(0) Obligation:
The Runtime Complexity (innermost) of the given
CpxTRS could be proven to be
BOUNDS(1, n^1).
The TRS R consists of the following rules:
foldl#3(x2, Nil) → x2
foldl#3(x16, Cons(x24, x6)) → foldl#3(Cons(x24, x16), x6)
main(x1) → foldl#3(Nil, x1)
Rewrite Strategy: INNERMOST
(1) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1.
The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by:
final states : [1, 2]
transitions:
Nil0() → 0
Cons0(0, 0) → 0
foldl#30(0, 0) → 1
main0(0) → 2
Cons1(0, 0) → 3
foldl#31(3, 0) → 1
Nil1() → 4
foldl#31(4, 0) → 2
Cons1(0, 3) → 3
Cons1(0, 4) → 3
foldl#31(3, 0) → 2
0 → 1
3 → 1
3 → 2
4 → 2
(2) BOUNDS(1, n^1)