3.98/1.32	YES
3.98/1.32	
3.98/1.32	Problem:
3.98/1.32	 a(p(x1)) -> p(a(A(x1)))
3.98/1.32	 a(A(x1)) -> A(a(x1))
3.98/1.32	 p(A(A(x1))) -> a(p(x1))
3.98/1.32	
3.98/1.32	Proof:
3.98/1.32	 Matrix Interpretation Processor: dim=3
3.98/1.32	  
3.98/1.32	  interpretation:
3.98/1.32	             [1 0 1]     [1]
3.98/1.32	   [A](x0) = [0 0 1]x0 + [0]
3.98/1.32	             [0 1 0]     [0],
3.98/1.32	   
3.98/1.32	             [1 0 1]  
3.98/1.32	   [a](x0) = [0 0 1]x0
3.98/1.32	             [0 1 0]  ,
3.98/1.32	   
3.98/1.32	             [1 0 0]     [0]
3.98/1.32	   [p](x0) = [0 1 1]x0 + [1]
3.98/1.32	             [0 1 1]     [1]
3.98/1.32	  orientation:
3.98/1.32	              [1 1 1]     [1]    [1 1 1]     [1]              
3.98/1.32	   a(p(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = p(a(A(x1)))
3.98/1.32	              [0 1 1]     [1]    [0 1 1]     [1]              
3.98/1.32	   
3.98/1.32	              [1 1 1]     [1]    [1 1 1]     [1]           
3.98/1.32	   a(A(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = A(a(x1))
3.98/1.32	              [0 0 1]     [0]    [0 0 1]     [0]           
3.98/1.32	   
3.98/1.32	                 [1 1 1]     [2]    [1 1 1]     [1]           
3.98/1.32	   p(A(A(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a(p(x1))
3.98/1.32	                 [0 1 1]     [1]    [0 1 1]     [1]           
3.98/1.32	  problem:
3.98/1.32	   a(p(x1)) -> p(a(A(x1)))
3.98/1.32	   a(A(x1)) -> A(a(x1))
3.98/1.32	  Bounds Processor:
3.98/1.32	   bound: 1
3.98/1.32	   enrichment: match
3.98/1.32	   automaton:
3.98/1.32	    final states: {5,1}
3.98/1.32	    transitions:
3.98/1.32	     A1(8) -> 9*
3.98/1.32	     a1(7) -> 8*
3.98/1.32	     f30() -> 2*
3.98/1.32	     p0(4) -> 1*
3.98/1.32	     a0(2) -> 6*
3.98/1.32	     a0(3) -> 4*
3.98/1.32	     A0(2) -> 3*
3.98/1.32	     A0(6) -> 5*
3.98/1.32	     1 -> 8,6
3.98/1.32	     2 -> 7*
3.98/1.32	     5 -> 8,6
3.98/1.32	     9 -> 4*
3.98/1.32	   problem:
3.98/1.32	    
3.98/1.32	   Qed
3.98/1.33	EOF