11.66/3.69	YES
11.66/3.70	
11.66/3.70	Problem:
11.66/3.70	 c(c(b(x1))) -> a(c(b(x1)))
11.66/3.70	 a(c(b(a(x1)))) -> b(c(c(x1)))
11.66/3.70	 b(a(c(x1))) -> a(b(c(a(x1))))
11.66/3.70	 b(c(a(x1))) -> c(a(b(x1)))
11.66/3.70	
11.66/3.70	Proof:
11.66/3.70	 Matrix Interpretation Processor: dim=4
11.66/3.70	  
11.66/3.70	  interpretation:
11.66/3.70	             [1 1 0 0]     [0]
11.66/3.70	             [0 0 0 0]     [0]
11.66/3.70	   [a](x0) = [0 1 0 1]x0 + [1]
11.66/3.70	             [0 1 0 0]     [0],
11.66/3.70	   
11.66/3.70	             [1 1 0 0]     [0]
11.66/3.70	             [0 0 0 1]     [0]
11.66/3.70	   [c](x0) = [0 1 0 0]x0 + [1]
11.66/3.70	             [0 1 0 0]     [0],
11.66/3.70	   
11.66/3.70	             [1 0 0 0]     [0]
11.66/3.70	             [0 0 0 0]     [0]
11.66/3.70	   [b](x0) = [0 0 1 0]x0 + [1]
11.66/3.70	             [0 0 1 0]     [0]
11.66/3.70	  orientation:
11.66/3.70	                 [1 0 1 0]     [0]    [1 0 1 0]     [0]              
11.66/3.70	                 [0 0 0 0]     [0]    [0 0 0 0]     [0]              
11.66/3.70	   c(c(b(x1))) = [0 0 1 0]x1 + [1] >= [0 0 1 0]x1 + [1] = a(c(b(x1)))
11.66/3.70	                 [0 0 1 0]     [0]    [0 0 1 0]     [0]              
11.66/3.70	   
11.66/3.70	                    [1 2 0 1]     [1]    [1 1 0 1]     [0]              
11.66/3.70	                    [0 0 0 0]     [0]    [0 0 0 0]     [0]              
11.66/3.70	   a(c(b(a(x1)))) = [0 1 0 1]x1 + [2] >= [0 0 0 1]x1 + [2] = b(c(c(x1)))
11.66/3.70	                    [0 1 0 1]     [1]    [0 0 0 1]     [1]              
11.66/3.70	   
11.66/3.70	                 [1 1 0 1]     [0]    [1 1 0 0]     [0]                 
11.66/3.70	                 [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
11.66/3.70	   b(a(c(x1))) = [0 1 0 1]x1 + [2] >= [0 0 0 0]x1 + [2] = a(b(c(a(x1))))
11.66/3.70	                 [0 1 0 1]     [1]    [0 0 0 0]     [0]                 
11.66/3.70	   
11.66/3.70	                 [1 1 0 0]     [0]    [1 0 0 0]     [0]              
11.66/3.70	                 [0 0 0 0]     [0]    [0 0 0 0]     [0]              
11.66/3.70	   b(c(a(x1))) = [0 0 0 0]x1 + [2] >= [0 0 0 0]x1 + [1] = c(a(b(x1)))
11.66/3.70	                 [0 0 0 0]     [1]    [0 0 0 0]     [0]              
11.66/3.70	  problem:
11.66/3.70	   c(c(b(x1))) -> a(c(b(x1)))
11.66/3.70	   b(a(c(x1))) -> a(b(c(a(x1))))
11.66/3.70	   b(c(a(x1))) -> c(a(b(x1)))
11.66/3.70	  Bounds Processor:
11.66/3.70	   bound: 1
11.66/3.70	   enrichment: match
11.66/3.70	   automaton:
11.66/3.70	    final states: {9,5,1}
11.66/3.70	    transitions:
11.66/3.70	     c1(13) -> 14*
11.66/3.70	     a1(12) -> 13*
11.66/3.70	     b1(11) -> 12*
11.66/3.70	     f30() -> 2*
11.66/3.70	     a0(2) -> 6*
11.66/3.70	     a0(4) -> 1*
11.66/3.70	     a0(8) -> 5*
11.66/3.70	     a0(3) -> 10*
11.66/3.70	     c0(10) -> 9*
11.66/3.70	     c0(6) -> 7*
11.66/3.70	     c0(3) -> 4*
11.66/3.70	     b0(7) -> 8*
11.66/3.70	     b0(2) -> 3*
11.66/3.70	     2 -> 11*
11.66/3.70	     5 -> 12,3
11.66/3.70	     9 -> 12,3
11.66/3.70	     14 -> 8*
11.66/3.70	   problem:
11.66/3.70	    
11.66/3.70	   Qed
13.24/3.70	EOF