15.70/4.32	YES
15.70/4.33	
15.70/4.33	Problem:
15.70/4.33	 a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
15.70/4.33	 a(d(x1)) -> c(x1)
15.70/4.33	 a(f(f(x1))) -> g(x1)
15.70/4.33	 b(g(x1)) -> g(b(x1))
15.70/4.33	 c(x1) -> f(f(x1))
15.70/4.33	 c(a(c(x1))) -> b(c(a(b(c(x1)))))
15.70/4.33	 c(d(x1)) -> a(a(x1))
15.70/4.33	 g(x1) -> c(a(x1))
15.70/4.33	 g(x1) -> d(d(d(d(x1))))
15.70/4.33	
15.70/4.33	Proof:
15.70/4.33	 Matrix Interpretation Processor: dim=1
15.70/4.33	  
15.70/4.33	  interpretation:
15.70/4.33	   [g](x0) = x0 + 10,
15.70/4.33	   
15.70/4.33	   [f](x0) = x0 + 3,
15.70/4.33	   
15.70/4.33	   [d](x0) = x0 + 2,
15.70/4.33	   
15.70/4.33	   [b](x0) = x0,
15.70/4.33	   
15.70/4.33	   [c](x0) = x0 + 6,
15.70/4.33	   
15.70/4.33	   [a](x0) = x0 + 4
15.70/4.33	  orientation:
15.70/4.33	   a(b(c(a(x1)))) = x1 + 14 >= x1 + 14 = b(a(c(b(a(b(x1))))))
15.70/4.33	   
15.70/4.33	   a(d(x1)) = x1 + 6 >= x1 + 6 = c(x1)
15.70/4.33	   
15.70/4.33	   a(f(f(x1))) = x1 + 10 >= x1 + 10 = g(x1)
15.70/4.33	   
15.70/4.33	   b(g(x1)) = x1 + 10 >= x1 + 10 = g(b(x1))
15.70/4.33	   
15.70/4.33	   c(x1) = x1 + 6 >= x1 + 6 = f(f(x1))
15.70/4.33	   
15.70/4.33	   c(a(c(x1))) = x1 + 16 >= x1 + 16 = b(c(a(b(c(x1)))))
15.70/4.33	   
15.70/4.33	   c(d(x1)) = x1 + 8 >= x1 + 8 = a(a(x1))
15.70/4.33	   
15.70/4.33	   g(x1) = x1 + 10 >= x1 + 10 = c(a(x1))
15.70/4.33	   
15.70/4.33	   g(x1) = x1 + 10 >= x1 + 8 = d(d(d(d(x1))))
15.70/4.33	  problem:
15.70/4.33	   a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
15.70/4.33	   a(d(x1)) -> c(x1)
15.70/4.33	   a(f(f(x1))) -> g(x1)
15.70/4.33	   b(g(x1)) -> g(b(x1))
15.70/4.33	   c(x1) -> f(f(x1))
15.70/4.33	   c(a(c(x1))) -> b(c(a(b(c(x1)))))
15.70/4.33	   c(d(x1)) -> a(a(x1))
15.70/4.33	   g(x1) -> c(a(x1))
15.70/4.33	  Matrix Interpretation Processor: dim=1
15.70/4.33	   
15.70/4.33	   interpretation:
15.70/4.33	    [g](x0) = x0,
15.70/4.33	    
15.70/4.33	    [f](x0) = x0,
15.70/4.33	    
15.70/4.33	    [d](x0) = x0 + 1,
15.70/4.33	    
15.70/4.33	    [b](x0) = x0,
15.70/4.33	    
15.70/4.33	    [c](x0) = x0,
15.70/4.33	    
15.70/4.33	    [a](x0) = x0
15.70/4.33	   orientation:
15.70/4.33	    a(b(c(a(x1)))) = x1 >= x1 = b(a(c(b(a(b(x1))))))
15.70/4.33	    
15.70/4.33	    a(d(x1)) = x1 + 1 >= x1 = c(x1)
15.70/4.33	    
15.70/4.33	    a(f(f(x1))) = x1 >= x1 = g(x1)
15.70/4.33	    
15.70/4.33	    b(g(x1)) = x1 >= x1 = g(b(x1))
15.70/4.33	    
15.70/4.33	    c(x1) = x1 >= x1 = f(f(x1))
15.70/4.33	    
15.70/4.33	    c(a(c(x1))) = x1 >= x1 = b(c(a(b(c(x1)))))
15.70/4.33	    
15.70/4.33	    c(d(x1)) = x1 + 1 >= x1 = a(a(x1))
15.70/4.33	    
15.70/4.33	    g(x1) = x1 >= x1 = c(a(x1))
15.70/4.33	   problem:
15.70/4.33	    a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
15.70/4.33	    a(f(f(x1))) -> g(x1)
15.70/4.33	    b(g(x1)) -> g(b(x1))
15.70/4.33	    c(x1) -> f(f(x1))
