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(cons(N, L), Y) -> cons(N, app(L, Y))
, low(N, nil()) -> nil()
, low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
, iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
, iflow(false(), N, cons(M, L)) -> low(N, L)
, high(N, nil()) -> nil()
, high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
, ifhigh(true(), N, cons(M, L)) -> high(N, L)
, ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
, quicksort(nil()) -> nil()
, quicksort(cons(N, L)) ->
app(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))}
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(cons(N, L), Y) -> cons(N, app(L, Y))
, low(N, nil()) -> nil()
, low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
, iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
, iflow(false(), N, cons(M, L)) -> low(N, L)
, high(N, nil()) -> nil()
, high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
, ifhigh(true(), N, cons(M, L)) -> high(N, L)
, ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
, quicksort(nil()) -> nil()
, quicksort(cons(N, L)) ->
app(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))}
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(cons(N, L), Y) -> cons(N, app(L, Y))
, low(N, nil()) -> nil()
, low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
, iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
, iflow(false(), N, cons(M, L)) -> low(N, L)
, high(N, nil()) -> nil()
, high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
, ifhigh(true(), N, cons(M, L)) -> high(N, L)
, ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
, quicksort(nil()) -> nil()
, quicksort(cons(N, L)) ->
app(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))}
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(cons(N, L), Y) -> cons(N, app(L, Y))
, low(N, nil()) -> nil()
, low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
, iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
, iflow(false(), N, cons(M, L)) -> low(N, L)
, high(N, nil()) -> nil()
, high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
, ifhigh(true(), N, cons(M, L)) -> high(N, L)
, ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
, quicksort(nil()) -> nil()
, quicksort(cons(N, L)) ->
app(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))}
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(cons(N, L), Y) -> cons(N, app(L, Y))
, low(N, nil()) -> nil()
, low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
, iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
, iflow(false(), N, cons(M, L)) -> low(N, L)
, high(N, nil()) -> nil()
, high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
, ifhigh(true(), N, cons(M, L)) -> high(N, L)
, ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
, quicksort(nil()) -> nil()
, quicksort(cons(N, L)) ->
app(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))}
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(cons(N, L), Y) -> cons(N, app(L, Y))
, low(N, nil()) -> nil()
, low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L))
, iflow(true(), N, cons(M, L)) -> cons(M, low(N, L))
, iflow(false(), N, cons(M, L)) -> low(N, L)
, high(N, nil()) -> nil()
, high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
, ifhigh(true(), N, cons(M, L)) -> high(N, L)
, ifhigh(false(), N, cons(M, L)) -> cons(M, high(N, L))
, quicksort(nil()) -> nil()
, quicksort(cons(N, L)) ->
app(quicksort(low(N, L)), cons(N, quicksort(high(N, L))))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..