Tool LMPO
Execution Time | 0.054 |
---|
Answer | YES(?,ELEMENTARY) |
---|
Input | Der95 08 |
---|
stdout:
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))}
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}
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;))}
Weak Trs : {}
Hurray, we answered YES(?,ELEMENTARY)
Tool MPO
Execution Time | 0.097 |
---|
Answer | YES(?,PRIMREC) |
---|
Input | Der95 08 |
---|
stdout:
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))}
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 > -, constant > 0 .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
Execution Time | 0.034 |
---|
Answer | MAYBE |
---|
Input | Der95 08 |
---|
stdout:
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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool POP* (PS)
Execution Time | 0.048 |
---|
Answer | MAYBE |
---|
Input | Der95 08 |
---|
stdout:
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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP*
Execution Time | 0.049 |
---|
Answer | MAYBE |
---|
Input | Der95 08 |
---|
stdout:
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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP* (PS)
Execution Time | 0.050 |
---|
Answer | MAYBE |
---|
Input | Der95 08 |
---|
stdout:
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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..