(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:
anchored(Cons(x, xs), y) → anchored(xs, Cons(Cons(Nil, Nil), y))
anchored(Nil, y) → y
goal(x, y) → anchored(x, y)
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:
Cons0(0, 0) → 0
Nil0() → 0
anchored0(0, 0) → 1
goal0(0, 0) → 2
Nil1() → 5
Nil1() → 6
Cons1(5, 6) → 4
Cons1(4, 0) → 3
anchored1(0, 3) → 1
anchored1(0, 0) → 2
Cons1(4, 3) → 3
anchored1(0, 3) → 2
0 → 1
0 → 2
3 → 1
3 → 2
(2) BOUNDS(1, n^1)