*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
*(x,+(y,z)) -> +(*(x,y),*(x,z))
Weak DP Rules:
Weak TRS Rules:
Signature:
{*/2} / {+/2}
Obligation:
Innermost
basic terms: {*}/{+}
Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
Proof:
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:
{}
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.
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
*(x,+(y,z)) -> +(*(x,y),*(x,z))
Signature:
{*/2} / {+/2}
Obligation:
Innermost
basic terms: {*}/{+}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).