LMPO
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ zeros() -> cons(0(), n__zeros())
, tail(cons(X, XS)) -> activate(XS)
, zeros() -> n__zeros()
, activate(n__zeros()) -> zeros()
, activate(X) -> 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(zeros) = {}, safe(cons) = {1, 2}, safe(0) = {},
safe(n__zeros) = {}, safe(tail) = {}, safe(activate) = {}
and precedence
tail > activate, activate > zeros .
Following symbols are considered recursive:
{tail, activate}
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:
{ zeros() -> cons(; 0(), n__zeros())
, tail(cons(; X, XS);) -> activate(XS;)
, zeros() -> n__zeros()
, activate(n__zeros();) -> zeros()
, activate(X;) -> X}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ zeros() -> cons(0(), n__zeros())
, tail(cons(X, XS)) -> activate(XS)
, zeros() -> n__zeros()
, activate(n__zeros()) -> zeros()
, activate(X) -> 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
zeros > cons, zeros > 0, zeros > n__zeros, zeros ~ activate,
tail ~ activate .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ zeros() -> cons(0(), n__zeros())
, tail(cons(X, XS)) -> activate(XS)
, zeros() -> n__zeros()
, activate(n__zeros()) -> zeros()
, activate(X) -> 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(zeros) = {}, safe(cons) = {1, 2}, safe(0) = {},
safe(n__zeros) = {}, safe(tail) = {}, safe(activate) = {}
and precedence
tail > activate, activate > zeros .
Following symbols are considered recursive:
{tail, activate}
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:
{ zeros() -> cons(; 0(), n__zeros())
, tail(cons(; X, XS);) -> activate(XS;)
, zeros() -> n__zeros()
, activate(n__zeros();) -> zeros()
, activate(X;) -> X}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ zeros() -> cons(0(), n__zeros())
, tail(cons(X, XS)) -> activate(XS)
, zeros() -> n__zeros()
, activate(n__zeros()) -> zeros()
, activate(X) -> 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(zeros) = {}, safe(cons) = {1, 2}, safe(0) = {},
safe(n__zeros) = {}, safe(tail) = {}, safe(activate) = {1}
and precedence
tail > activate, activate > zeros .
Following symbols are considered recursive:
{tail, activate}
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:
{ zeros() -> cons(; 0(), n__zeros())
, tail(cons(; X, XS);) -> activate(; XS)
, zeros() -> n__zeros()
, activate(; n__zeros()) -> zeros()
, activate(; X) -> X}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ zeros() -> cons(0(), n__zeros())
, tail(cons(X, XS)) -> activate(XS)
, zeros() -> n__zeros()
, activate(n__zeros()) -> zeros()
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
Nat 0-bounded) as induced by the safe mapping
safe(zeros) = {}, safe(cons) = {1, 2}, safe(0) = {},
safe(n__zeros) = {}, safe(tail) = {1}, safe(activate) = {1}
and precedence
tail > activate, activate > zeros .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ zeros() -> cons(; 0(), n__zeros())
, tail(; cons(; X, XS)) -> activate(; XS)
, zeros() -> n__zeros()
, activate(; n__zeros()) -> zeros()
, activate(; X) -> X}
Weak Trs : {}
Hurray, we answered YES(?,O(1))
Small POP* (PS)
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ zeros() -> cons(0(), n__zeros())
, tail(cons(X, XS)) -> activate(XS)
, zeros() -> n__zeros()
, activate(n__zeros()) -> zeros()
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS,
Nat 0-bounded) as induced by the safe mapping
safe(zeros) = {}, safe(cons) = {1, 2}, safe(0) = {},
safe(n__zeros) = {}, safe(tail) = {1}, safe(activate) = {1}
and precedence
tail > activate, activate > zeros .
Following symbols are considered recursive:
{}
The recursion depth is 0 .
For your convenience, here are the oriented rules in predicative
notation (possibly applying argument filtering):
Strict DPs: {}
Weak DPs : {}
Strict Trs:
{ zeros() -> cons(; 0(), n__zeros())
, tail(; cons(; X, XS)) -> activate(; XS)
, zeros() -> n__zeros()
, activate(; n__zeros()) -> zeros()
, activate(; X) -> X}
Weak Trs : {}
Hurray, we answered YES(?,O(1))