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