Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/Ex4_7_77_Bor03_FR)

The rewrite relation of the following TRS is considered.

zeros → cons(0,n__zeros) (1)
tail(cons(X,XS)) → activate(XS) (2)
zeros → n__zeros (3)
activate(n__zeros) → zeros (4)
activate(X) → X (5)

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.
activate#(n__zeros) → zeros# (6)
tail#(cons(X,XS)) → activate#(XS) (7)

1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.