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


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


YES
We consider the system theBenchmark.

  Alphabet:

    uncurry : [a -> b -> c * a * b] --> c 

  Rules:

    uncurry(f, x, y) => f x y 

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

We use rule removal, following [Kop12, Theorem 2.23].

This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]):

  uncurry(F, X, Y) >? F X Y 

We orient these requirements with a polynomial interpretation in the natural numbers.

The following interpretation satisfies the requirements:

  uncurry = \G0y1y2.1 + y1 + y2 + G0(y1,y2) 

Using this interpretation, the requirements translate to:

  [[uncurry(_F0, _x1, _x2)]] = 1 + x1 + x2 + F0(x1,x2) > x1 + x2 + F0(x1,x2) = [[_F0 _x1 _x2]] 

We can thus remove the following rules:

  uncurry(F, X, Y) => F X Y 

All rules were succesfully removed.  Thus, termination of the original system has been reduced to termination of the beta-rule, which is well-known to hold.


+++ Citations +++

[Kop12]  C. Kop.  Higher Order Termination.  PhD Thesis, 2012.