LMPO
Execution Time (secs) | 0.134 |
Answer | YES(?,ELEMENTARY) |
Input | Der95 11 |
YES(?,ELEMENTARY)
We consider the following Problem:
Strict Trs:
{ D(t()) -> 1()
, D(constant()) -> 0()
, D(+(x, y)) -> +(D(x), D(y))
, D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
, D(-(x, y)) -> -(D(x), D(y))
, D(minus(x)) -> minus(D(x))
, D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
, D(ln(x)) -> div(D(x), x)
, D(pow(x, y)) ->
+(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))}
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(t) = {}, safe(1) = {}, safe(constant) = {},
safe(0) = {}, safe(+) = {1, 2}, safe(*) = {1, 2}, safe(-) = {1, 2},
safe(minus) = {1}, safe(div) = {1, 2}, safe(pow) = {1, 2},
safe(2) = {}, safe(ln) = {1}
and precedence
empty .
Following symbols are considered recursive:
{D}
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:
{ D(t();) -> 1()
, D(constant();) -> 0()
, D(+(; x, y);) -> +(; D(x;), D(y;))
, D(*(; x, y);) -> +(; *(; y, D(x;)), *(; x, D(y;)))
, D(-(; x, y);) -> -(; D(x;), D(y;))
, D(minus(; x);) -> minus(; D(x;))
, D(div(; x, y);) ->
-(; div(; D(x;), y), div(; *(; x, D(y;)), pow(; y, 2())))
, D(ln(; x);) -> div(; D(x;), x)
, D(pow(; x, y);) ->
+(; *(; *(; y, pow(; x, -(; y, 1()))), D(x;)),
*(; *(; pow(; x, y), ln(; x)), D(y;)))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
MPO
Execution Time (secs) | 0.196 |
Answer | YES(?,PRIMREC) |
Input | Der95 11 |
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ D(t()) -> 1()
, D(constant()) -> 0()
, D(+(x, y)) -> +(D(x), D(y))
, D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
, D(-(x, y)) -> -(D(x), D(y))
, D(minus(x)) -> minus(D(x))
, D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
, D(ln(x)) -> div(D(x), x)
, D(pow(x, y)) ->
+(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))}
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 > 1, D > +, D > *, D > -, D > minus, D > div, D > pow, D > 2,
D > ln, constant > 0 .
Hurray, we answered YES(?,PRIMREC)
POP*
Execution Time (secs) | 0.094 |
Answer | MAYBE |
Input | Der95 11 |
MAYBE
We consider the following Problem:
Strict Trs:
{ D(t()) -> 1()
, D(constant()) -> 0()
, D(+(x, y)) -> +(D(x), D(y))
, D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
, D(-(x, y)) -> -(D(x), D(y))
, D(minus(x)) -> minus(D(x))
, D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
, D(ln(x)) -> div(D(x), x)
, D(pow(x, y)) ->
+(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
Execution Time (secs) | 0.096 |
Answer | MAYBE |
Input | Der95 11 |
MAYBE
We consider the following Problem:
Strict Trs:
{ D(t()) -> 1()
, D(constant()) -> 0()
, D(+(x, y)) -> +(D(x), D(y))
, D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
, D(-(x, y)) -> -(D(x), D(y))
, D(minus(x)) -> minus(D(x))
, D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
, D(ln(x)) -> div(D(x), x)
, D(pow(x, y)) ->
+(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
Execution Time (secs) | 0.094 |
Answer | MAYBE |
Input | Der95 11 |
MAYBE
We consider the following Problem:
Strict Trs:
{ D(t()) -> 1()
, D(constant()) -> 0()
, D(+(x, y)) -> +(D(x), D(y))
, D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
, D(-(x, y)) -> -(D(x), D(y))
, D(minus(x)) -> minus(D(x))
, D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
, D(ln(x)) -> div(D(x), x)
, D(pow(x, y)) ->
+(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
Execution Time (secs) | 0.111 |
Answer | MAYBE |
Input | Der95 11 |
MAYBE
We consider the following Problem:
Strict Trs:
{ D(t()) -> 1()
, D(constant()) -> 0()
, D(+(x, y)) -> +(D(x), D(y))
, D(*(x, y)) -> +(*(y, D(x)), *(x, D(y)))
, D(-(x, y)) -> -(D(x), D(y))
, D(minus(x)) -> minus(D(x))
, D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2())))
, D(ln(x)) -> div(D(x), x)
, D(pow(x, y)) ->
+(*(*(y, pow(x, -(y, 1()))), D(x)), *(*(pow(x, y), ln(x)), D(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..