LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__pairNs() -> cons(0(), incr(oddNs()))
, a__oddNs() -> a__incr(a__pairNs())
, a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__zip(nil(), XS) -> nil()
, a__zip(X, nil()) -> nil()
, a__zip(cons(X, XS), cons(Y, YS)) ->
cons(pair(mark(X), mark(Y)), zip(XS, YS))
, a__tail(cons(X, XS)) -> mark(XS)
, a__repItems(nil()) -> nil()
, a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
, mark(pairNs()) -> a__pairNs()
, mark(incr(X)) -> a__incr(mark(X))
, mark(oddNs()) -> a__oddNs()
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
, mark(tail(X)) -> a__tail(mark(X))
, mark(repItems(X)) -> a__repItems(mark(X))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(nil()) -> nil()
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, a__pairNs() -> pairNs()
, a__incr(X) -> incr(X)
, a__oddNs() -> oddNs()
, a__take(X1, X2) -> take(X1, X2)
, a__zip(X1, X2) -> zip(X1, X2)
, a__tail(X) -> tail(X)
, a__repItems(X) -> repItems(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:
{ a__pairNs() -> cons(0(), incr(oddNs()))
, a__oddNs() -> a__incr(a__pairNs())
, a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__zip(nil(), XS) -> nil()
, a__zip(X, nil()) -> nil()
, a__zip(cons(X, XS), cons(Y, YS)) ->
cons(pair(mark(X), mark(Y)), zip(XS, YS))
, a__tail(cons(X, XS)) -> mark(XS)
, a__repItems(nil()) -> nil()
, a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
, mark(pairNs()) -> a__pairNs()
, mark(incr(X)) -> a__incr(mark(X))
, mark(oddNs()) -> a__oddNs()
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
, mark(tail(X)) -> a__tail(mark(X))
, mark(repItems(X)) -> a__repItems(mark(X))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(nil()) -> nil()
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, a__pairNs() -> pairNs()
, a__incr(X) -> incr(X)
, a__oddNs() -> oddNs()
, a__take(X1, X2) -> take(X1, X2)
, a__zip(X1, X2) -> zip(X1, X2)
, a__tail(X) -> tail(X)
, a__repItems(X) -> repItems(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:
{ a__pairNs() -> cons(0(), incr(oddNs()))
, a__oddNs() -> a__incr(a__pairNs())
, a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__zip(nil(), XS) -> nil()
, a__zip(X, nil()) -> nil()
, a__zip(cons(X, XS), cons(Y, YS)) ->
cons(pair(mark(X), mark(Y)), zip(XS, YS))
, a__tail(cons(X, XS)) -> mark(XS)
, a__repItems(nil()) -> nil()
, a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
, mark(pairNs()) -> a__pairNs()
, mark(incr(X)) -> a__incr(mark(X))
, mark(oddNs()) -> a__oddNs()
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
, mark(tail(X)) -> a__tail(mark(X))
, mark(repItems(X)) -> a__repItems(mark(X))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(nil()) -> nil()
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, a__pairNs() -> pairNs()
, a__incr(X) -> incr(X)
, a__oddNs() -> oddNs()
, a__take(X1, X2) -> take(X1, X2)
, a__zip(X1, X2) -> zip(X1, X2)
, a__tail(X) -> tail(X)
, a__repItems(X) -> repItems(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:
{ a__pairNs() -> cons(0(), incr(oddNs()))
, a__oddNs() -> a__incr(a__pairNs())
, a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__zip(nil(), XS) -> nil()
, a__zip(X, nil()) -> nil()
, a__zip(cons(X, XS), cons(Y, YS)) ->
cons(pair(mark(X), mark(Y)), zip(XS, YS))
, a__tail(cons(X, XS)) -> mark(XS)
, a__repItems(nil()) -> nil()
, a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
, mark(pairNs()) -> a__pairNs()
, mark(incr(X)) -> a__incr(mark(X))
, mark(oddNs()) -> a__oddNs()
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
, mark(tail(X)) -> a__tail(mark(X))
, mark(repItems(X)) -> a__repItems(mark(X))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(nil()) -> nil()
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, a__pairNs() -> pairNs()
, a__incr(X) -> incr(X)
, a__oddNs() -> oddNs()
, a__take(X1, X2) -> take(X1, X2)
, a__zip(X1, X2) -> zip(X1, X2)
, a__tail(X) -> tail(X)
, a__repItems(X) -> repItems(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:
{ a__pairNs() -> cons(0(), incr(oddNs()))
, a__oddNs() -> a__incr(a__pairNs())
, a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__zip(nil(), XS) -> nil()
, a__zip(X, nil()) -> nil()
, a__zip(cons(X, XS), cons(Y, YS)) ->
cons(pair(mark(X), mark(Y)), zip(XS, YS))
, a__tail(cons(X, XS)) -> mark(XS)
, a__repItems(nil()) -> nil()
, a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
, mark(pairNs()) -> a__pairNs()
, mark(incr(X)) -> a__incr(mark(X))
, mark(oddNs()) -> a__oddNs()
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
, mark(tail(X)) -> a__tail(mark(X))
, mark(repItems(X)) -> a__repItems(mark(X))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(nil()) -> nil()
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, a__pairNs() -> pairNs()
, a__incr(X) -> incr(X)
, a__oddNs() -> oddNs()
, a__take(X1, X2) -> take(X1, X2)
, a__zip(X1, X2) -> zip(X1, X2)
, a__tail(X) -> tail(X)
, a__repItems(X) -> repItems(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:
{ a__pairNs() -> cons(0(), incr(oddNs()))
, a__oddNs() -> a__incr(a__pairNs())
, a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__zip(nil(), XS) -> nil()
, a__zip(X, nil()) -> nil()
, a__zip(cons(X, XS), cons(Y, YS)) ->
cons(pair(mark(X), mark(Y)), zip(XS, YS))
, a__tail(cons(X, XS)) -> mark(XS)
, a__repItems(nil()) -> nil()
, a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
, mark(pairNs()) -> a__pairNs()
, mark(incr(X)) -> a__incr(mark(X))
, mark(oddNs()) -> a__oddNs()
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
, mark(tail(X)) -> a__tail(mark(X))
, mark(repItems(X)) -> a__repItems(mark(X))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(0()) -> 0()
, mark(s(X)) -> s(mark(X))
, mark(nil()) -> nil()
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, a__pairNs() -> pairNs()
, a__incr(X) -> incr(X)
, a__oddNs() -> oddNs()
, a__take(X1, X2) -> take(X1, X2)
, a__zip(X1, X2) -> zip(X1, X2)
, a__tail(X) -> tail(X)
, a__repItems(X) -> repItems(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..