Certification Problem

Input (TPDB Runtime_Complexity_Innermost_Rewriting/SK90/4.47)

The rewrite relation of the following TRS is considered.

f(g(i(a,b,b'),c),d) if(e,f(.(b,c),d'),f(.(b',c),d')) (1)
f(g(h(a,b),c),d) if(e,f(.(b,g(h(a,b),c)),d),f(c,d')) (2)
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.