Certification Problem

Input (TPDB TRS_Standard/AotoYamada_05/003)

The rewrite relation of the following TRS is considered.

app(app(app(if,true),x),y) → x (1)
app(app(app(if,false),x),y) → y (2)
app(app(app(until,p),f),x) → app(app(app(if,app(p,x)),x),app(app(app(until,p),f),app(f,x))) (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(app(until,p),f),x)
→ app(app(app(if,app(p,x)),x),app(app(app(until,p),f),app(f,x)))
= t1
where t1 = C[t0σ] and σ = {f/f, p/p, x/app(f,x)} and C = app(app(app(if,app(p,x)),x),☐)