pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X
TAKE(s(N), cons(X, XS)) → CONS(X, n__take(N, activate(XS)))
INCR(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__incr(X)) → INCR(X)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ODDNS → INCR(pairNs)
INCR(cons(X, XS)) → CONS(s(X), n__incr(activate(XS)))
ACTIVATE(n__repItems(X)) → REPITEMS(X)
TAKE(s(N), cons(X, XS)) → ACTIVATE(XS)
PAIRNS → ODDNS
PAIRNS → CONS(0, n__incr(oddNs))
ODDNS → PAIRNS
ACTIVATE(n__cons(X1, X2)) → CONS(X1, X2)
ZIP(cons(X, XS), cons(Y, YS)) → CONS(pair(X, Y), n__zip(activate(XS), activate(YS)))
REPITEMS(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__zip(X1, X2)) → ZIP(X1, X2)
ACTIVATE(n__take(X1, X2)) → TAKE(X1, X2)
REPITEMS(cons(X, XS)) → CONS(X, n__cons(X, n__repItems(activate(XS))))
TAIL(cons(X, XS)) → ACTIVATE(XS)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
TAKE(s(N), cons(X, XS)) → CONS(X, n__take(N, activate(XS)))
INCR(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__incr(X)) → INCR(X)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ODDNS → INCR(pairNs)
INCR(cons(X, XS)) → CONS(s(X), n__incr(activate(XS)))
ACTIVATE(n__repItems(X)) → REPITEMS(X)
TAKE(s(N), cons(X, XS)) → ACTIVATE(XS)
PAIRNS → ODDNS
PAIRNS → CONS(0, n__incr(oddNs))
ODDNS → PAIRNS
ACTIVATE(n__cons(X1, X2)) → CONS(X1, X2)
ZIP(cons(X, XS), cons(Y, YS)) → CONS(pair(X, Y), n__zip(activate(XS), activate(YS)))
REPITEMS(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__zip(X1, X2)) → ZIP(X1, X2)
ACTIVATE(n__take(X1, X2)) → TAKE(X1, X2)
REPITEMS(cons(X, XS)) → CONS(X, n__cons(X, n__repItems(activate(XS))))
TAIL(cons(X, XS)) → ACTIVATE(XS)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
INCR(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__incr(X)) → INCR(X)
REPITEMS(cons(X, XS)) → ACTIVATE(XS)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__zip(X1, X2)) → ZIP(X1, X2)
ACTIVATE(n__take(X1, X2)) → TAKE(X1, X2)
ACTIVATE(n__repItems(X)) → REPITEMS(X)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
TAKE(s(N), cons(X, XS)) → ACTIVATE(XS)
pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
INCR(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__incr(X)) → INCR(X)
REPITEMS(cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__zip(X1, X2)) → ZIP(X1, X2)
ACTIVATE(n__take(X1, X2)) → TAKE(X1, X2)
ACTIVATE(n__repItems(X)) → REPITEMS(X)
TAKE(s(N), cons(X, XS)) → ACTIVATE(XS)
Used ordering: Polynomial interpretation [25,35]:
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
The value of delta used in the strict ordering is 1.
POL(cons(x1, x2)) = (3)x_2
POL(n__incr(x1)) = 4 + (2)x_1
POL(TAKE(x1, x2)) = x_1 + (3)x_2
POL(n__take(x1, x2)) = 2 + (4)x_1 + (2)x_2
POL(ZIP(x1, x2)) = (3)x_1 + x_2
POL(n__repItems(x1)) = 4 + (4)x_1
POL(s(x1)) = 1
POL(n__zip(x1, x2)) = 4 + (2)x_1 + (3)x_2
POL(REPITEMS(x1)) = 4 + (3)x_1
POL(INCR(x1)) = 3 + (3)x_1
POL(ACTIVATE(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ZIP(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
PAIRNS → ODDNS
ODDNS → PAIRNS
pairNs → cons(0, n__incr(oddNs))
oddNs → incr(pairNs)
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, n__take(N, activate(XS)))
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X, XS), cons(Y, YS)) → cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
tail(cons(X, XS)) → activate(XS)
repItems(nil) → nil
repItems(cons(X, XS)) → cons(X, n__cons(X, n__repItems(activate(XS))))
incr(X) → n__incr(X)
take(X1, X2) → n__take(X1, X2)
zip(X1, X2) → n__zip(X1, X2)
cons(X1, X2) → n__cons(X1, X2)
repItems(X) → n__repItems(X)
activate(n__incr(X)) → incr(X)
activate(n__take(X1, X2)) → take(X1, X2)
activate(n__zip(X1, X2)) → zip(X1, X2)
activate(n__cons(X1, X2)) → cons(X1, X2)
activate(n__repItems(X)) → repItems(X)
activate(X) → X