2.07/0.96	YES
2.61/0.97	
2.61/0.97	Problem:
2.61/0.97	 a(a(a(x1))) -> b(b(x1))
2.61/0.97	 b(b(b(x1))) -> c(x1)
2.61/0.97	 c(x1) -> d(d(x1))
2.61/0.97	 d(x1) -> a(a(x1))
2.61/0.97	
2.61/0.97	Proof:
2.61/0.97	 Matrix Interpretation Processor: dim=1
2.61/0.97	  
2.61/0.97	  interpretation:
2.61/0.97	   [d](x0) = x0 + 6,
2.61/0.97	   
2.61/0.97	   [c](x0) = x0 + 12,
2.61/0.97	   
2.61/0.97	   [b](x0) = x0 + 4,
2.61/0.97	   
2.61/0.97	   [a](x0) = x0 + 3
2.61/0.97	  orientation:
2.61/0.97	   a(a(a(x1))) = x1 + 9 >= x1 + 8 = b(b(x1))
2.61/0.97	   
2.61/0.97	   b(b(b(x1))) = x1 + 12 >= x1 + 12 = c(x1)
2.61/0.97	   
2.61/0.97	   c(x1) = x1 + 12 >= x1 + 12 = d(d(x1))
2.61/0.97	   
2.61/0.97	   d(x1) = x1 + 6 >= x1 + 6 = a(a(x1))
2.61/0.97	  problem:
2.61/0.97	   b(b(b(x1))) -> c(x1)
2.61/0.97	   c(x1) -> d(d(x1))
2.61/0.97	   d(x1) -> a(a(x1))
2.61/0.97	  Bounds Processor:
2.61/0.97	   bound: 2
2.61/0.97	   enrichment: match
2.61/0.97	   automaton:
2.61/0.97	    final states: {5,3,1}
2.61/0.97	    transitions:
2.61/0.97	     a0(2) -> 6*
2.61/0.97	     a0(6) -> 5*
2.61/0.97	     a1(20) -> 21*
2.61/0.97	     a1(17) -> 18*
2.61/0.97	     a1(19) -> 20*
2.61/0.97	     a1(16) -> 17*
2.61/0.97	     d1(7) -> 8*
2.61/0.97	     d1(8) -> 9*
2.61/0.97	     a2(32) -> 33*
2.61/0.97	     a2(29) -> 30*
2.61/0.97	     a2(31) -> 32*
2.61/0.97	     a2(28) -> 29*
2.61/0.97	     f40() -> 2*
2.61/0.97	     c0(2) -> 1*
2.61/0.97	     d0(2) -> 4*
2.61/0.97	     d0(4) -> 3*
2.61/0.97	     2 -> 19,7
2.61/0.97	     4 -> 16*
2.61/0.97	     7 -> 31*
2.61/0.97	     8 -> 28*
2.61/0.97	     9 -> 1*
2.61/0.97	     18 -> 3*
2.61/0.97	     21 -> 4*
2.61/0.97	     30 -> 9*
2.61/0.97	     33 -> 8*
2.61/0.97	   problem:
2.61/0.97	    
2.61/0.97	   Qed
2.61/0.97	EOF