(f(x1)))))
12.67/3.63	      b(a(x1)) -> a(b(x1))
12.67/3.63	     Bounds Processor:
12.67/3.63	      bound: 1
12.67/3.63	      enrichment: match
12.67/3.63	      automaton:
12.67/3.63	       final states: {14,9,2,5,1}
12.67/3.63	       transitions:
12.67/3.63	        g1(18) -> 19*
12.67/3.63	        f1(17) -> 18*
12.67/3.63	        f1(26) -> 27*
12.67/3.63	        s1(25) -> 26*
12.67/3.63	        s1(16) -> 17*
12.67/3.63	        h1(40) -> 41*
12.67/3.63	        h1(27) -> 28*
12.67/3.63	        h1(44) -> 45*
12.67/3.63	        h1(34) -> 35*
12.67/3.63	        h1(24) -> 25*
12.67/3.63	        f60() -> 2*
12.67/3.63	        g0(4) -> 1*
12.67/3.63	        f0(10) -> 11*
12.67/3.63	        f0(7) -> 8*
12.67/3.63	        f0(2) -> 10*
12.67/3.63	        f0(3) -> 4*
12.67/3.63	        s0(12) -> 13*
12.67/3.63	        s0(2) -> 3*
12.67/3.63	        s0(11) -> 12*
12.67/3.63	        s0(6) -> 7*
12.67/3.63	        s0(13) -> 9*
12.67/3.63	        h0(2) -> 6*
12.67/3.63	        h0(8) -> 5*
12.67/3.63	        a0(15) -> 14*
12.67/3.63	        b0(2) -> 15*
12.67/3.63	        2 -> 6*
12.67/3.63	        5 -> 10,4,8
12.67/3.63	        8 -> 24,16,5
12.67/3.63	        9 -> 10,11
12.67/3.63	        11 -> 34*
12.67/3.63	        12 -> 40*
12.67/3.63	        13 -> 44*
12.67/3.63	        14 -> 15*
12.67/3.63	        19 -> 1*
12.67/3.63	        24 -> 25*
12.67/3.63	        27 -> 28,11
12.67/3.63	        28 -> 27,11
12.67/3.63	        34 -> 35,25
12.67/3.63	        35 -> 25*
12.67/3.63	        40 -> 41,25
12.67/3.63	        41 -> 25*
12.67/3.63	        44 -> 45,25
12.67/3.63	        45 -> 25*
12.67/3.63	      problem:
12.67/3.63	       
12.67/3.63	      Qed
12.67/3.63	EOF