a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
↳ QTRS
↳ DependencyPairsProof
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
A__2ND(cons(X, cons(Y, Z))) → MARK(Y)
MARK(from(X)) → MARK(X)
MARK(from(X)) → A__FROM(mark(X))
MARK(s(X)) → MARK(X)
MARK(2nd(X)) → MARK(X)
MARK(cons(X1, X2)) → MARK(X1)
MARK(2nd(X)) → A__2ND(mark(X))
A__FROM(X) → MARK(X)
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A__2ND(cons(X, cons(Y, Z))) → MARK(Y)
MARK(from(X)) → MARK(X)
MARK(from(X)) → A__FROM(mark(X))
MARK(s(X)) → MARK(X)
MARK(2nd(X)) → MARK(X)
MARK(cons(X1, X2)) → MARK(X1)
MARK(2nd(X)) → A__2ND(mark(X))
A__FROM(X) → MARK(X)
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A__2ND(cons(X, cons(Y, Z))) → MARK(Y)
MARK(from(X)) → MARK(X)
MARK(from(X)) → A__FROM(mark(X))
MARK(2nd(X)) → MARK(X)
MARK(cons(X1, X2)) → MARK(X1)
MARK(2nd(X)) → A__2ND(mark(X))
Used ordering: Polynomial interpretation [25,35]:
MARK(s(X)) → MARK(X)
A__FROM(X) → MARK(X)
The value of delta used in the strict ordering is 1.
POL(A__2ND(x1)) = 2 + (4)x_1
POL(cons(x1, x2)) = 1 + x_1 + (1/4)x_2
POL(from(x1)) = 4 + (4)x_1
POL(MARK(x1)) = x_1
POL(A__FROM(x1)) = (2)x_1
POL(a__2nd(x1)) = 4 + (4)x_1
POL(2nd(x1)) = 4 + (4)x_1
POL(mark(x1)) = x_1
POL(s(x1)) = (2)x_1
POL(a__from(x1)) = 4 + (4)x_1
a__from(X) → cons(mark(X), from(s(X)))
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
MARK(s(X)) → MARK(X)
A__FROM(X) → MARK(X)
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
MARK(s(X)) → MARK(X)
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(s(X)) → MARK(X)
The value of delta used in the strict ordering is 1/16.
POL(MARK(x1)) = (1/4)x_1
POL(s(x1)) = 1/4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a__2nd(cons(X, cons(Y, Z))) → mark(Y)
a__from(X) → cons(mark(X), from(s(X)))
mark(2nd(X)) → a__2nd(mark(X))
mark(from(X)) → a__from(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
a__2nd(X) → 2nd(X)
a__from(X) → from(X)