Certification Problem

Input (TPDB TRS_Standard/Applicative_05/TypeEx3)

The rewrite relation of the following TRS is considered.

app(app(f,0),n) → app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) (1)
app(app(map,f),nil) → nil (2)
app(app(map,f),app(app(cons,x),xs)) → app(app(cons,app(f,x)),app(app(map,f),xs)) (3)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = app(app(f,0),n)
→ app(app(hd,app(app(map,f),app(app(cons,0),nil))),n)
= t1
where t1 = C[t0σ] and σ = {n/nil, f/cons} and C = app(app(hd,app(app(map,f),☐)),n)