Tool LMPO
Execution Time | 0.044 |
---|
Answer | YES(?,ELEMENTARY) |
---|
Input | SK90 4.45 |
---|
stdout:
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ f(x, x) -> a()
, f(g(x), y) -> f(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,ELEMENTARY)
Proof:
The input was oriented with the instance of
Lightweight Multiset Path Order () as induced by the safe mapping
safe(f) = {2}, safe(a) = {}, 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(x; x) -> a()
, f(g(; x); y) -> f(x; y)}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
Tool MPO
Execution Time | 0.029 |
---|
Answer | YES(?,PRIMREC) |
---|
Input | SK90 4.45 |
---|
stdout:
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ f(x, x) -> a()
, f(g(x), y) -> f(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,PRIMREC)
Proof:
The input was oriented with the instance of
'multiset path orders' as induced by the precedence
f > a, f ~ g .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
Execution Time | 0.025 |
---|
Answer | YES(?,POLY) |
---|
Input | SK90 4.45 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ f(x, x) -> a()
, f(g(x), y) -> f(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,POLY)
Proof:
The input was oriented with the instance of
Polynomial Path Order () as induced by the safe mapping
safe(f) = {2}, safe(a) = {}, 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(x; x) -> a()
, f(g(; x); y) -> f(x; y)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Tool POP* (PS)
Execution Time | 0.034 |
---|
Answer | YES(?,POLY) |
---|
Input | SK90 4.45 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ f(x, x) -> a()
, f(g(x), y) -> f(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,POLY)
Proof:
The input was oriented with the instance of
Polynomial Path Order (PS) as induced by the safe mapping
safe(f) = {2}, safe(a) = {}, 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(x; x) -> a()
, f(g(; x); y) -> f(x; y)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Tool Small POP*
Execution Time | 0.023 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.45 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, x) -> a()
, f(g(x), y) -> f(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC) as induced by the safe mapping
safe(f) = {2}, safe(a) = {}, 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(x; x) -> a()
, f(g(; x); y) -> f(x; y)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Tool Small POP* (PS)
Execution Time | 0.028 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.45 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, x) -> a()
, f(g(x), y) -> f(x, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS) as induced by the safe mapping
safe(f) = {2}, safe(a) = {}, 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(x; x) -> a()
, f(g(; x); y) -> f(x; y)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))