* Step 1: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(g(x),y,y) -> g(f(x,x,y))
- Signature:
{f/3} / {g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {g}
+ 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(g) = {1}
Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(f) = [8] x1 + [0]
p(g) = [1] x1 + [1]
Following rules are strictly oriented:
f(g(x),y,y) = [8] x + [8]
> [8] x + [1]
= g(f(x,x,y))
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:
f(g(x),y,y) -> g(f(x,x,y))
- Signature:
{f/3} / {g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {g}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))