from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
QUOT(s(X), s(Y)) → QUOT(minus(X, Y), s(Y))
ACTIVATE(n__from(X)) → ACTIVATE(X)
SEL(s(N), cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__s(X)) → S(activate(X))
ZWQUOT(cons(X, XS), cons(Y, YS)) → QUOT(X, Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
QUOT(s(X), s(Y)) → MINUS(X, Y)
QUOT(s(X), s(Y)) → S(quot(minus(X, Y), s(Y)))
MINUS(s(X), s(Y)) → MINUS(X, Y)
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__from(X)) → FROM(activate(X))
SEL(s(N), cons(X, XS)) → SEL(N, activate(XS))
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
QUOT(s(X), s(Y)) → QUOT(minus(X, Y), s(Y))
ACTIVATE(n__from(X)) → ACTIVATE(X)
SEL(s(N), cons(X, XS)) → ACTIVATE(XS)
ACTIVATE(n__s(X)) → S(activate(X))
ZWQUOT(cons(X, XS), cons(Y, YS)) → QUOT(X, Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
QUOT(s(X), s(Y)) → MINUS(X, Y)
QUOT(s(X), s(Y)) → S(quot(minus(X, Y), s(Y)))
MINUS(s(X), s(Y)) → MINUS(X, Y)
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__from(X)) → FROM(activate(X))
SEL(s(N), cons(X, XS)) → SEL(N, activate(XS))
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
MINUS(s(X), s(Y)) → MINUS(X, Y)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MINUS(s(X), s(Y)) → MINUS(X, Y)
The value of delta used in the strict ordering is 12.
POL(MINUS(x1, x2)) = (3)x_2
POL(s(x1)) = 4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
QUOT(s(X), s(Y)) → QUOT(minus(X, Y), s(Y))
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
QUOT(s(X), s(Y)) → QUOT(minus(X, Y), s(Y))
The value of delta used in the strict ordering is 2.
POL(minus(x1, x2)) = 3 + x_1
POL(QUOT(x1, x2)) = (2)x_1
POL(s(x1)) = 4 + (4)x_1
POL(n__s(x1)) = 3 + (3)x_1
POL(0) = 0
minus(s(X), s(Y)) → minus(X, Y)
minus(X, 0) → 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
ACTIVATE(n__from(X)) → ACTIVATE(X)
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__from(X)) → ACTIVATE(X)
Used ordering: Polynomial interpretation [25,35]:
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
The value of delta used in the strict ordering is 16.
POL(from(x1)) = 4 + (2)x_1
POL(minus(x1, x2)) = 4 + (4)x_1
POL(activate(x1)) = x_1
POL(n__s(x1)) = x_1
POL(0) = 2
POL(cons(x1, x2)) = x_2
POL(n__from(x1)) = 4 + (2)x_1
POL(quot(x1, x2)) = 1 + (4)x_1 + (3)x_2
POL(ZWQUOT(x1, x2)) = (4)x_1 + (4)x_2
POL(s(x1)) = x_1
POL(zWquot(x1, x2)) = (4)x_1 + x_2
POL(n__zWquot(x1, x2)) = (4)x_1 + x_2
POL(ACTIVATE(x1)) = (4)x_1
POL(nil) = 2
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
from(X) → cons(X, n__from(n__s(X)))
zWquot(nil, XS) → nil
zWquot(XS, nil) → nil
from(X) → n__from(X)
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
zWquot(X1, X2) → n__zWquot(X1, X2)
s(X) → n__s(X)
activate(n__s(X)) → s(activate(X))
activate(n__from(X)) → from(activate(X))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__s(X)) → ACTIVATE(X)
Used ordering: Polynomial interpretation [25,35]:
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
The value of delta used in the strict ordering is 1.
POL(from(x1)) = 0
POL(minus(x1, x2)) = 1 + (4)x_2
POL(activate(x1)) = x_1
POL(n__s(x1)) = 1 + (4)x_1
POL(0) = 4
POL(cons(x1, x2)) = x_2
POL(n__from(x1)) = 0
POL(quot(x1, x2)) = 2 + (4)x_1 + x_2
POL(ZWQUOT(x1, x2)) = x_1 + x_2
POL(s(x1)) = 1 + (4)x_1
POL(zWquot(x1, x2)) = x_1 + x_2
POL(n__zWquot(x1, x2)) = x_1 + x_2
POL(ACTIVATE(x1)) = x_1
POL(nil) = 0
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
from(X) → cons(X, n__from(n__s(X)))
zWquot(nil, XS) → nil
zWquot(XS, nil) → nil
from(X) → n__from(X)
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
zWquot(X1, X2) → n__zWquot(X1, X2)
s(X) → n__s(X)
activate(n__s(X)) → s(activate(X))
activate(n__from(X)) → from(activate(X))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(XS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X1)
ZWQUOT(cons(X, XS), cons(Y, YS)) → ACTIVATE(YS)
ACTIVATE(n__zWquot(X1, X2)) → ACTIVATE(X2)
Used ordering: Polynomial interpretation [25,35]:
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
The value of delta used in the strict ordering is 1.
POL(from(x1)) = 0
POL(minus(x1, x2)) = 3 + (2)x_1
POL(activate(x1)) = x_1
POL(n__s(x1)) = 0
POL(0) = 3
POL(cons(x1, x2)) = x_2
POL(n__from(x1)) = 0
POL(quot(x1, x2)) = 4 + (2)x_1 + (3)x_2
POL(ZWQUOT(x1, x2)) = 1 + (2)x_1 + x_2
POL(s(x1)) = 0
POL(zWquot(x1, x2)) = 1 + (2)x_1 + x_2
POL(n__zWquot(x1, x2)) = 1 + (2)x_1 + x_2
POL(ACTIVATE(x1)) = x_1
POL(nil) = 0
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
from(X) → cons(X, n__from(n__s(X)))
zWquot(nil, XS) → nil
zWquot(XS, nil) → nil
from(X) → n__from(X)
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
zWquot(X1, X2) → n__zWquot(X1, X2)
s(X) → n__s(X)
activate(n__s(X)) → s(activate(X))
activate(n__from(X)) → from(activate(X))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
ACTIVATE(n__zWquot(X1, X2)) → ZWQUOT(activate(X1), activate(X2))
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
SEL(s(N), cons(X, XS)) → SEL(N, activate(XS))
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
SEL(s(N), cons(X, XS)) → SEL(N, activate(XS))
The value of delta used in the strict ordering is 4.
POL(from(x1)) = 3
POL(minus(x1, x2)) = 2 + x_1 + (2)x_2
POL(activate(x1)) = 0
POL(n__s(x1)) = 0
POL(0) = 3
POL(cons(x1, x2)) = 2 + (2)x_1 + (2)x_2
POL(n__from(x1)) = 0
POL(quot(x1, x2)) = 0
POL(s(x1)) = 1 + (4)x_1
POL(SEL(x1, x2)) = (4)x_1
POL(zWquot(x1, x2)) = 2 + x_1 + x_2
POL(n__zWquot(x1, x2)) = x_1
POL(nil) = 1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, activate(XS))
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X, XS), cons(Y, YS)) → cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))
from(X) → n__from(X)
s(X) → n__s(X)
zWquot(X1, X2) → n__zWquot(X1, X2)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(n__zWquot(X1, X2)) → zWquot(activate(X1), activate(X2))
activate(X) → X