0.00/0.05	YES
0.00/0.05	We consider the system theBenchmark.
0.00/0.05	
0.00/0.05	  Alphabet:
0.00/0.05	
0.00/0.05	    f : [o -> o] --> o 
0.00/0.05	    g : [] --> o -> o 
0.00/0.05	
0.00/0.05	  Rules:
0.00/0.05	
0.00/0.05	    f(g) => f(/\x.g x) 
0.00/0.05	
0.00/0.05	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
0.00/0.05	
0.00/0.05	We use the dependency pair framework as described in [Kop12, Ch. 6/7], with dynamic dependency pairs.
0.00/0.05	
0.00/0.05	We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative):
0.00/0.05	
0.00/0.05	  Dependency Pairs P_0:
0.00/0.05	
0.00/0.05	    0] f#(g) =#> f#(/\x.g x)   
0.00/0.05	
0.00/0.05	  Rules R_0:
0.00/0.05	
0.00/0.05	    f(g) => f(/\x.g x) 
0.00/0.05	
0.00/0.05	Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite.
0.00/0.05	
0.00/0.05	We consider the dependency pair problem (P_0, R_0, minimal, formative).
0.00/0.05	
0.00/0.05	We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows:
0.00/0.05	
0.00/0.05	    * 0 :  
0.00/0.05	
0.00/0.05	This graph has no strongly connected components.  By [Kop12, Thm. 7.31], this implies finiteness of the dependency pair problem.
0.00/0.05	
0.00/0.05	As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination.
0.00/0.05	
0.00/0.05	
0.00/0.05	+++ Citations +++
0.00/0.05	
0.00/0.05	[Kop12]  C. Kop.  Higher Order Termination.  PhD Thesis, 2012.
0.00/0.05	EOF