Problem Rubio 04 enno

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Rubio 04 enno

stdout:

MAYBE

Problem:
lt(0(),s(X)) -> true()
lt(s(X),0()) -> false()
lt(s(X),s(Y)) -> lt(X,Y)
append(nil(),Y) -> Y
append(add(N,X),Y) -> add(N,append(X,Y))
split(N,nil()) -> pair(nil(),nil())
split(N,add(M,Y)) -> f_1(split(N,Y),N,M,Y)
f_1(pair(X,Z),N,M,Y) -> f_2(lt(N,M),N,M,Y,X,Z)
f_2(true(),N,M,Y,X,Z) -> pair(X,add(M,Z))
f_2(false(),N,M,Y,X,Z) -> pair(add(M,X),Z)
qsort(nil()) -> nil()
qsort(add(N,X)) -> f_3(split(N,X),N,X)
f_3(pair(Y,Z),N,X) -> append(qsort(Y),add(X,qsort(Z)))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Rubio 04 enno

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Rubio 04 enno

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  lt(0(), s(X)) -> true()
     , lt(s(X), 0()) -> false()
     , lt(s(X), s(Y)) -> lt(X, Y)
     , append(nil(), Y) -> Y
     , append(add(N, X), Y) -> add(N, append(X, Y))
     , split(N, nil()) -> pair(nil(), nil())
     , split(N, add(M, Y)) -> f_1(split(N, Y), N, M, Y)
     , f_1(pair(X, Z), N, M, Y) -> f_2(lt(N, M), N, M, Y, X, Z)
     , f_2(true(), N, M, Y, X, Z) -> pair(X, add(M, Z))
     , f_2(false(), N, M, Y, X, Z) -> pair(add(M, X), Z)
     , qsort(nil()) -> nil()
     , qsort(add(N, X)) -> f_3(split(N, X), N, X)
     , f_3(pair(Y, Z), N, X) -> append(qsort(Y), add(X, qsort(Z)))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Rubio 04 enno

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Rubio 04 enno

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  lt(0(), s(X)) -> true()
     , lt(s(X), 0()) -> false()
     , lt(s(X), s(Y)) -> lt(X, Y)
     , append(nil(), Y) -> Y
     , append(add(N, X), Y) -> add(N, append(X, Y))
     , split(N, nil()) -> pair(nil(), nil())
     , split(N, add(M, Y)) -> f_1(split(N, Y), N, M, Y)
     , f_1(pair(X, Z), N, M, Y) -> f_2(lt(N, M), N, M, Y, X, Z)
     , f_2(true(), N, M, Y, X, Z) -> pair(X, add(M, Z))
     , f_2(false(), N, M, Y, X, Z) -> pair(add(M, X), Z)
     , qsort(nil()) -> nil()
     , qsort(add(N, X)) -> f_3(split(N, X), N, X)
     , f_3(pair(Y, Z), N, X) -> append(qsort(Y), add(X, qsort(Z)))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds