first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
↳ QTRS
↳ DependencyPairsProof
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
FIRST(s(X), cons(Y, Z)) → FIRST(X, Z)
FROM(X) → FROM(s(X))
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
FIRST(s(X), cons(Y, Z)) → FIRST(X, Z)
FROM(X) → FROM(s(X))
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
FROM(X) → FROM(s(X))
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
FIRST(s(X), cons(Y, Z)) → FIRST(X, Z)
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
FIRST(s(X), cons(Y, Z)) → FIRST(X, Z)
The value of delta used in the strict ordering is 16.
POL(FIRST(x1, x2)) = (4)x_2
POL(cons(x1, x2)) = 4 + (2)x_1 + (4)x_2
POL(s(x1)) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))