LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ U11(tt(), N, XS) -> U12(tt(), N, XS)
, U12(tt(), N, XS) -> snd(splitAt(N, XS))
, U21(tt(), X) -> U22(tt(), X)
, U22(tt(), X) -> X
, U31(tt(), N) -> U32(tt(), N)
, U32(tt(), N) -> N
, U41(tt(), N, XS) -> U42(tt(), N, XS)
, U42(tt(), N, XS) -> head(afterNth(N, XS))
, U51(tt(), Y) -> U52(tt(), Y)
, U52(tt(), Y) -> Y
, U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
, U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
, U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
, U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
, U71(tt(), XS) -> U72(tt(), XS)
, U72(tt(), XS) -> XS
, U81(tt(), N, XS) -> U82(tt(), N, XS)
, U82(tt(), N, XS) -> fst(splitAt(N, XS))
, afterNth(N, XS) -> U11(tt(), N, XS)
, fst(pair(X, Y)) -> U21(tt(), X)
, head(cons(N, XS)) -> U31(tt(), N)
, natsFrom(N) -> cons(N, natsFrom(s(N)))
, sel(N, XS) -> U41(tt(), N, XS)
, snd(pair(X, Y)) -> U51(tt(), Y)
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
, tail(cons(N, XS)) -> U71(tt(), XS)
, take(N, XS) -> U81(tt(), 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, XS) -> U12(tt(), N, XS)
, U12(tt(), N, XS) -> snd(splitAt(N, XS))
, U21(tt(), X) -> U22(tt(), X)
, U22(tt(), X) -> X
, U31(tt(), N) -> U32(tt(), N)
, U32(tt(), N) -> N
, U41(tt(), N, XS) -> U42(tt(), N, XS)
, U42(tt(), N, XS) -> head(afterNth(N, XS))
, U51(tt(), Y) -> U52(tt(), Y)
, U52(tt(), Y) -> Y
, U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
, U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
, U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
, U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
, U71(tt(), XS) -> U72(tt(), XS)
, U72(tt(), XS) -> XS
, U81(tt(), N, XS) -> U82(tt(), N, XS)
, U82(tt(), N, XS) -> fst(splitAt(N, XS))
, afterNth(N, XS) -> U11(tt(), N, XS)
, fst(pair(X, Y)) -> U21(tt(), X)
, head(cons(N, XS)) -> U31(tt(), N)
, natsFrom(N) -> cons(N, natsFrom(s(N)))
, sel(N, XS) -> U41(tt(), N, XS)
, snd(pair(X, Y)) -> U51(tt(), Y)
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
, tail(cons(N, XS)) -> U71(tt(), XS)
, take(N, XS) -> U81(tt(), 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, XS) -> U12(tt(), N, XS)
, U12(tt(), N, XS) -> snd(splitAt(N, XS))
, U21(tt(), X) -> U22(tt(), X)
, U22(tt(), X) -> X
, U31(tt(), N) -> U32(tt(), N)
, U32(tt(), N) -> N
, U41(tt(), N, XS) -> U42(tt(), N, XS)
, U42(tt(), N, XS) -> head(afterNth(N, XS))
, U51(tt(), Y) -> U52(tt(), Y)
, U52(tt(), Y) -> Y
, U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
, U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
, U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
, U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
, U71(tt(), XS) -> U72(tt(), XS)
, U72(tt(), XS) -> XS
, U81(tt(), N, XS) -> U82(tt(), N, XS)
, U82(tt(), N, XS) -> fst(splitAt(N, XS))
, afterNth(N, XS) -> U11(tt(), N, XS)
, fst(pair(X, Y)) -> U21(tt(), X)
, head(cons(N, XS)) -> U31(tt(), N)
, natsFrom(N) -> cons(N, natsFrom(s(N)))
, sel(N, XS) -> U41(tt(), N, XS)
, snd(pair(X, Y)) -> U51(tt(), Y)
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
, tail(cons(N, XS)) -> U71(tt(), XS)
, take(N, XS) -> U81(tt(), 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, XS) -> U12(tt(), N, XS)
