(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
isLeaf(leaf) → true
isLeaf(cons(u, v)) → false
left(cons(u, v)) → u
right(cons(u, v)) → v
concat(leaf, y) → y
concat(cons(u, v), y) → cons(u, concat(v, y))
less_leaves(u, v) → if1(isLeaf(u), isLeaf(v), u, v)
if1(b, true, u, v) → false
if1(b, false, u, v) → if2(b, u, v)
if2(true, u, v) → true
if2(false, u, v) → less_leaves(concat(left(u), right(u)), concat(left(v), right(v)))
Rewrite Strategy: FULL
(1) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
concat(cons(u, v), y) →+ cons(u, concat(v, y))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [v / cons(u, v)].
The result substitution is [ ].
(2) BOUNDS(n^1, INF)