(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, z))
Rewrite Strategy: FULL
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, z))
S is empty.
Rewrite Strategy: FULL
(3) SlicingProof (LOWER BOUND(ID) transformation)
Sliced the following arguments:
*/0
(4) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
*(+(y, z)) → +(*(y), *(z))
S is empty.
Rewrite Strategy: FULL
(5) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
*(+(y, z)) →+ +(*(y), *(z))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [y / +(y, z)].
The result substitution is [ ].
(6) BOUNDS(n^1, INF)