15.70/4.33	    c(a(c(x1))) -> b(c(a(b(c(x1)))))
15.70/4.33	    g(x1) -> c(a(x1))
15.70/4.33	   String Reversal Processor:
15.70/4.33	    a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
15.70/4.33	    f(f(a(x1))) -> g(x1)
15.70/4.33	    g(b(x1)) -> b(g(x1))
15.70/4.33	    c(x1) -> f(f(x1))
15.70/4.33	    c(a(c(x1))) -> c(b(a(c(b(x1)))))
15.70/4.33	    g(x1) -> a(c(x1))
15.70/4.33	    Matrix Interpretation Processor: dim=1
15.70/4.33	     
15.70/4.33	     interpretation:
15.70/4.33	      [g](x0) = 4x0 + 7,
15.70/4.33	      
15.70/4.33	      [f](x0) = 2x0 + 1,
15.70/4.33	      
15.70/4.33	      [b](x0) = x0,
15.70/4.33	      
15.70/4.33	      [c](x0) = 4x0 + 3,
15.70/4.33	      
15.70/4.33	      [a](x0) = x0 + 1
15.70/4.33	     orientation:
15.70/4.33	      a(c(b(a(x1)))) = 4x1 + 8 >= 4x1 + 8 = b(a(b(c(a(b(x1))))))
15.70/4.33	      
15.70/4.33	      f(f(a(x1))) = 4x1 + 7 >= 4x1 + 7 = g(x1)
15.70/4.33	      
15.70/4.33	      g(b(x1)) = 4x1 + 7 >= 4x1 + 7 = b(g(x1))
15.70/4.33	      
15.70/4.33	      c(x1) = 4x1 + 3 >= 4x1 + 3 = f(f(x1))
15.70/4.33	      
15.70/4.33	      c(a(c(x1))) = 16x1 + 19 >= 16x1 + 19 = c(b(a(c(b(x1)))))
15.70/4.33	      
15.70/4.33	      g(x1) = 4x1 + 7 >= 4x1 + 4 = a(c(x1))
15.70/4.33	     problem:
15.70/4.33	      a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
15.70/4.33	      f(f(a(x1))) -> g(x1)
15.70/4.33	      g(b(x1)) -> b(g(x1))
15.70/4.33	      c(x1) -> f(f(x1))
15.70/4.33	      c(a(c(x1))) -> c(b(a(c(b(x1)))))
15.70/4.33	     Bounds Processor:
15.70/4.33	      bound: 1
15.70/4.33	      enrichment: match
15.70/4.33	      automaton:
15.70/4.33	       final states: {12,10,9,8,1}
15.70/4.33	       transitions:
15.70/4.33	        f60() -> 2*
15.70/4.33	        b0(5) -> 6*
15.70/4.33	        b0(7) -> 1*
15.70/4.33	        b0(2) -> 3*
15.70/4.33	        b0(14) -> 15*
15.70/4.33	        b0(8) -> 9*
15.70/4.33	        a0(6) -> 7*
15.70/4.33	        a0(13) -> 14*
15.70/4.33	        a0(3) -> 4*
15.70/4.33	        c0(15) -> 12*
15.70/4.33	        c0(4) -> 5*
15.70/4.33	        c0(3) -> 13*
15.70/4.33	        g0(2) -> 8*
15.70/4.33	        f0(2) -> 11*
15.70/4.33	        f0(11) -> 10*
15.70/4.33	        f1(20) -> 21*
15.70/4.33	        f1(32) -> 33*
15.70/4.33	        f1(22) -> 23*
15.70/4.33	        f1(19) -> 20*
15.70/4.33	        f1(31) -> 32*
15.70/4.33	        f1(23) -> 24*
15.70/4.33	        g1(34) -> 35*
15.70/4.33	        g1(38) -> 39*
15.70/4.33	        b1(39) -> 40*
15.70/4.33	        1 -> 14*
15.70/4.33	        2 -> 38*
15.70/4.33	        3 -> 34,22
15.70/4.33	        4 -> 19*
15.70/4.33	        8 -> 11,10
15.70/4.33	        9 -> 39,8
15.70/4.33	        15 -> 31*
15.70/4.33	        21 -> 5*
15.70/4.33	        24 -> 13*
15.70/4.33	        33 -> 12*
15.70/4.33	        35 -> 21,5
15.70/4.33	        40 -> 35,21
15.70/4.33	      problem:
15.70/4.33	       
15.70/4.33	      Qed
15.70/4.33	EOF