We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(n^1)).
Strict Trs: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) }
Obligation:
runtime complexity
Answer:
YES(O(1),O(n^1))
We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.
Trs: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) }
The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).
Sub-proof:
----------
The following argument positions are usable:
Uargs(+) = {1, 2}
TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA).
[*](x1, x2) = [2] x2 + [0]
[+](x1, x2) = [1] x1 + [1] x2 + [4]
The order satisfies the following ordering constraints:
[*(x, +(y, z))] = [2] y + [2] z + [8]
> [2] y + [2] z + [4]
= [+(*(x, y), *(x, z))]
We return to the main proof.
We are left with following problem, upon which TcT provides the
certificate YES(O(1),O(1)).
Weak Trs: { *(x, +(y, z)) -> +(*(x, y), *(x, z)) }
Obligation:
runtime complexity
Answer:
YES(O(1),O(1))
Empty rules are trivially bounded
Hurray, we answered YES(O(1),O(n^1))