interpretations
Execution Time (secs) | - |
Answer | YES(?,O(n^1)) |
Input | SK90 2.47 |
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ a(b(x)) -> b(a(x))
, a(c(x)) -> x }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(a) = {}, Uargs(b) = {1}, Uargs(c) = {}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[a](x1) = [3] x1 + [2]
[b](x1) = [1] x1 + [2]
[c](x1) = [1] x1 + [3]
This order satisfies following ordering constraints
[a(b(x))] = [3] x + [8]
> [3] x + [4]
= [b(a(x))]
[a(c(x))] = [3] x + [11]
> [1] x + [0]
= [x]
Hurray, we answered YES(?,O(n^1))
lmpo
Execution Time (secs) | - |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.47 |
YES(?,ELEMENTARY)
We are left with following problem, upon which TcT provides the
certificate YES(?,ELEMENTARY).
Strict Trs:
{ a(b(x)) -> b(a(x))
, a(c(x)) -> x }
Obligation:
innermost runtime complexity
Answer:
YES(?,ELEMENTARY)
The input was oriented with the instance of 'Lightweight Multiset
Path Order' as induced by the safe mapping
safe(a) = {}, safe(b) = {1}, safe(c) = {1}
and precedence
empty .
Following symbols are considered recursive:
{a}
The recursion depth is 1.
For your convenience, here are the oriented rules in predicative
notation, possibly applying argument filtering:
Strict DPs:
Weak DPs :
Strict Trs:
{ a(b(; x);) -> b(; a(x;))
, a(c(; x);) -> x }
Weak Trs :
Hurray, we answered YES(?,ELEMENTARY)
mpo
Execution Time (secs) | - |
Answer | YES(?,PRIMREC) |
Input | SK90 2.47 |
YES(?,PRIMREC)
We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).
Strict Trs:
{ a(b(x)) -> b(a(x))
, a(c(x)) -> x }
Obligation:
innermost runtime complexity
Answer:
YES(?,PRIMREC)
The input was oriented with the instance of'multiset path orders'
as induced by the precedence
a > b .
Hurray, we answered YES(?,PRIMREC)
popstar
Execution Time (secs) | 0.090 |
Answer | YES(?,POLY) |
Input | SK90 2.47 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ a(b(x)) -> b(a(x))
, a(c(x)) -> x }
Obligation:
innermost runtime complexity
Answer:
YES(?,POLY)
The input was oriented with the instance of 'Polynomial Path Order'
as induced by the safe mapping
safe(a) = {}, safe(b) = {1}, safe(c) = {1}
and precedence
empty .
Following symbols are considered recursive:
{a}
The recursion depth is 1.
For your convenience, here are the oriented rules in predicative
notation, possibly applying argument filtering:
Strict DPs:
Weak DPs :
Strict Trs:
{ a(b(; x);) -> b(; a(x;))
, a(c(; x);) -> x }
Weak Trs :
Hurray, we answered YES(?,POLY)
popstar-ps
Execution Time (secs) | 0.076 |
Answer | YES(?,POLY) |
Input | SK90 2.47 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ a(b(x)) -> b(a(x))
, a(c(x)) -> x }
Obligation:
innermost runtime complexity
Answer:
YES(?,POLY)
The input was oriented with the instance of 'Polynomial Path Order
(PS)' as induced by the safe mapping
safe(a) = {}, safe(b) = {1}, safe(c) = {1}
and precedence
empty .
Following symbols are considered recursive:
{a}
The recursion depth is 1.
For your convenience, here are the oriented rules in predicative
notation, possibly applying argument filtering:
Strict DPs:
Weak DPs :
Strict Trs:
{ a(b(; x);) -> b(; a(x;))
, a(c(; x);) -> x }
Weak Trs :
Hurray, we answered YES(?,POLY)