Certification Problem

Input (COPS 932)

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

f(g(x)) b | xa
g(x) c | xc

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)

f(g(a)) b |
g(c) c |
f(g(x)) b | xa
xa
g(x) c | xc
xc

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.