LMPO
| Execution Time (secs) | 0.060 |
| Answer | YES(?,ELEMENTARY) |
| Input | SK90 4.29 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ merge(x, nil()) -> x
, merge(nil(), y) -> y
, merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
, merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))}
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(merge) = {}, safe(nil) = {}, safe(++) = {1, 2}, safe(u) = {},
safe(v) = {}
and precedence
empty .
Following symbols are considered recursive:
{merge}
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:
{ merge(x, nil();) -> x
, merge(nil(), y;) -> y
, merge(++(; x, y), ++(; u(), v());) ->
++(; x, merge(y, ++(; u(), v());))
, merge(++(; x, y), ++(; u(), v());) ->
++(; u(), merge(++(; x, y), v();))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
| Execution Time (secs) | 0.082 |
| Answer | YES(?,PRIMREC) |
| Input | SK90 4.29 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ merge(x, nil()) -> x
, merge(nil(), y) -> y
, merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
, merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))}
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
merge > ++ .
Hurray, we answered YES(?,PRIMREC)
POP*
| Execution Time (secs) | 0.055 |
| Answer | YES(?,POLY) |
| Input | SK90 4.29 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ merge(x, nil()) -> x
, merge(nil(), y) -> y
, merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
, merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))}
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(merge) = {}, safe(nil) = {}, safe(++) = {1, 2}, safe(u) = {},
safe(v) = {}
and precedence
empty .
Following symbols are considered recursive:
{merge}
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:
{ merge(x, nil();) -> x
, merge(nil(), y;) -> y
, merge(++(; x, y), ++(; u(), v());) ->
++(; x, merge(y, ++(; u(), v());))
, merge(++(; x, y), ++(; u(), v());) ->
++(; u(), merge(++(; x, y), v();))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
| Execution Time (secs) | 0.058 |
| Answer | YES(?,POLY) |
| Input | SK90 4.29 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ merge(x, nil()) -> x
, merge(nil(), y) -> y
, merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
, merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))}
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(merge) = {}, safe(nil) = {}, safe(++) = {1, 2}, safe(u) = {},
safe(v) = {}
and precedence
empty .
Following symbols are considered recursive:
{merge}
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:
{ merge(x, nil();) -> x
, merge(nil(), y;) -> y
, merge(++(; x, y), ++(; u(), v());) ->
++(; x, merge(y, ++(; u(), v());))
, merge(++(; x, y), ++(; u(), v());) ->
++(; u(), merge(++(; x, y), v();))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
| Execution Time (secs) | 0.112 |
| Answer | YES(?,O(n^1)) |
| Input | SK90 4.29 |
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ merge(x, nil()) -> x
, merge(nil(), y) -> y
, merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
, merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))}
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(merge) = {}, safe(nil) = {}, safe(++) = {1, 2}, safe(u) = {},
safe(v) = {}
and precedence
empty .
Following symbols are considered recursive:
{merge}
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:
{ merge(x, nil();) -> x
, merge(nil(), y;) -> y
, merge(++(; x, y), ++(; u(), v());) ->
++(; x, merge(y, ++(; u(), v());))
, merge(++(; x, y), ++(; u(), v());) ->
++(; u(), merge(++(; x, y), v();))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
| Execution Time (secs) | 0.112 |
| Answer | YES(?,O(n^1)) |
| Input | SK90 4.29 |
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ merge(x, nil()) -> x
, merge(nil(), y) -> y
, merge(++(x, y), ++(u(), v())) -> ++(x, merge(y, ++(u(), v())))
, merge(++(x, y), ++(u(), v())) -> ++(u(), merge(++(x, y), v()))}
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(merge) = {}, safe(nil) = {}, safe(++) = {1, 2}, safe(u) = {},
safe(v) = {}
and precedence
empty .
Following symbols are considered recursive:
{merge}
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:
{ merge(x, nil();) -> x
, merge(nil(), y;) -> y
, merge(++(; x, y), ++(; u(), v());) ->
++(; x, merge(y, ++(; u(), v());))
, merge(++(; x, y), ++(; u(), v());) ->
++(; u(), merge(++(; x, y), v();))}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))