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


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


NO
We consider the system theBenchmark.

  Alphabet:

    0 : [] --> b 
    1 : [] --> b 
    cons : [d * e] --> e 
    f : [b] --> a 
    false : [] --> c 
    filter : [d -> c * e] --> e 
    filter2 : [c * d -> c * d * e] --> e 
    map : [d -> d * e] --> e 
    nil : [] --> e 
    true : [] --> c 

  Rules:

    f(0) => f(0) 
    0 => 1 
    map(g, nil) => nil 
    map(g, cons(x, y)) => cons(g x, map(g, y)) 
    filter(g, nil) => nil 
    filter(g, cons(x, y)) => filter2(g x, g, x, y) 
    filter2(true, g, x, y) => cons(x, filter(g, y)) 
    filter2(false, g, x, y) => filter(g, y) 

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) 
    => f(0) 

That is, a term s reduces to a term t which instantiates s.