Certification Problem

Input (COPS 920)

The rewrite relation of the following (conditional) TRS is considered.

a → b |
f(g(a)) → f(a) |

The question is whether the following conditions are infeasible, i.e., there is no substitution σ such that all of the following is true:

Property / Task

Prove or disprove an infeasibility problem.

Answer / Result

Yes.

Proof (by nonreach @ CoCo 2023)

1 Infeasible Compound Conditions

We collect the conditions in the fresh compound-symbol |.

1.1 Non-reachability

We show non-reachability w.r.t. the underlying TRS.

1.1.1 Non-reachability by TCAP

Non-reachability is shown by the TCAP approximation.