11.52/3.30	YES
11.52/3.31	
11.52/3.31	Problem:
11.52/3.31	 b(a(a(b(x1)))) -> b(a(a(a(x1))))
11.52/3.31	 a(b(b(a(x1)))) -> a(a(b(b(x1))))
11.52/3.31	 b(a(a(a(x1)))) -> b(b(b(a(x1))))
11.52/3.31	
11.52/3.31	Proof:
11.52/3.31	 Matrix Interpretation Processor: dim=4
11.52/3.31	  
11.52/3.31	  interpretation:
11.52/3.31	             [1 1 0 0]     [0]
11.52/3.31	             [0 0 0 0]     [0]
11.52/3.31	   [a](x0) = [0 1 1 0]x0 + [1]
11.52/3.31	             [0 0 0 1]     [0],
11.52/3.31	   
11.52/3.31	             [1 0 0 0]     [0]
11.52/3.31	             [0 1 1 1]     [0]
11.52/3.31	   [b](x0) = [0 0 0 0]x0 + [0]
11.52/3.31	             [0 0 0 0]     [1]
11.52/3.31	  orientation:
11.52/3.31	                    [1 1 1 1]     [0]    [1 1 0 0]     [0]                 
11.52/3.31	                    [0 1 1 1]     [3]    [0 1 1 1]     [3]                 
11.52/3.31	   b(a(a(b(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(a(a(a(x1))))
11.52/3.31	                    [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
11.52/3.31	   
11.52/3.31	                    [1 2 1 1]     [2]    [1 1 1 1]     [1]                 
11.52/3.31	                    [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
11.52/3.31	   a(b(b(a(x1)))) = [0 1 1 1]x1 + [3] >= [0 1 1 1]x1 + [3] = a(a(b(b(x1))))
11.52/3.31	                    [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
11.52/3.31	   
11.52/3.31	                    [1 1 0 0]     [0]    [1 1 0 0]     [0]                 
11.52/3.31	                    [0 1 1 1]     [3]    [0 1 1 1]     [3]                 
11.52/3.31	   b(a(a(a(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(b(b(a(x1))))
11.52/3.31	                    [0 0 0 0]     [1]    [0 0 0 0]     [1]                 
11.52/3.31	  problem:
11.52/3.31	   b(a(a(b(x1)))) -> b(a(a(a(x1))))
11.52/3.31	   b(a(a(a(x1)))) -> b(b(b(a(x1))))
11.52/3.31	  Bounds Processor:
11.52/3.31	   bound: 1
11.52/3.31	   enrichment: match
11.52/3.31	   automaton:
11.52/3.31	    final states: {6,1}
11.52/3.31	    transitions:
11.52/3.31	     b1(10) -> 11*
11.52/3.31	     b1(12) -> 13*
11.52/3.31	     b1(11) -> 12*
11.52/3.31	     a1(9) -> 10*
11.52/3.31	     f20() -> 2*
11.52/3.31	     b0(5) -> 1*
11.52/3.31	     b0(7) -> 8*
11.52/3.31	     b0(8) -> 6*
11.52/3.31	     b0(3) -> 7*
11.52/3.31	     a0(2) -> 3*
11.52/3.31	     a0(4) -> 5*
11.52/3.31	     a0(3) -> 4*
11.52/3.31	     1 -> 11,7
11.52/3.31	     2 -> 9*
11.52/3.31	     13 -> 1*
11.52/3.31	   problem:
11.52/3.31	    
11.52/3.31	   Qed
11.52/3.31	EOF