LMPO
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ a__f(f(a())) -> c(f(g(f(a()))))
, mark(f(X)) -> a__f(mark(X))
, mark(a()) -> a()
, mark(c(X)) -> c(X)
, mark(g(X)) -> g(mark(X))
, 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__f) = {1}, safe(f) = {1}, safe(a) = {}, safe(c) = {1},
safe(g) = {1}, safe(mark) = {}
and precedence
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__f(; f(; a())) -> c(; f(; g(; f(; a()))))
, mark(f(; X);) -> a__f(; mark(X;))
, mark(a();) -> a()
, mark(c(; X);) -> c(; X)
, mark(g(; X);) -> g(; mark(X;))
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ a__f(f(a())) -> c(f(g(f(a()))))
, mark(f(X)) -> a__f(mark(X))
, mark(a()) -> a()
, mark(c(X)) -> c(X)
, mark(g(X)) -> g(mark(X))
, 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__f > f, a__f > c, a__f > g, mark > a__f, mark > g .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ a__f(f(a())) -> c(f(g(f(a()))))
, mark(f(X)) -> a__f(mark(X))
, mark(a()) -> a()
, mark(c(X)) -> c(X)
, mark(g(X)) -> g(mark(X))
, 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__f) = {1}, safe(f) = {1}, safe(a) = {}, safe(c) = {1},
safe(g) = {1}, safe(mark) = {}
and precedence
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__f(; f(; a())) -> c(; f(; g(; f(; a()))))
, mark(f(; X);) -> a__f(; mark(X;))
, mark(a();) -> a()
, mark(c(; X);) -> c(; X)
, mark(g(; X);) -> g(; mark(X;))
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ a__f(f(a())) -> c(f(g(f(a()))))
, mark(f(X)) -> a__f(mark(X))
, mark(a()) -> a()
, mark(c(X)) -> c(X)
, mark(g(X)) -> g(mark(X))
, 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__f) = {1}, safe(f) = {1}, safe(a) = {}, safe(c) = {1},
safe(g) = {1}, safe(mark) = {}
and precedence
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__f(; f(; a())) -> c(; f(; g(; f(; a()))))
, mark(f(; X);) -> a__f(; mark(X;))
, mark(a();) -> a()
, mark(c(; X);) -> c(; X)
, mark(g(; X);) -> g(; mark(X;))
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a__f(f(a())) -> c(f(g(f(a()))))
, mark(f(X)) -> a__f(mark(X))
, mark(a()) -> a()
, mark(c(X)) -> c(X)
, mark(g(X)) -> g(mark(X))
, a__f(X) -> f(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Proof:
The input was oriented with the instance of
Small Polynomial Path Order (WSC,
Nat 1-bounded) as induced by the safe mapping
safe(a__f) = {1}, safe(f) = {1}, safe(a) = {}, safe(c) = {1},
safe(g) = {1}, safe(mark) = {}
and precedence
mark > a__f .
Following symbols are considered recursive:
{mark}
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:
{ a__f(; f(; a())) -> c(; f(; g(; f(; a()))))
, mark(f(; X);) -> a__f(; mark(X;))
, mark(a();) -> a()
, mark(c(; X);) -> c(; X)
, mark(g(; X);) -> g(; mark(X;))
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a__f(f(a())) -> c(f(g(f(a()))))
, mark(f(X)) -> a__f(mark(X))
, mark(a()) -> a()
, mark(c(X)) -> c(X)
, mark(g(X)) -> g(mark(X))
, a__f(X) -> f(X)}
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,
Nat 1-bounded) as induced by the safe mapping
safe(a__f) = {1}, safe(f) = {1}, safe(a) = {}, safe(c) = {1},
safe(g) = {1}, safe(mark) = {}
and precedence
mark > a__f .
Following symbols are considered recursive:
{mark}
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:
{ a__f(; f(; a())) -> c(; f(; g(; f(; a()))))
, mark(f(; X);) -> a__f(; mark(X;))
, mark(a();) -> a()
, mark(c(; X);) -> c(; X)
, mark(g(; X);) -> g(; mark(X;))
, a__f(; X) -> f(; X)}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))