(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(s(x1), x2, x3, x4, x5) → f(x1, x2, x3, x4, x5)
f(0, s(x2), x3, x4, x5) → f(x2, x2, x3, x4, x5)
f(0, 0, s(x3), x4, x5) → f(x3, x3, x3, x4, x5)
f(0, 0, 0, s(x4), x5) → f(x4, x4, x4, x4, x5)
f(0, 0, 0, 0, s(x5)) → f(x5, x5, x5, x5, x5)
f(0, 0, 0, 0, 0) → 0
Rewrite Strategy: INNERMOST
(1) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
f(s(x1), x2, x3, x4, x5) →+ f(x1, x2, x3, x4, x5)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [x1 / s(x1)].
The result substitution is [ ].
(2) BOUNDS(n^1, INF)