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


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MAYBE
We consider the system theBenchmark.

  Alphabet:

    0 : [] --> N 
    false : [] --> B 
    g : [] --> N -> B 
    h : [] --> N -> N -> B -> N -> B 
    iszero : [] --> N -> N -> B 
    rec : [] --> N -> N -> B -> N -> B -> B -> N -> B 
    s : [] --> N -> N 
    true : [] --> B 

  Rules:

    rec f (i 0) => i 
    rec f (i (s x)) => f x (rec f (i x)) 
    g x => true 
    h x f y => false 
    iszero x y => rec h (g x) y 

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 : [] --> N 
    false : [] --> B 
    g : [] --> N -> B 
    h : [] --> N -> N -> B -> N -> B 
    iszero : [N] --> N -> B 
    rec : [N -> N -> B -> N -> B * B] --> N -> B 
    s : [N] --> N 
    true : [] --> B 
    ~AP1 : [N -> B * N] --> B 

  Rules:

    rec(F, ~AP1(G, 0)) => G 
    rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) 
    g X => true 
    h X F Y => false 
    iszero(X) Y => rec(h, g X) Y 
    rec(F, g 0) => g 
    rec(F, h X G 0) => h X G 
    rec(F, iszero(X) 0) => iszero(X) 
    rec(F, rec(G, X) 0) => rec(G, X) 
    rec(F, g s(X)) => F X rec(F, g X) 
    rec(F, h X G s(Y)) => F Y rec(F, h X G Y) 
    rec(F, iszero(X) s(Y)) => F Y rec(F, iszero(X) Y) 
    rec(F, rec(G, X) s(Y)) => F Y rec(F, rec(G, X) Y) 
    ~AP1(F, X) => F X 


+++ Citations +++

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