/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:

    0 : [] --> nat 
    f : [nat] --> nat 
    g : [nat -> nat] --> nat 

  Rules:

    f(0) => g(/\x.0) 
    g(h) => h f(0) 

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:

  f(0) 
    => g(/\x.0) 
    => (/\x.0) f(0) 
    |> f(0) 

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