LMPO

Execution Time (secs)	0.112
Answer	MAYBE
Input	Rubio 04 quick

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

Execution Time (secs)	0.146
Answer	MAYBE
Input	Rubio 04 quick

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*

Execution Time (secs)	0.094
Answer	MAYBE
Input	Rubio 04 quick

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)

Execution Time (secs)	0.111
Answer	MAYBE
Input	Rubio 04 quick

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*

Execution Time (secs)	0.102
Answer	MAYBE
Input	Rubio 04 quick

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)

Execution Time (secs)	0.145
Answer	MAYBE
Input	Rubio 04 quick

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..

Problem Rubio 04 quick

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)