LMPO
Execution Time (secs) | 0.031 |
Answer | YES(?,ELEMENTARY) |
Input | TCT 09 append |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))}
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(app) = {}, safe(nil) = {}, safe(cons) = {1, 2}
and precedence
empty .
Following symbols are considered recursive:
{app}
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:
{ app(nil(), xs;) -> nil()
, app(cons(; x, xs), ys;) -> cons(; x, app(xs, ys;))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))}
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
app > cons .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))}
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(app) = {}, safe(nil) = {}, safe(cons) = {1, 2}
and precedence
empty .
Following symbols are considered recursive:
{app}
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:
{ app(nil(), xs;) -> nil()
, app(cons(; x, xs), ys;) -> cons(; x, app(xs, ys;))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))}
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(app) = {}, safe(nil) = {}, safe(cons) = {1, 2}
and precedence
empty .
Following symbols are considered recursive:
{app}
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:
{ app(nil(), xs;) -> nil()
, app(cons(; x, xs), ys;) -> cons(; x, app(xs, ys;))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))}
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(app) = {}, safe(nil) = {}, safe(cons) = {1, 2}
and precedence
empty .
Following symbols are considered recursive:
{app}
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:
{ app(nil(), xs;) -> nil()
, app(cons(; x, xs), ys;) -> cons(; x, app(xs, ys;))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ app(nil(), xs) -> nil()
, app(cons(x, xs), ys) -> cons(x, app(xs, ys))}
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(app) = {2}, safe(nil) = {}, safe(cons) = {1, 2}
and precedence
empty .
Following symbols are considered recursive:
{app}
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:
{ app(nil(); xs) -> nil()
, app(cons(; x, xs); ys) -> cons(; x, app(xs; ys))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))