Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/Ex9_BLR02_L)

The rewrite relation of the following TRS is considered.

filter(cons(X),0,M) → cons(0) (1)
filter(cons(X),s(N),M) → cons(X) (2)
sieve(cons(0)) → cons(0) (3)
sieve(cons(s(N))) → cons(s(N)) (4)
nats(N) → cons(N) (5)
zprimes → sieve(nats(s(s(0)))) (6)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
zprimes# → nats#(s(s(0))) (7)
zprimes# → sieve#(nats(s(s(0)))) (8)

1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.