LMPO
Execution Time (secs) | 0.046 |
Answer | YES(?,ELEMENTARY) |
Input | TCT 09 ma4 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, q(0()) -> 0()
, q(s(x)) -> s(plus(q(x), d(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(plus) = {1}, safe(0) = {}, safe(s) = {1}, safe(d) = {},
safe(q) = {}
and precedence
q > plus, q > d .
Following symbols are considered recursive:
{plus, d, q}
The recursion depth is 2 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ plus(0(); x) -> x
, plus(s(; y); x) -> s(; plus(y; x))
, d(0();) -> 0()
, d(s(; x);) -> s(; s(; d(x;)))
, q(0();) -> 0()
, q(s(; x);) -> s(; plus(d(x;); q(x;)))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.068 |
Answer | YES(?,PRIMREC) |
Input | TCT 09 ma4 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, q(0()) -> 0()
, q(s(x)) -> s(plus(q(x), d(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
plus > s, d > s, q > plus, q > s, q > d .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.061 |
Answer | YES(?,POLY) |
Input | TCT 09 ma4 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, q(0()) -> 0()
, q(s(x)) -> s(plus(q(x), d(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(plus) = {1}, safe(0) = {}, safe(s) = {1}, safe(d) = {},
safe(q) = {}
and precedence
q > plus, q > d .
Following symbols are considered recursive:
{plus, d, q}
The recursion depth is 2 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ plus(0(); x) -> x
, plus(s(; y); x) -> s(; plus(y; x))
, d(0();) -> 0()
, d(s(; x);) -> s(; s(; d(x;)))
, q(0();) -> 0()
, q(s(; x);) -> s(; plus(d(x;); q(x;)))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.079 |
Answer | YES(?,POLY) |
Input | TCT 09 ma4 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, q(0()) -> 0()
, q(s(x)) -> s(plus(q(x), d(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(plus) = {1}, safe(0) = {}, safe(s) = {1}, safe(d) = {},
safe(q) = {}
and precedence
q > plus, q > d .
Following symbols are considered recursive:
{plus, d, q}
The recursion depth is 2 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ plus(0(); x) -> x
, plus(s(; y); x) -> s(; plus(y; x))
, d(0();) -> 0()
, d(s(; x);) -> s(; s(; d(x;)))
, q(0();) -> 0()
, q(s(; x);) -> s(; plus(d(x;); q(x;)))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.081 |
Answer | MAYBE |
Input | TCT 09 ma4 |
MAYBE
We consider the following Problem:
Strict Trs:
{ plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, q(0()) -> 0()
, q(s(x)) -> s(plus(q(x), d(x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
Execution Time (secs) | 0.041 |
Answer | MAYBE |
Input | TCT 09 ma4 |
MAYBE
We consider the following Problem:
Strict Trs:
{ plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, d(0()) -> 0()
, d(s(x)) -> s(s(d(x)))
, q(0()) -> 0()
, q(s(x)) -> s(plus(q(x), d(x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..