LMPO
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ a__c() -> a__f(g(c()))
, a__f(g(X)) -> g(X)
, mark(c()) -> a__c()
, mark(f(X)) -> a__f(X)
, mark(g(X)) -> g(X)
, a__c() -> c()
, a__f(X) -> f(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(a__c) = {}, safe(a__f) = {}, safe(g) = {1}, safe(c) = {},
safe(mark) = {}, safe(f) = {1}
and precedence
a__c > a__f, mark > a__c, mark > a__f .
Following symbols are considered recursive:
{a__f, mark}
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:
{ a__c() -> a__f(g(; c());)
, a__f(g(; X);) -> g(; X)
, mark(c();) -> a__c()
, mark(f(; X);) -> a__f(X;)
, mark(g(; X);) -> g(; X)
, a__c() -> c()
, a__f(X;) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ a__c() -> a__f(g(c()))
, a__f(g(X)) -> g(X)
, mark(c()) -> a__c()
, mark(f(X)) -> a__f(X)
, mark(g(X)) -> g(X)
, a__c() -> c()
, a__f(X) -> f(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
a__c > a__f, a__c > g, a__c > c, a__f > f, mark > a__c,
mark > a__f .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ a__c() -> a__f(g(c()))
, a__f(g(X)) -> g(X)
, mark(c()) -> a__c()
, mark(f(X)) -> a__f(X)
, mark(g(X)) -> g(X)
, a__c() -> c()
, a__f(X) -> f(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(a__c) = {}, safe(a__f) = {}, safe(g) = {1}, safe(c) = {},
safe(mark) = {}, safe(f) = {1}
and precedence
a__c > a__f, mark > a__c, mark > a__f .
Following symbols are considered recursive:
{a__f, mark}
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:
{ a__c() -> a__f(g(; c());)
, a__f(g(; X);) -> g(; X)
, mark(c();) -> a__c()
, mark(f(; X);) -> a__f(X;)
, mark(g(; X);) -> g(; X)
, a__c() -> c()
, a__f(X;) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ a__c() -> a__f(g(c()))
, a__f(g(X)) -> g(X)
, mark(c()) -> a__c()
, mark(f(X)) -> a__f(X)
, mark(g(X)) -> g(X)
, a__c() -> c()
, a__f(X) -> f(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(a__c) = {}, safe(a__f) = {1}, safe(g) = {1}, safe(c) = {},
safe(mark) = {}, safe(f) = {1}
and precedence
a__c > a__f, mark > a__c, mark > a__f .
Following symbols are considered recursive:
{a__f, mark}
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:
{ a__c() -> a__f(; g(; c()))
, a__f(; g(; X)) -> g(; X)
, mark(c();) -> a__c()
, mark(f(; X);) -> a__f(; X)
, mark(g(; X);) -> g(; X)
, a__c() -> c()
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ a__c() -> a__f(g(c()))
, a__f(g(X)) -> g(X)
, mark(c()) -> a__c()
, mark(f(X)) -> a__f(X)
, mark(g(X)) -> g(X)
, a__c() -> c()
, a__f(X) -> f(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(a__c) = {}, safe(a__f) = {1}, safe(g) = {1}, safe(c) = {},
safe(mark) = {1}, safe(f) = {1}
and precedence
a__c > a__f, mark > a__c, mark > a__f .
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:
{ a__c() -> a__f(; g(; c()))
, a__f(; g(; X)) -> g(; X)
, mark(; c()) -> a__c()
, mark(; f(; X)) -> a__f(; X)
, mark(; g(; X)) -> g(; X)
, a__c() -> c()
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,O(1))
Small POP* (PS)
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ a__c() -> a__f(g(c()))
, a__f(g(X)) -> g(X)
, mark(c()) -> a__c()
, mark(f(X)) -> a__f(X)
, mark(g(X)) -> g(X)
, a__c() -> c()
, a__f(X) -> f(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(a__c) = {}, safe(a__f) = {1}, safe(g) = {1}, safe(c) = {},
safe(mark) = {1}, safe(f) = {1}
and precedence
a__c > a__f, mark > a__c, mark > a__f .
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:
{ a__c() -> a__f(; g(; c()))
, a__f(; g(; X)) -> g(; X)
, mark(; c()) -> a__c()
, mark(; f(; X)) -> a__f(; X)
, mark(; g(; X)) -> g(; X)
, a__c() -> c()
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,O(1))