10.92/3.12	YES
10.92/3.13	
10.92/3.13	Problem:
10.92/3.13	 r(e(x1)) -> w(r(x1))
10.92/3.13	 i(t(x1)) -> e(r(x1))
10.92/3.13	 e(w(x1)) -> r(i(x1))
10.92/3.13	 t(e(x1)) -> r(e(x1))
10.92/3.13	 w(r(x1)) -> i(t(x1))
10.92/3.13	 e(r(x1)) -> e(w(x1))
10.92/3.13	 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
10.92/3.13	
10.92/3.13	Proof:
10.92/3.13	 Matrix Interpretation Processor: dim=1
10.92/3.13	  
10.92/3.13	  interpretation:
10.92/3.13	   [i](x0) = x0,
10.92/3.13	   
10.92/3.13	   [t](x0) = x0 + 3,
10.92/3.13	   
10.92/3.13	   [w](x0) = x0 + 1,
10.92/3.13	   
10.92/3.13	   [r](x0) = x0 + 2,
10.92/3.13	   
10.92/3.13	   [e](x0) = x0 + 1
10.92/3.13	  orientation:
10.92/3.13	   r(e(x1)) = x1 + 3 >= x1 + 3 = w(r(x1))
10.92/3.13	   
10.92/3.13	   i(t(x1)) = x1 + 3 >= x1 + 3 = e(r(x1))
10.92/3.13	   
10.92/3.13	   e(w(x1)) = x1 + 2 >= x1 + 2 = r(i(x1))
10.92/3.13	   
10.92/3.13	   t(e(x1)) = x1 + 4 >= x1 + 3 = r(e(x1))
10.92/3.13	   
10.92/3.13	   w(r(x1)) = x1 + 3 >= x1 + 3 = i(t(x1))
10.92/3.13	   
10.92/3.13	   e(r(x1)) = x1 + 3 >= x1 + 2 = e(w(x1))
10.92/3.13	   
10.92/3.13	   r(i(t(e(r(x1))))) = x1 + 8 >= x1 + 8 = e(w(r(i(t(e(x1))))))
10.92/3.13	  problem:
10.92/3.13	   r(e(x1)) -> w(r(x1))
10.92/3.13	   i(t(x1)) -> e(r(x1))
10.92/3.13	   e(w(x1)) -> r(i(x1))
10.92/3.13	   w(r(x1)) -> i(t(x1))
10.92/3.13	   r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
10.92/3.13	  String Reversal Processor:
10.92/3.13	   e(r(x1)) -> r(w(x1))
10.92/3.13	   t(i(x1)) -> r(e(x1))
10.92/3.13	   w(e(x1)) -> i(r(x1))
10.92/3.13	   r(w(x1)) -> t(i(x1))
10.92/3.13	   r(e(t(i(r(x1))))) -> e(t(i(r(w(e(x1))))))
10.92/3.13	   Matrix Interpretation Processor: dim=3
10.92/3.13	    
10.92/3.13	    interpretation:
10.92/3.13	               [1 0 0]  
10.92/3.13	     [i](x0) = [0 0 0]x0
10.92/3.13	               [0 1 0]  ,
10.92/3.13	     
10.92/3.13	               [1 0 1]     [0]
10.92/3.13	     [t](x0) = [0 0 0]x0 + [1]
10.92/3.13	               [0 0 0]     [0],
10.92/3.13	     
10.92/3.13	               [1 1 0]     [0]
10.92/3.13	     [w](x0) = [0 0 0]x0 + [0]
10.92/3.13	               [0 0 0]     [1],
10.92/3.13	     
10.92/3.13	               [1 1 0]     [0]
10.92/3.13	     [r](x0) = [0 0 0]x0 + [1]
10.92/3.13	               [0 0 0]     [0],
10.92/3.13	     
10.92/3.13	               [1 0 0]  
10.92/3.13	     [e](x0) = [0 1 0]x0
10.92/3.13	               [0 0 0]  
10.92/3.13	    orientation:
10.92/3.13	                [1 1 0]     [0]    [1 1 0]     [0]           
10.92/3.13	     e(r(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = r(w(x1))
10.92/3.13	                [0 0 0]     [0]    [0 0 0]     [0]           
