1.80/1.10	YES
1.80/1.10	
1.80/1.10	Problem:
1.80/1.10	 a(a(a(x1))) -> b(b(x1))
1.80/1.10	 b(b(b(x1))) -> c(d(x1))
1.80/1.10	 c(x1) -> a(a(x1))
1.80/1.10	 d(x1) -> c(x1)
1.80/1.10	
1.80/1.10	Proof:
1.80/1.10	 Matrix Interpretation Processor: dim=1
1.80/1.10	  
1.80/1.10	  interpretation:
1.80/1.10	   [c](x0) = x0 + 12,
1.80/1.10	   
1.80/1.10	   [d](x0) = x0 + 15,
1.80/1.10	   
1.80/1.10	   [b](x0) = x0 + 9,
1.80/1.10	   
1.80/1.10	   [a](x0) = x0 + 6
1.80/1.10	  orientation:
1.80/1.10	   a(a(a(x1))) = x1 + 18 >= x1 + 18 = b(b(x1))
1.80/1.10	   
1.80/1.10	   b(b(b(x1))) = x1 + 27 >= x1 + 27 = c(d(x1))
1.80/1.10	   
1.80/1.10	   c(x1) = x1 + 12 >= x1 + 12 = a(a(x1))
1.80/1.10	   
1.80/1.10	   d(x1) = x1 + 15 >= x1 + 12 = c(x1)
1.80/1.10	  problem:
1.80/1.10	   a(a(a(x1))) -> b(b(x1))
1.80/1.10	   b(b(b(x1))) -> c(d(x1))
1.80/1.10	   c(x1) -> a(a(x1))
1.80/1.10	  Bounds Processor:
1.80/1.10	   bound: 1
1.80/1.10	   enrichment: match
1.80/1.10	   automaton:
1.80/1.10	    final states: {6,4,1}
1.80/1.10	    transitions:
1.80/1.10	     f40() -> 2*
1.80/1.10	     b0(2) -> 3*
1.80/1.10	     b0(3) -> 1*
1.80/1.10	     c0(5) -> 4*
1.80/1.10	     d0(2) -> 5*
1.80/1.10	     a0(7) -> 6*
1.80/1.10	     a0(2) -> 7*
1.80/1.10	     a1(12) -> 13*
1.80/1.10	     a1(11) -> 12*
1.80/1.10	     b1(17) -> 18*
1.80/1.10	     b1(18) -> 19*
1.80/1.10	     1 -> 7,6
1.80/1.10	     4 -> 3,1
1.80/1.10	     5 -> 11*
1.80/1.10	     11 -> 17*
1.80/1.10	     13 -> 4*
1.80/1.10	     19 -> 6*
1.80/1.10	   problem:
1.80/1.10	    
1.80/1.10	   Qed
3.13/1.11	EOF