Tool LMPO
Execution Time | 0.033 |
---|
Answer | YES(?,ELEMENTARY) |
---|
Input | Der95 06 |
---|
stdout:
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x)))}
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) = {}, 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)
Tool MPO
Execution Time | 0.034 |
---|
Answer | YES(?,PRIMREC) |
---|
Input | Der95 06 |
---|
stdout:
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x)))}
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 > g .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
Execution Time | 0.051 |
---|
Answer | YES(?,POLY) |
---|
Input | Der95 06 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x)))}
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) = {}, 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)
Tool POP* (PS)
Execution Time | 0.024 |
---|
Answer | YES(?,POLY) |
---|
Input | Der95 06 |
---|
stdout:
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x)))}
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) = {}, 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)
Tool Small POP*
Execution Time | 0.053 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 06 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x)))}
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) = {}, 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(?,O(n^1))
Tool Small POP* (PS)
Execution Time | 0.033 |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 06 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(g(x)) -> g(g(f(x)))
, f(g(x)) -> g(g(g(x)))}
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) = {}, 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(?,O(n^1))