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