LMPO
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ p(m, n, s(r)) -> p(m, r, n)
, p(m, s(n), 0()) -> p(0(), n, m)
, p(m, 0(), 0()) -> m}
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(p) = {}, safe(s) = {1}, safe(0) = {}
and precedence
empty .
Following symbols are considered recursive:
{p}
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:
{ p(m, n, s(; r);) -> p(m, r, n;)
, p(m, s(; n), 0();) -> p(0(), n, m;)
, p(m, 0(), 0();) -> m}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ p(m, n, s(r)) -> p(m, r, n)
, p(m, s(n), 0()) -> p(0(), n, m)
, p(m, 0(), 0()) -> m}
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
empty .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ p(m, n, s(r)) -> p(m, r, n)
, p(m, s(n), 0()) -> p(0(), n, m)
, p(m, 0(), 0()) -> m}
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(p) = {}, safe(s) = {1}, safe(0) = {}
and precedence
empty .
Following symbols are considered recursive:
{p}
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:
{ p(m, n, s(; r);) -> p(m, r, n;)
, p(m, s(; n), 0();) -> p(0(), n, m;)
, p(m, 0(), 0();) -> m}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ p(m, n, s(r)) -> p(m, r, n)
, p(m, s(n), 0()) -> p(0(), n, m)
, p(m, 0(), 0()) -> m}
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(p) = {}, safe(s) = {1}, safe(0) = {}
and precedence
empty .
Following symbols are considered recursive:
{p}
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:
{ p(m, n, s(; r);) -> p(m, r, n;)
, p(m, s(; n), 0();) -> p(0(), n, m;)
, p(m, 0(), 0();) -> m}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(m, n, s(r)) -> p(m, r, n)
, p(m, s(n), 0()) -> p(0(), n, m)
, p(m, 0(), 0()) -> m}
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(p) = {}, safe(s) = {1}, safe(0) = {}
and precedence
empty .
Following symbols are considered recursive:
{p}
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:
{ p(m, n, s(; r);) -> p(m, r, n;)
, p(m, s(; n), 0();) -> p(0(), n, m;)
, p(m, 0(), 0();) -> m}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(m, n, s(r)) -> p(m, r, n)
, p(m, s(n), 0()) -> p(0(), n, m)
, p(m, 0(), 0()) -> m}
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(p) = {}, safe(s) = {1}, safe(0) = {}
and precedence
empty .
Following symbols are considered recursive:
{p}
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:
{ p(m, n, s(; r);) -> p(m, r, n;)
, p(m, s(; n), 0();) -> p(0(), n, m;)
, p(m, 0(), 0();) -> m}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))