5.73/1.81	YES
5.73/1.81	
5.73/1.81	Problem:
5.73/1.81	 d(a(x1)) -> b(d(x1))
5.73/1.81	 b(x1) -> a(a(a(x1)))
5.73/1.81	 c(d(c(x1))) -> a(d(x1))
5.73/1.81	 b(d(d(x1))) -> c(c(d(d(c(x1)))))
5.73/1.81	
5.73/1.81	Proof:
5.73/1.81	 Matrix Interpretation Processor: dim=1
5.73/1.81	  
5.73/1.81	  interpretation:
5.73/1.81	   [c](x0) = x0 + 1,
5.73/1.81	   
5.73/1.81	   [b](x0) = x0 + 12,
5.73/1.81	   
5.73/1.81	   [d](x0) = 3x0,
5.73/1.81	   
5.73/1.81	   [a](x0) = x0 + 4
5.73/1.81	  orientation:
5.73/1.81	   d(a(x1)) = 3x1 + 12 >= 3x1 + 12 = b(d(x1))
5.73/1.81	   
5.73/1.81	   b(x1) = x1 + 12 >= x1 + 12 = a(a(a(x1)))
5.73/1.81	   
5.73/1.81	   c(d(c(x1))) = 3x1 + 4 >= 3x1 + 4 = a(d(x1))
5.73/1.81	   
5.73/1.81	   b(d(d(x1))) = 9x1 + 12 >= 9x1 + 11 = c(c(d(d(c(x1)))))
5.73/1.81	  problem:
5.73/1.81	   d(a(x1)) -> b(d(x1))
5.73/1.81	   b(x1) -> a(a(a(x1)))
5.73/1.81	   c(d(c(x1))) -> a(d(x1))
5.73/1.81	  Bounds Processor:
5.73/1.81	   bound: 1
5.73/1.81	   enrichment: match
5.73/1.81	   automaton:
5.73/1.81	    final states: {7,4,1}
5.73/1.81	    transitions:
5.73/1.81	     f40() -> 2*
5.73/1.81	     b0(3) -> 1*
5.73/1.81	     d0(2) -> 3*
5.73/1.81	     a0(5) -> 6*
5.73/1.81	     a0(2) -> 5*
5.73/1.81	     a0(6) -> 4*
5.73/1.81	     a0(3) -> 7*
5.73/1.81	     a1(12) -> 13*
5.73/1.81	     a1(14) -> 15*
5.73/1.81	     a1(13) -> 14*
5.73/1.81	     1 -> 3*
5.73/1.81	     3 -> 12*
5.73/1.81	     15 -> 1*
5.73/1.81	   problem:
5.73/1.81	    
5.73/1.81	   Qed
5.73/1.82	EOF