Certification Problem

Input (TPDB Runtime_Complexity_Innermost_Rewriting/Frederiksen_Glenstrup/evenodd)

The rewrite relation of the following TRS is considered.

odd(Cons(x,xs)) → even(xs) (1)
odd(Nil) → False (2)
even(Cons(x,xs)) → odd(xs) (3)
notEmpty(Cons(x,xs)) → True (4)
notEmpty(Nil) → False (5)
even(Nil) → True (6)
evenodd(x) → even(x) (7)
The evaluation strategy is innermost.

Property / Task

Determine bounds on the runtime complexity.

Answer / Result

An upperbound for the complexity is O(n).

Proof (by AProVE @ termCOMP 2023)

1 Bounds

The given TRS is match-(raise)-bounded by 1. This is shown by the following automaton.