Certification Problem

Input (TPDB Runtime_Complexity_Innermost_Rewriting/SK90/2.36)

The rewrite relation of the following TRS is considered.

implies(not(x),y) or(x,y) (1)
implies(not(x),or(y,z)) implies(y,or(x,z)) (2)
implies(x,or(y,z)) or(y,implies(x,z)) (3)
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.