* Step 1: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
*(x,+(y,z)) -> +(*(x,y),*(x,z))
- Signature:
{*/2} / {+/2}
- Obligation:
runtime complexity wrt. defined symbols {*} and constructors {+}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
+ Details:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(+) = {1,2}
Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(*) = [6] x2 + [1]
p(+) = [1] x1 + [1] x2 + [2]
Following rules are strictly oriented:
*(x,+(y,z)) = [6] y + [6] z + [13]
> [6] y + [6] z + [4]
= +(*(x,y),*(x,z))
Following rules are (at-least) weakly oriented:
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
*(x,+(y,z)) -> +(*(x,y),*(x,z))
- Signature:
{*/2} / {+/2}
- Obligation:
runtime complexity wrt. defined symbols {*} and constructors {+}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))