Certification Problem

Input (COPS 906)

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

le(x,0) false |
le(0,s(y)) true |
le(s(x),s(y)) le(x,y) |
min(cons(x,nil)) x |
min(cons(x,xs)) x | le(x,min(xs)) ≈ true
min(cons(x,xs)) min(xs) | le(x,min(xs)) ≈ false

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.