finding  a+rev(a) +.* is as good as finding --> a+rev(a)
The pattern searching is usuaally done in O(n) time if I'm not mistaken.

find the info below..

DID YOU ASK something else?
Single pattern algorithms 

Let *m* be the length of the pattern and let *n* be the length of the 
searchable text.
 Algorithm Preprocessing time Matching time1  Naïve string search algorithm 0 
(no preprocessing) Θ((n-m+1) m)  Rabin–Karp string search 
algorithm<http://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_string_search_algorithm>
 
Θ(m) average Θ(n+m),
worst Θ((n-m+1) m)  Finite-state 
automaton<http://en.wikipedia.org/wiki/Finite-state_machine>based search Θ(m 
|Σ|) Θ(n)  Knuth–Morris–Pratt 
algorithm<http://en.wikipedia.org/wiki/Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm>
 
Θ(m) Θ(n)  Boyer–Moore string search 
algorithm<http://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string_search_algorithm>
 Θ(m 
+ |Σ|) Ω(n/m), O(n)  Bitap 
algorithm<http://en.wikipedia.org/wiki/Bitap_algorithm>(
*shift-or*, *shift-and*, *Baeza–Yates–Gonnet*) Θ(m + |Σ|) O(mn)


SOURCE: http://en.wikipedia.org/wiki/String_searching_algorithm

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