from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X
ACTIVATE(n__from(X)) → ACTIVATE(X)
SEL(s(X), cons(Y, Z)) → ACTIVATE(Z)
ACTIVATE(n__s(X)) → S(activate(X))
ACTIVATE(n__from(X)) → FROM(activate(X))
SEL(s(X), cons(Y, Z)) → SEL(X, activate(Z))
ACTIVATE(n__s(X)) → ACTIVATE(X)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE(n__from(X)) → ACTIVATE(X)
SEL(s(X), cons(Y, Z)) → ACTIVATE(Z)
ACTIVATE(n__s(X)) → S(activate(X))
ACTIVATE(n__from(X)) → FROM(activate(X))
SEL(s(X), cons(Y, Z)) → SEL(X, activate(Z))
ACTIVATE(n__s(X)) → ACTIVATE(X)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
ACTIVATE(n__from(X)) → ACTIVATE(X)
ACTIVATE(n__s(X)) → ACTIVATE(X)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
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]:
ACTIVATE(n__from(X)) → ACTIVATE(X)
The value of delta used in the strict ordering is 8.
POL(n__from(x1)) = (2)x_1
POL(n__s(x1)) = 4 + (2)x_1
POL(ACTIVATE(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
ACTIVATE(n__from(X)) → ACTIVATE(X)
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
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)
The value of delta used in the strict ordering is 1/16.
POL(n__from(x1)) = 1/4 + (2)x_1
POL(ACTIVATE(x1)) = (1/4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
SEL(s(X), cons(Y, Z)) → SEL(X, activate(Z))
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
SEL(s(X), cons(Y, Z)) → SEL(X, activate(Z))
The value of delta used in the strict ordering is 1/16.
POL(cons(x1, x2)) = 0
POL(from(x1)) = 0
POL(n__from(x1)) = 0
POL(s(x1)) = 1/4 + (4)x_1
POL(activate(x1)) = 0
POL(SEL(x1, x2)) = (1/4)x_1
POL(n__s(x1)) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
from(X) → cons(X, n__from(n__s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X