Certification Problem

Input (TPDB Runtime_Complexity_Innermost_Rewriting/hoca/id)

The rewrite relation of the following TRS is considered.

compS_f#1(compS_f(x2),x1) compS_f#1(x2,S(x1)) (1)
compS_f#1(id,x3) S(x3) (2)
iter#3(0) id (3)
iter#3(S(x6)) compS_f(iter#3(x6)) (4)
main(0) 0 (5)
main(S(x9)) compS_f#1(iter#3(x9),0) (6)
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.