interpretations
Execution Time (secs) | - |
Answer | YES(?,O(n^1)) |
Input | Der95 06 |
YES(?,O(n^1))
We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x))) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
TcT has computed following constructor-based matrix interpretation
satisfying not(EDA).
[f](x1) = [3] x1 + [2]
[g](x1) = [1] x1 + [2]
This order satisfies following ordering constraints
[f(g(x))] = [3] x + [8]
> [3] x + [6]
= [g(g(f(x)))]
[f(g(x))] = [3] x + [8]
> [1] x + [6]
= [g(g(g(x)))]
Hurray, we answered YES(?,O(n^1))
lmpo
Execution Time (secs) | - |
Answer | YES(?,ELEMENTARY) |
Input | Der95 06 |
YES(?,ELEMENTARY)
We are left with following problem, upon which TcT provides the
certificate YES(?,ELEMENTARY).
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(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(f) = {}, safe(g) = {1}
and precedence
empty .
Following symbols are considered recursive:
{f}
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:
{ f(g(; x);) -> g(; g(; f(x;)))
, f(g(; x);) -> g(; g(; g(; x))) }
Weak Trs :
Hurray, we answered YES(?,ELEMENTARY)
mpo
Execution Time (secs) | - |
Answer | YES(?,PRIMREC) |
Input | Der95 06 |
YES(?,PRIMREC)
We are left with following problem, upon which TcT provides the
certificate YES(?,PRIMREC).
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x))) }
Obligation:
innermost runtime complexity
Answer:
YES(?,PRIMREC)
The input was oriented with the instance of'multiset path orders'
as induced by the precedence
f > g .
Hurray, we answered YES(?,PRIMREC)
popstar
Execution Time (secs) | 0.070 |
Answer | YES(?,POLY) |
Input | Der95 06 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(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(f) = {}, safe(g) = {1}
and precedence
empty .
Following symbols are considered recursive:
{f}
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:
{ f(g(; x);) -> g(; g(; f(x;)))
, f(g(; x);) -> g(; g(; g(; x))) }
Weak Trs :
Hurray, we answered YES(?,POLY)
popstar-ps
Execution Time (secs) | 0.064 |
Answer | YES(?,POLY) |
Input | Der95 06 |
YES(?,POLY)
We are left with following problem, upon which TcT provides the
certificate YES(?,POLY).
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(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(f) = {}, safe(g) = {1}
and precedence
empty .
Following symbols are considered recursive:
{f}
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:
{ f(g(; x);) -> g(; g(; f(x;)))
, f(g(; x);) -> g(; g(; g(; x))) }
Weak Trs :
Hurray, we answered YES(?,POLY)