29.09/7.77	YES
29.09/7.78	
29.09/7.78	Problem:
29.09/7.78	 strict:
29.09/7.78	  b(b(b(x1))) -> b(a(c(x1)))
29.09/7.78	  a(a(c(x1))) -> b(b(a(x1)))
29.09/7.78	 weak:
29.09/7.78	  a(b(c(x1))) -> c(b(a(x1)))
29.09/7.78	  b(b(a(x1))) -> c(b(c(x1)))
29.09/7.78	  c(a(c(x1))) -> a(b(c(x1)))
29.09/7.78	  a(b(b(x1))) -> c(b(a(x1)))
29.09/7.78	
29.09/7.78	Proof:
29.09/7.78	 Arctic Interpretation Processor:
29.09/7.78	  dimension: 2
29.09/7.78	  interpretation:
29.09/7.78	             [5  -&]  
29.09/7.78	   [a](x0) = [4  -&]x0,
29.09/7.78	   
29.09/7.78	             [5  -&]  
29.09/7.78	   [c](x0) = [4  -&]x0,
29.09/7.78	   
29.09/7.78	             [0 2]  
29.09/7.78	   [b](x0) = [4 5]x0
29.09/7.78	  orientation:
29.09/7.78	                 [11 12]      [11 -&]                
29.09/7.78	   b(b(b(x1))) = [14 15]x1 >= [14 -&]x1 = b(a(c(x1)))
29.09/7.78	   
29.09/7.78	                 [15 -&]      [11 -&]                
29.09/7.78	   a(a(c(x1))) = [14 -&]x1 >= [14 -&]x1 = b(b(a(x1)))
29.09/7.78	   
29.09/7.78	                 [11 -&]      [11 -&]                
29.09/7.78	   a(b(c(x1))) = [10 -&]x1 >= [10 -&]x1 = c(b(a(x1)))
29.09/7.78	   
29.09/7.78	                 [11 -&]      [11 -&]                
29.09/7.78	   b(b(a(x1))) = [14 -&]x1 >= [10 -&]x1 = c(b(c(x1)))
29.09/7.78	   
29.09/7.78	                 [15 -&]      [11 -&]                
29.09/7.78	   c(a(c(x1))) = [14 -&]x1 >= [10 -&]x1 = a(b(c(x1)))
29.09/7.78	   
29.09/7.78	                 [11 12]      [11 -&]                
29.09/7.78	   a(b(b(x1))) = [10 11]x1 >= [10 -&]x1 = c(b(a(x1)))
29.09/7.78	  problem:
29.09/7.78	   strict:
29.09/7.78	    b(b(b(x1))) -> b(a(c(x1)))
29.09/7.78	    a(a(c(x1))) -> b(b(a(x1)))
29.09/7.78	   weak:
29.09/7.78	    a(b(c(x1))) -> c(b(a(x1)))
29.09/7.78	    b(b(a(x1))) -> c(b(c(x1)))
29.09/7.78	    a(b(b(x1))) -> c(b(a(x1)))
29.09/7.78	  Arctic Interpretation Processor:
29.09/7.78	   dimension: 1
29.09/7.78	   interpretation:
29.09/7.78	    [a](x0) = 9x0,
29.09/7.78	    
29.09/7.78	    [c](x0) = 7x0,
29.09/7.78	    
29.09/7.78	    [b](x0) = 8x0
29.09/7.78	   orientation:
29.09/7.78	    b(b(b(x1))) = 24x1 >= 24x1 = b(a(c(x1)))
29.09/7.78	    
29.09/7.78	    a(a(c(x1))) = 25x1 >= 25x1 = b(b(a(x1)))
29.09/7.78	    
29.09/7.78	    a(b(c(x1))) = 24x1 >= 24x1 = c(b(a(x1)))
29.09/7.78	    
29.09/7.78	    b(b(a(x1))) = 25x1 >= 22x1 = c(b(c(x1)))
29.09/7.78	    
29.09/7.78	    a(b(b(x1))) = 25x1 >= 24x1 = c(b(a(x1)))
29.09/7.78	   problem:
29.09/7.78	    strict:
29.09/7.78	     b(b(b(x1))) -> b(a(c(x1)))
29.09/7.78	     a(a(c(x1))) -> b(b(a(x1)))
29.09/7.78	    weak:
29.09/7.78	     a(b(c(x1))) -> c(b(a(x1)))
29.09/7.78	   Bounds Processor:
29.09/7.78	    bound: 1
29.09/7.78	    enrichment: match-rt
29.09/7.78	    automaton:
29.09/7.78	     final states: {4}
29.09/7.78	     transitions:
29.09/7.78	      b1(11) -> 12*
29.09/7.78	      a1(10) -> 11*
29.09/7.78	      c1(9) -> 10*
29.09/7.78	      c1(23) -> 24*
29.09/7.78	      b0(4) -> 4*
29.09/7.78	      a0(4) -> 4*
29.09/7.78	      c0(4) -> 4*
29.09/7.78	      4 -> 9*
29.09/7.78	      11 -> 23*
29.09/7.78	      12 -> 4*
29.09/7.78	      24 -> 10*
29.09/7.78	    problem:
29.09/7.78	     strict:
29.09/7.78	      a(a(c(x1))) -> b(b(a(x1)))
29.09/7.78	     weak:
29.09/7.78	      a(b(c(x1))) -> c(b(a(x1)))
29.09/7.78	    RT Transformation Processor:
29.09/7.78	     a(a(c(x1))) -> b(b(a(x1)))
29.09/7.78	     a(b(c(x1))) -> c(b(a(x1)))
29.09/7.78	     Matrix Interpretation Processor: dim=1
29.09/7.78	      
29.09/7.78	      interpretation:
29.09/7.78	       [a](x0) = 2x0,
29.09/7.78	       
29.09/7.78	       [c](x0) = 2x0 + 4,
29.09/7.78	       
29.09/7.78	       [b](x0) = x0
29.09/7.78	      orientation:
29.09/7.78	       a(a(c(x1))) = 8x1 + 16 >= 2x1 = b(b(a(x1)))
29.09/7.78	       
29.09/7.78	       a(b(c(x1))) = 4x1 + 8 >= 4x1 + 4 = c(b(a(x1)))
29.09/7.78	      problem:
29.09/7.78	       
29.09/7.78	      Qed
29.09/7.78	EOF