LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, low(n, nil()) -> nil()
, low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
, if_low(true(), n, add(m, x)) -> add(m, low(n, x))
, if_low(false(), n, add(m, x)) -> low(n, x)
, high(n, nil()) -> nil()
, high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
, if_high(true(), n, add(m, x)) -> high(n, x)
, if_high(false(), n, add(m, x)) -> add(m, high(n, x))
, head(add(n, x)) -> n
, tail(add(n, x)) -> x
, isempty(nil()) -> true()
, isempty(add(n, x)) -> false()
, quicksort(x) ->
if_qs(isempty(x),
low(head(x), tail(x)),
head(x),
high(head(x), tail(x)))
, if_qs(true(), x, n, y) -> nil()
, if_qs(false(), x, n, y) ->
app(quicksort(x), add(n, quicksort(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, low(n, nil()) -> nil()
, low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
, if_low(true(), n, add(m, x)) -> add(m, low(n, x))
, if_low(false(), n, add(m, x)) -> low(n, x)
, high(n, nil()) -> nil()
, high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
, if_high(true(), n, add(m, x)) -> high(n, x)
, if_high(false(), n, add(m, x)) -> add(m, high(n, x))
, head(add(n, x)) -> n
, tail(add(n, x)) -> x
, isempty(nil()) -> true()
, isempty(add(n, x)) -> false()
, quicksort(x) ->
if_qs(isempty(x),
low(head(x), tail(x)),
head(x),
high(head(x), tail(x)))
, if_qs(true(), x, n, y) -> nil()
, if_qs(false(), x, n, y) ->
app(quicksort(x), add(n, quicksort(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, low(n, nil()) -> nil()
, low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
, if_low(true(), n, add(m, x)) -> add(m, low(n, x))
, if_low(false(), n, add(m, x)) -> low(n, x)
, high(n, nil()) -> nil()
, high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
, if_high(true(), n, add(m, x)) -> high(n, x)
, if_high(false(), n, add(m, x)) -> add(m, high(n, x))
, head(add(n, x)) -> n
, tail(add(n, x)) -> x
, isempty(nil()) -> true()
, isempty(add(n, x)) -> false()
, quicksort(x) ->
if_qs(isempty(x),
low(head(x), tail(x)),
head(x),
high(head(x), tail(x)))
, if_qs(true(), x, n, y) -> nil()
, if_qs(false(), x, n, y) ->
app(quicksort(x), add(n, quicksort(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, low(n, nil()) -> nil()
, low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
, if_low(true(), n, add(m, x)) -> add(m, low(n, x))
, if_low(false(), n, add(m, x)) -> low(n, x)
, high(n, nil()) -> nil()
, high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
, if_high(true(), n, add(m, x)) -> high(n, x)
, if_high(false(), n, add(m, x)) -> add(m, high(n, x))
, head(add(n, x)) -> n
, tail(add(n, x)) -> x
, isempty(nil()) -> true()
, isempty(add(n, x)) -> false()
, quicksort(x) ->
if_qs(isempty(x),
low(head(x), tail(x)),
head(x),
high(head(x), tail(x)))
, if_qs(true(), x, n, y) -> nil()
, if_qs(false(), x, n, y) ->
app(quicksort(x), add(n, quicksort(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, low(n, nil()) -> nil()
, low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
, if_low(true(), n, add(m, x)) -> add(m, low(n, x))
, if_low(false(), n, add(m, x)) -> low(n, x)
, high(n, nil()) -> nil()
, high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
, if_high(true(), n, add(m, x)) -> high(n, x)
, if_high(false(), n, add(m, x)) -> add(m, high(n, x))
, head(add(n, x)) -> n
, tail(add(n, x)) -> x
, isempty(nil()) -> true()
, isempty(add(n, x)) -> false()
, quicksort(x) ->
if_qs(isempty(x),
low(head(x), tail(x)),
head(x),
high(head(x), tail(x)))
, if_qs(true(), x, n, y) -> nil()
, if_qs(false(), x, n, y) ->
app(quicksort(x), add(n, quicksort(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, low(n, nil()) -> nil()
, low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
, if_low(true(), n, add(m, x)) -> add(m, low(n, x))
, if_low(false(), n, add(m, x)) -> low(n, x)
, high(n, nil()) -> nil()
, high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
, if_high(true(), n, add(m, x)) -> high(n, x)
, if_high(false(), n, add(m, x)) -> add(m, high(n, x))
, head(add(n, x)) -> n
, tail(add(n, x)) -> x
, isempty(nil()) -> true()
, isempty(add(n, x)) -> false()
, quicksort(x) ->
if_qs(isempty(x),
low(head(x), tail(x)),
head(x),
high(head(x), tail(x)))
, if_qs(true(), x, n, y) -> nil()
, if_qs(false(), x, n, y) ->
app(quicksort(x), add(n, quicksort(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..