LMPO
Execution Time (secs) | 0.044 |
Answer | YES(?,ELEMENTARY) |
Input | SK90 2.48 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ d(x) -> e(u(x))
, d(u(x)) -> c(x)
, c(u(x)) -> b(x)
, v(e(x)) -> x
, b(u(x)) -> a(e(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(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {},
safe(b) = {}, safe(v) = {}, safe(a) = {1}
and precedence
d > c, c ~ b .
Following symbols are considered recursive:
{d, c, b}
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:
{ d(x;) -> e(; u(; x))
, d(u(; x);) -> c(x;)
, c(u(; x);) -> b(x;)
, v(e(; x);) -> x
, b(u(; x);) -> a(; e(; x))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.042 |
Answer | YES(?,PRIMREC) |
Input | SK90 2.48 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ d(x) -> e(u(x))
, d(u(x)) -> c(x)
, c(u(x)) -> b(x)
, v(e(x)) -> x
, b(u(x)) -> a(e(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
d > e, d > u, d > c, b > e, b > a, c ~ b .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.037 |
Answer | YES(?,POLY) |
Input | SK90 2.48 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ d(x) -> e(u(x))
, d(u(x)) -> c(x)
, c(u(x)) -> b(x)
, v(e(x)) -> x
, b(u(x)) -> a(e(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(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {},
safe(b) = {}, safe(v) = {}, safe(a) = {1}
and precedence
d > c, c ~ b .
Following symbols are considered recursive:
{d, c, b}
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:
{ d(x;) -> e(; u(; x))
, d(u(; x);) -> c(x;)
, c(u(; x);) -> b(x;)
, v(e(; x);) -> x
, b(u(; x);) -> a(; e(; x))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
POP* (PS)
Execution Time (secs) | 0.034 |
Answer | YES(?,POLY) |
Input | SK90 2.48 |
YES(?,POLY)
We consider the following Problem:
Strict Trs:
{ d(x) -> e(u(x))
, d(u(x)) -> c(x)
, c(u(x)) -> b(x)
, v(e(x)) -> x
, b(u(x)) -> a(e(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(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {1},
safe(b) = {1}, safe(v) = {}, safe(a) = {1}
and precedence
c > b, d ~ c .
Following symbols are considered recursive:
{d, c, b}
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:
{ d(x;) -> e(; u(; x))
, d(u(; x);) -> c(; x)
, c(; u(; x)) -> b(; x)
, v(e(; x);) -> x
, b(; u(; x)) -> a(; e(; x))}
Weak Trs : {}
Hurray, we answered YES(?,POLY)
Small POP*
Execution Time (secs) | 0.058 |
Answer | YES(?,O(1)) |
Input | SK90 2.48 |
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ d(x) -> e(u(x))
, d(u(x)) -> c(x)
, c(u(x)) -> b(x)
, v(e(x)) -> x
, b(u(x)) -> a(e(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(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {1},
safe(b) = {1}, safe(v) = {}, safe(a) = {1}
and precedence
d > c, c > b .
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:
{ d(x;) -> e(; u(; x))
, d(u(; x);) -> c(; x)
, c(; u(; x)) -> b(; x)
, v(e(; x);) -> x
, b(; u(; x)) -> a(; e(; x))}
Weak Trs : {}
Hurray, we answered YES(?,O(1))
Small POP* (PS)
Execution Time (secs) | 0.069 |
Answer | YES(?,O(1)) |
Input | SK90 2.48 |
YES(?,O(1))
We consider the following Problem:
Strict Trs:
{ d(x) -> e(u(x))
, d(u(x)) -> c(x)
, c(u(x)) -> b(x)
, v(e(x)) -> x
, b(u(x)) -> a(e(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(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {},
safe(b) = {1}, safe(v) = {}, safe(a) = {1}
and precedence
d > c, c > b .
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:
{ d(x;) -> e(; u(; x))
, d(u(; x);) -> c(x;)
, c(u(; x);) -> b(; x)
, v(e(; x);) -> x
, b(; u(; x)) -> a(; e(; x))}
Weak Trs : {}
Hurray, we answered YES(?,O(1))