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