LMPO
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ app(nil(), YS) -> YS
, app(cons(X), YS) -> cons(X)
, from(X) -> cons(X)
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
, prefix(L) -> cons(nil())}
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(app) = {1, 2}, safe(nil) = {}, safe(cons) = {1},
safe(from) = {1}, safe(zWadr) = {1}, safe(prefix) = {}
and precedence
zWadr > app .
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:
{ app(; nil(), YS) -> YS
, app(; cons(; X), YS) -> cons(; X)
, from(; X) -> cons(; X)
, zWadr(YS; nil()) -> nil()
, zWadr(nil(); XS) -> nil()
, zWadr(cons(; Y); cons(; X)) -> cons(; app(; Y, cons(; X)))
, prefix(L;) -> cons(; nil())}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ app(nil(), YS) -> YS
, app(cons(X), YS) -> cons(X)
, from(X) -> cons(X)
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
, prefix(L) -> cons(nil())}
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
from > cons, zWadr > app, zWadr > cons, prefix > nil,
prefix > cons .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ app(nil(), YS) -> YS
, app(cons(X), YS) -> cons(X)
, from(X) -> cons(X)
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
, prefix(L) -> cons(nil())}
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(app) = {}, safe(nil) = {}, safe(cons) = {1}, safe(from) = {1},
safe(zWadr) = {}, safe(prefix) = {}
and precedence
app ~ zWadr .
Following symbols are considered recursive:
{app, zWadr}
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:
{ app(nil(), YS;) -> YS
, app(cons(; X), YS;) -> cons(; X)
, from(; X) -> cons(; X)
, zWadr(nil(), YS;) -> nil()
, zWadr(XS, nil();) -> nil()
, zWadr(cons(; X), cons(; Y);) -> cons(; app(Y, cons(; X);))
, prefix(L;) -> cons(; nil())}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ app(nil(), YS) -> YS
, app(cons(X), YS) -> cons(X)
, from(X) -> cons(X)
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
, prefix(L) -> cons(nil())}
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(app) = {1, 2}, safe(nil) = {}, safe(cons) = {1},
safe(from) = {1}, safe(zWadr) = {2}, safe(prefix) = {}
and precedence
zWadr > app .
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:
{ app(; nil(), YS) -> YS
, app(; cons(; X), YS) -> cons(; X)
, from(; X) -> cons(; X)
, zWadr(nil(); YS) -> nil()
, zWadr(XS; nil()) -> nil()
, zWadr(cons(; X); cons(; Y)) -> cons(; app(; Y, cons(; X)))
, prefix(L;) -> cons(; nil())}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ app(nil(), YS) -> YS
, app(cons(X), YS) -> cons(X)
, from(X) -> cons(X)
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
, prefix(L) -> cons(nil())}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC) as induced by the safe mapping
safe(app) = {}, safe(nil) = {}, safe(cons) = {1}, safe(from) = {1},
safe(zWadr) = {}, safe(prefix) = {}
and precedence
zWadr > app .
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:
{ app(nil(), YS;) -> YS
, app(cons(; X), YS;) -> cons(; X)
, from(; X) -> cons(; X)
, zWadr(nil(), YS;) -> nil()
, zWadr(XS, nil();) -> nil()
, zWadr(cons(; X), cons(; Y);) -> cons(; app(Y, cons(; X);))
, prefix(L;) -> cons(; nil())}
Weak Trs : {}
Hurray, we answered YES(?,O(1))
Small POP* (PS)
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ app(nil(), YS) -> YS
, app(cons(X), YS) -> cons(X)
, from(X) -> cons(X)
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
, prefix(L) -> cons(nil())}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
PS) as induced by the safe mapping
safe(app) = {1, 2}, safe(nil) = {}, safe(cons) = {1},
safe(from) = {1}, safe(zWadr) = {1}, safe(prefix) = {}
and precedence
zWadr > app .
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:
{ app(; nil(), YS) -> YS
, app(; cons(; X), YS) -> cons(; X)
, from(; X) -> cons(; X)
, zWadr(YS; nil()) -> nil()
, zWadr(nil(); XS) -> nil()
, zWadr(cons(; Y); cons(; X)) -> cons(; app(; Y, cons(; X)))
, prefix(L;) -> cons(; nil())}
Weak Trs : {}
Hurray, we answered YES(?,O(1))