1.17/1.19	MAYBE
1.17/1.19	We consider the system theBenchmark.
1.17/1.19	
1.17/1.19	  Alphabet:
1.17/1.19	
1.17/1.19	    0 : [] --> a -> b 
1.17/1.19	    cons : [] --> (a -> b) -> c -> c 
1.17/1.19	    hd : [] --> c -> a -> b 
1.17/1.19	    map : [] --> ((a -> b) -> a -> b) -> c -> c 
1.17/1.19	    nil : [] --> c 
1.17/1.19	
1.17/1.19	  Rules:
1.17/1.19	
1.17/1.19	    f 0 x => hd (map f (cons 0 nil)) x 
1.17/1.19	    map f nil => nil 
1.17/1.19	    map f (cons g x) => cons (f g) (map f x) 
1.17/1.19	
1.17/1.19	Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term.
1.17/1.19	
1.17/1.19	We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0).  This leads to the following AFSM:
1.17/1.19	
1.17/1.19	  Alphabet:
1.17/1.19	
1.17/1.19	    0 : [] --> a -> b 
1.17/1.19	    cons : [a -> b * c] --> c 
1.17/1.19	    hd : [c * a] --> b 
1.17/1.19	    map : [(a -> b) -> a -> b * c] --> c 
1.17/1.19	    nil : [] --> c 
1.17/1.19	    ~AP1 : [(a -> b) -> a -> b * a -> b] --> a -> b 
1.17/1.19	
1.17/1.19	  Rules:
1.17/1.19	
1.17/1.19	    ~AP1(F, 0) X => hd(map(F, cons(0, nil)), X) 
1.17/1.19	    map(F, nil) => nil 
1.17/1.19	    map(F, cons(G, X)) => cons(~AP1(F, G), map(F, X)) 
1.17/1.19	    ~AP1(F, G) => F G 
1.17/1.19	
1.17/1.19	
1.17/1.19	+++ Citations +++
1.17/1.19	
1.17/1.19	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
1.17/1.20	EOF