/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


MAYBE
We consider the system theBenchmark.

  Alphabet:

    0 : [] --> a -> b 
    cons : [] --> a -> b -> c -> c 
    hd : [] --> c -> a -> b 
    map : [] --> a -> b -> a -> b -> c -> c 
    nil : [] --> c 

  Rules:

    f 0 x => hd (map f (cons 0 nil)) x 
    map f nil => nil 
    map f (cons g x) => cons (f g) (map f x) 

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.

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:

  Alphabet:

    0 : [] --> a -> b 
    cons : [a -> b * c] --> c 
    hd : [c * a] --> b 
    map : [a -> b -> a -> b * c] --> c 
    nil : [] --> c 
    ~AP1 : [a -> b -> a -> b * a -> b] --> a -> b 

  Rules:

    ~AP1(F, 0) X => hd(map(F, cons(0, nil)), X) 
    map(F, nil) => nil 
    map(F, cons(G, X)) => cons(~AP1(F, G), map(F, X)) 
    ~AP1(F, G) => F G 


+++ Citations +++

[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.