0.00/0.79	YES
0.00/0.79	
0.00/0.79	Problem:
0.00/0.79	f(x) -> e() <= d() = l()
0.00/0.79	h(x, x) -> A()
0.00/0.79	
0.00/0.79	Proof:
0.00/0.79	This system is confluent.
0.00/0.79	By \cite{GNG13}, Theorem 9.
0.00/0.79	This system is of type 3 or smaller.
0.00/0.79	This system is deterministic.
0.00/0.79	This system is weakly left-linear.
0.00/0.79	System R transformed to optimized U(R).
0.00/0.79	This system is confluent.
0.00/0.80	Call external tool:
0.00/0.80	./csi.sh
0.00/0.80	Input:
0.00/0.80	  ?1(l(), x) -> e()
0.00/0.80	  f(x) -> ?1(d(), x)
0.00/0.80	  h(x, x) -> A()
0.00/0.80	
0.00/0.80	 sorted: (order)
0.00/0.80	 0:?1(l(),x) -> e()
0.00/0.80	   f(x) -> ?1(d(),x)
0.00/0.80	 1:h(x,x) -> A()
0.00/0.80	 -----
0.00/0.80	 sorts
0.00/0.80	   [0>1, 1>2, 1>5, 1>9, 3>4, 3>8, 5>6, 5>7, 9>10]
0.00/0.80	 sort attachment (non-strict)
0.00/0.80	   ?1 : 5 x 9 -> 1
0.00/0.80	   l : 7
0.00/0.80	   e : 2
0.00/0.80	   f : 10 -> 0
0.00/0.80	   d : 6
0.00/0.80	   h : 8 x 8 -> 3
0.00/0.80	   A : 4
0.00/0.80	 -----
0.00/0.80	 0:?1(l(),x) -> e()
0.00/0.80	   f(x) -> ?1(d(),x)
0.00/0.80	   Church Rosser Transformation Processor (kb):
0.00/0.80	    ?1(l(),x) -> e()
0.00/0.80	    f(x) -> ?1(d(),x)
0.00/0.80	    critical peaks: joinable
0.00/0.80	     Matrix Interpretation Processor: dim=1
0.00/0.80	      
0.00/0.80	      interpretation:
0.00/0.80	       [d] = 5,
0.00/0.80	       
0.00/0.80	       [f](x0) = 6x0 + 5,
0.00/0.80	       
0.00/0.80	       [e] = 0,
0.00/0.80	       
0.00/0.80	       [?1](x0, x1) = x0 + 4x1,
0.00/0.80	       
0.00/0.80	       [l] = 4
0.00/0.80	      orientation:
0.00/0.80	       ?1(l(),x) = 4x + 4 >= 0 = e()
0.00/0.80	       
0.00/0.80	       f(x) = 6x + 5 >= 4x + 5 = ?1(d(),x)
0.00/0.80	      problem:
0.00/0.80	       f(x) -> ?1(d(),x)
0.00/0.80	      Matrix Interpretation Processor: dim=1
0.00/0.80	       
0.00/0.80	       interpretation:
0.00/0.80	        [d] = 0,
0.00/0.80	        
0.00/0.80	        [f](x0) = x0 + 3,
0.00/0.80	        
0.00/0.80	        [?1](x0, x1) = x0 + x1 + 2
0.00/0.80	       orientation:
0.00/0.80	        f(x) = x + 3 >= x + 2 = ?1(d(),x)
0.00/0.80	       problem:
0.00/0.80	        
0.00/0.80	       Qed
0.00/0.80	 
0.00/0.80	 
0.00/0.80	 1:h(x,x) -> A()
0.00/0.80	   Church Rosser Transformation Processor (kb):
0.00/0.80	    h(x,x) -> A()
0.00/0.80	    critical peaks: joinable
0.00/0.80	     Matrix Interpretation Processor: dim=1
0.00/0.80	      
0.00/0.80	      interpretation:
0.00/0.80	       [A] = 0,
0.00/0.80	       
0.00/0.80	       [h](x0, x1) = x0 + 4x1 + 1
0.00/0.80	      orientation:
0.00/0.80	       h(x,x) = 5x + 1 >= 0 = A()
0.00/0.80	      problem:
0.00/0.80	       
0.00/0.80	      Qed
0.00/0.80	 
0.00/0.80	
0.00/0.81	EOF