LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)))}
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:
{ 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)))}
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:
{ 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)))}
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:
{ 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)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..