Certification Problem

Input (TPDB Runtime_Complexity_Innermost_Rewriting/Mixed_TRS/jones6)

The rewrite relation of the following TRS is considered.

f(a,empty) g(a,empty) (1)
f(a,cons(x,k)) f(cons(x,a),k) (2)
g(empty,d) d (3)
g(cons(x,k),d) g(k,cons(x,d)) (4)
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 2. This is shown by the following automaton.