LMPO
Execution Time (secs) | 0.021 |
Answer | YES(?,ELEMENTARY) |
Input | AProVE 10 ex5 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g, f}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0()}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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
s > g, s > f .
Hurray, we answered YES(?,PRIMREC)
POP*
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g, f}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0()}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g, f}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0()}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0()}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))
Small POP* (PS)
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}
and precedence
g > f .
Following symbols are considered recursive:
{g}
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:
{ g(0();) -> 0()
, g(s(; x);) -> f(; g(x;))
, f(; 0()) -> 0()}
Weak Trs : {}
Hurray, we answered YES(?,O(n^1))