, U12(tt(), N, XS) -> snd(splitAt(N, XS))
, U21(tt(), X) -> U22(tt(), X)
, U22(tt(), X) -> X
, U31(tt(), N) -> U32(tt(), N)
, U32(tt(), N) -> N
, U41(tt(), N, XS) -> U42(tt(), N, XS)
, U42(tt(), N, XS) -> head(afterNth(N, XS))
, U51(tt(), Y) -> U52(tt(), Y)
, U52(tt(), Y) -> Y
, U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
, U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
, U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
, U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
, U71(tt(), XS) -> U72(tt(), XS)
, U72(tt(), XS) -> XS
, U81(tt(), N, XS) -> U82(tt(), N, XS)
, U82(tt(), N, XS) -> fst(splitAt(N, XS))
, afterNth(N, XS) -> U11(tt(), N, XS)
, fst(pair(X, Y)) -> U21(tt(), X)
, head(cons(N, XS)) -> U31(tt(), N)
, natsFrom(N) -> cons(N, natsFrom(s(N)))
, sel(N, XS) -> U41(tt(), N, XS)
, snd(pair(X, Y)) -> U51(tt(), Y)
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
, tail(cons(N, XS)) -> U71(tt(), XS)
, take(N, XS) -> U81(tt(), 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, XS) -> U12(tt(), N, XS)
, U12(tt(), N, XS) -> snd(splitAt(N, XS))
, U21(tt(), X) -> U22(tt(), X)
, U22(tt(), X) -> X
, U31(tt(), N) -> U32(tt(), N)
, U32(tt(), N) -> N
, U41(tt(), N, XS) -> U42(tt(), N, XS)
, U42(tt(), N, XS) -> head(afterNth(N, XS))
, U51(tt(), Y) -> U52(tt(), Y)
, U52(tt(), Y) -> Y
, U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
, U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
, U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
, U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
, U71(tt(), XS) -> U72(tt(), XS)
, U72(tt(), XS) -> XS
, U81(tt(), N, XS) -> U82(tt(), N, XS)
, U82(tt(), N, XS) -> fst(splitAt(N, XS))
, afterNth(N, XS) -> U11(tt(), N, XS)
, fst(pair(X, Y)) -> U21(tt(), X)
, head(cons(N, XS)) -> U31(tt(), N)
, natsFrom(N) -> cons(N, natsFrom(s(N)))
, sel(N, XS) -> U41(tt(), N, XS)
, snd(pair(X, Y)) -> U51(tt(), Y)
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
, tail(cons(N, XS)) -> U71(tt(), XS)
, take(N, XS) -> U81(tt(), 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, XS) -> U12(tt(), N, XS)
, U12(tt(), N, XS) -> snd(splitAt(N, XS))
, U21(tt(), X) -> U22(tt(), X)
, U22(tt(), X) -> X
, U31(tt(), N) -> U32(tt(), N)
, U32(tt(), N) -> N
, U41(tt(), N, XS) -> U42(tt(), N, XS)
, U42(tt(), N, XS) -> head(afterNth(N, XS))
, U51(tt(), Y) -> U52(tt(), Y)
, U52(tt(), Y) -> Y
, U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
, U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
, U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
, U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
, U71(tt(), XS) -> U72(tt(), XS)
, U72(tt(), XS) -> XS
, U81(tt(), N, XS) -> U82(tt(), N, XS)
, U82(tt(), N, XS) -> fst(splitAt(N, XS))
, afterNth(N, XS) -> U11(tt(), N, XS)
, fst(pair(X, Y)) -> U21(tt(), X)
, head(cons(N, XS)) -> U31(tt(), N)
, natsFrom(N) -> cons(N, natsFrom(s(N)))
, sel(N, XS) -> U41(tt(), N, XS)
, snd(pair(X, Y)) -> U51(tt(), Y)
, splitAt(0(), XS) -> pair(nil(), XS)
, splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
, tail(cons(N, XS)) -> U71(tt(), XS)
, take(N, XS) -> U81(tt(), N, XS)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..