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


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NO
We consider the system theBenchmark.

  Alphabet:

    false : [] --> a 
    if : [a * b * b] --> b 
    true : [] --> a 
    until : [b -> a * b -> b * b] --> b 

  Rules:

    if(true, x, y) => x 
    if(false, x, y) => y 
    until(f, g, x) => if(f x, x, until(f, g, g x)) 

This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).

It is easy to see that this system is non-terminating:

  until(f, g, x) 
    => if(f x, x, until(f, g, g x)) 
    |> until(f, g, g x) 

That is, a term s reduces to a term t which has a subterm that is an instance of the original term.