LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ U11(tt(), N, X, XS) ->
U12(splitAt(activate(N), activate(XS)), activate(X))
, U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
, afterNth(N, XS) -> snd(splitAt(N, XS))
, and(tt(), X) -> activate(X)
, fst(pair(X, Y)) -> X
, head(cons(N, XS)) -> N
, natsFrom(N) -> cons(N, n__natsFrom(s(N)))
, sel(N, XS) -> head(afterNth(N, XS))
, snd(pair(X, Y)) -> Y
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
, tail(cons(N, XS)) -> activate(XS)
, take(N, XS) -> fst(splitAt(N, XS))
, natsFrom(X) -> n__natsFrom(X)
, activate(n__natsFrom(X)) -> natsFrom(X)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ U11(tt(), N, X, XS) ->
U12(splitAt(activate(N), activate(XS)), activate(X))
, U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
, afterNth(N, XS) -> snd(splitAt(N, XS))
, and(tt(), X) -> activate(X)
, fst(pair(X, Y)) -> X
, head(cons(N, XS)) -> N
, natsFrom(N) -> cons(N, n__natsFrom(s(N)))
, sel(N, XS) -> head(afterNth(N, XS))
, snd(pair(X, Y)) -> Y
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
, tail(cons(N, XS)) -> activate(XS)
, take(N, XS) -> fst(splitAt(N, XS))
, natsFrom(X) -> n__natsFrom(X)
, activate(n__natsFrom(X)) -> natsFrom(X)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ U11(tt(), N, X, XS) ->
U12(splitAt(activate(N), activate(XS)), activate(X))
, U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
, afterNth(N, XS) -> snd(splitAt(N, XS))
, and(tt(), X) -> activate(X)
, fst(pair(X, Y)) -> X
, head(cons(N, XS)) -> N
, natsFrom(N) -> cons(N, n__natsFrom(s(N)))
, sel(N, XS) -> head(afterNth(N, XS))
, snd(pair(X, Y)) -> Y
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
, tail(cons(N, XS)) -> activate(XS)
, take(N, XS) -> fst(splitAt(N, XS))
, natsFrom(X) -> n__natsFrom(X)
, activate(n__natsFrom(X)) -> natsFrom(X)
, activate(X) -> X}
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:
{ U11(tt(), N, X, XS) ->
U12(splitAt(activate(N), activate(XS)), activate(X))
, U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
, afterNth(N, XS) -> snd(splitAt(N, XS))
, and(tt(), X) -> activate(X)
, fst(pair(X, Y)) -> X
, head(cons(N, XS)) -> N
, natsFrom(N) -> cons(N, n__natsFrom(s(N)))
, sel(N, XS) -> head(afterNth(N, XS))
, snd(pair(X, Y)) -> Y
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
, tail(cons(N, XS)) -> activate(XS)
, take(N, XS) -> fst(splitAt(N, XS))
, natsFrom(X) -> n__natsFrom(X)
, activate(n__natsFrom(X)) -> natsFrom(X)
, activate(X) -> X}
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:
{ U11(tt(), N, X, XS) ->
U12(splitAt(activate(N), activate(XS)), activate(X))
, U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
, afterNth(N, XS) -> snd(splitAt(N, XS))
, and(tt(), X) -> activate(X)
, fst(pair(X, Y)) -> X
, head(cons(N, XS)) -> N
, natsFrom(N) -> cons(N, n__natsFrom(s(N)))
, sel(N, XS) -> head(afterNth(N, XS))
, snd(pair(X, Y)) -> Y
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
, tail(cons(N, XS)) -> activate(XS)
, take(N, XS) -> fst(splitAt(N, XS))
, natsFrom(X) -> n__natsFrom(X)
, activate(n__natsFrom(X)) -> natsFrom(X)
, activate(X) -> X}
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:
{ U11(tt(), N, X, XS) ->
U12(splitAt(activate(N), activate(XS)), activate(X))
, U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
, afterNth(N, XS) -> snd(splitAt(N, XS))
, and(tt(), X) -> activate(X)
, fst(pair(X, Y)) -> X
, head(cons(N, XS)) -> N
, natsFrom(N) -> cons(N, n__natsFrom(s(N)))
, sel(N, XS) -> head(afterNth(N, XS))
, snd(pair(X, Y)) -> Y
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U11(tt(), N, X, activate(XS))
, tail(cons(N, XS)) -> activate(XS)
, take(N, XS) -> fst(splitAt(N, XS))
, natsFrom(X) -> n__natsFrom(X)
, activate(n__natsFrom(X)) -> natsFrom(X)
, activate(X) -> X}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..