10.92/3.13	     
10.92/3.13	                [1 1 0]     [0]    [1 1 0]     [0]           
10.92/3.13	     t(i(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = r(e(x1))
10.92/3.13	                [0 0 0]     [0]    [0 0 0]     [0]           
10.92/3.13	     
10.92/3.13	                [1 1 0]     [0]    [1 1 0]     [0]           
10.92/3.13	     w(e(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = i(r(x1))
10.92/3.13	                [0 0 0]     [1]    [0 0 0]     [1]           
10.92/3.13	     
10.92/3.13	                [1 1 0]     [0]    [1 1 0]     [0]           
10.92/3.13	     r(w(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = t(i(x1))
10.92/3.13	                [0 0 0]     [0]    [0 0 0]     [0]           
10.92/3.13	     
10.92/3.13	                         [1 1 0]     [2]    [1 1 0]     [1]                       
10.92/3.13	     r(e(t(i(r(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = e(t(i(r(w(e(x1))))))
10.92/3.13	                         [0 0 0]     [0]    [0 0 0]     [0]                       
10.92/3.13	    problem:
10.92/3.13	     e(r(x1)) -> r(w(x1))
10.92/3.13	     t(i(x1)) -> r(e(x1))
10.92/3.13	     w(e(x1)) -> i(r(x1))
10.92/3.13	     r(w(x1)) -> t(i(x1))
10.92/3.13	    String Reversal Processor:
10.92/3.13	     r(e(x1)) -> w(r(x1))
10.92/3.13	     i(t(x1)) -> e(r(x1))
10.92/3.13	     e(w(x1)) -> r(i(x1))
10.92/3.13	     w(r(x1)) -> i(t(x1))
10.92/3.13	     Matrix Interpretation Processor: dim=1
10.92/3.13	      
10.92/3.13	      interpretation:
10.92/3.13	       [i](x0) = 2x0 + 5,
10.92/3.13	       
10.92/3.13	       [t](x0) = 6x0 + 1,
10.92/3.13	       
10.92/3.13	       [w](x0) = 4x0 + 6,
10.92/3.13	       
10.92/3.13	       [r](x0) = 3x0 + 1,
10.92/3.13	       
10.92/3.13	       [e](x0) = 4x0 + 3
10.92/3.13	      orientation:
10.92/3.13	       r(e(x1)) = 12x1 + 10 >= 12x1 + 10 = w(r(x1))
10.92/3.13	       
10.92/3.13	       i(t(x1)) = 12x1 + 7 >= 12x1 + 7 = e(r(x1))
10.92/3.13	       
10.92/3.13	       e(w(x1)) = 16x1 + 27 >= 6x1 + 16 = r(i(x1))
10.92/3.13	       
10.92/3.13	       w(r(x1)) = 12x1 + 10 >= 12x1 + 7 = i(t(x1))
10.92/3.13	      problem:
10.92/3.13	       r(e(x1)) -> w(r(x1))
10.92/3.13	       i(t(x1)) -> e(r(x1))
10.92/3.13	      String Reversal Processor:
10.92/3.13	       e(r(x1)) -> r(w(x1))
10.92/3.13	       t(i(x1)) -> r(e(x1))
10.92/3.13	       KBO Processor:
10.92/3.13	        weight function:
10.92/3.13	         w0 = 1
10.92/3.13	         w(i) = w(t) = w(w) = w(r) = w(e) = 1
10.92/3.13	        precedence:
10.92/3.13	         t > e > i ~ w ~ r
10.92/3.13	        problem:
10.92/3.13	         
10.92/3.13	        Qed
10.92/3.14	EOF