(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:
c(c(c(y))) → c(c(a(y, 0)))
c(a(a(0, x), y)) → a(c(c(c(0))), y)
c(y) → 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 2.
The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by:
final states : [1]
transitions:
a0(0, 0) → 0
00() → 0
c0(0) → 1
01() → 5
c1(5) → 4
c1(4) → 3
c1(3) → 2
a1(2, 0) → 1
02() → 8
a2(5, 8) → 7
c2(7) → 6
c2(6) → 2
0 → 1
5 → 4
4 → 3
3 → 2
6 → 2
7 → 6
(2) BOUNDS(1, n^1)