eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X
ACTIVATE1(n__take2(X1, X2)) -> TAKE2(X1, X2)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(L)
LENGTH1(cons2(X, L)) -> S1(n__length1(activate1(L)))
ACTIVATE1(n__0) -> 01
ACTIVATE1(n__s1(X)) -> S1(X)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(X)
EQ2(n__s1(X), n__s1(Y)) -> ACTIVATE1(X)
EQ2(n__s1(X), n__s1(Y)) -> EQ2(activate1(X), activate1(Y))
LENGTH1(cons2(X, L)) -> ACTIVATE1(L)
INF1(X) -> S1(X)
ACTIVATE1(n__length1(X)) -> LENGTH1(X)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(Y)
ACTIVATE1(n__inf1(X)) -> INF1(X)
EQ2(n__s1(X), n__s1(Y)) -> ACTIVATE1(Y)
LENGTH1(nil) -> 01
eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE1(n__take2(X1, X2)) -> TAKE2(X1, X2)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(L)
LENGTH1(cons2(X, L)) -> S1(n__length1(activate1(L)))
ACTIVATE1(n__0) -> 01
ACTIVATE1(n__s1(X)) -> S1(X)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(X)
EQ2(n__s1(X), n__s1(Y)) -> ACTIVATE1(X)
EQ2(n__s1(X), n__s1(Y)) -> EQ2(activate1(X), activate1(Y))
LENGTH1(cons2(X, L)) -> ACTIVATE1(L)
INF1(X) -> S1(X)
ACTIVATE1(n__length1(X)) -> LENGTH1(X)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(Y)
ACTIVATE1(n__inf1(X)) -> INF1(X)
EQ2(n__s1(X), n__s1(Y)) -> ACTIVATE1(Y)
LENGTH1(nil) -> 01
eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
ACTIVATE1(n__take2(X1, X2)) -> TAKE2(X1, X2)
ACTIVATE1(n__length1(X)) -> LENGTH1(X)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(L)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(Y)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(X)
LENGTH1(cons2(X, L)) -> ACTIVATE1(L)
eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE1(n__length1(X)) -> LENGTH1(X)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(L)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(Y)
TAKE2(s1(X), cons2(Y, L)) -> ACTIVATE1(X)
LENGTH1(cons2(X, L)) -> ACTIVATE1(L)
Used ordering: Polynomial Order [17,21] with Interpretation:
ACTIVATE1(n__take2(X1, X2)) -> TAKE2(X1, X2)
POL( n__length1(x1) ) = 2x1 + 2
POL( ACTIVATE1(x1) ) = max{0, 2x1 - 3}
POL( TAKE2(x1, x2) ) = 2x1 + 2x2 + 3
POL( s1(x1) ) = max{0, 3x1 - 1}
POL( cons2(x1, x2) ) = 3x1 + x2 + 2
POL( LENGTH1(x1) ) = 2x1
POL( n__take2(x1, x2) ) = 3x1 + 3x2 + 3
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
ACTIVATE1(n__take2(X1, X2)) -> TAKE2(X1, X2)
eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
EQ2(n__s1(X), n__s1(Y)) -> EQ2(activate1(X), activate1(Y))
eq2(n__0, n__0) -> true
eq2(n__s1(X), n__s1(Y)) -> eq2(activate1(X), activate1(Y))
eq2(X, Y) -> false
inf1(X) -> cons2(X, n__inf1(s1(X)))
take2(0, X) -> nil
take2(s1(X), cons2(Y, L)) -> cons2(activate1(Y), n__take2(activate1(X), activate1(L)))
length1(nil) -> 0
length1(cons2(X, L)) -> s1(n__length1(activate1(L)))
0 -> n__0
s1(X) -> n__s1(X)
inf1(X) -> n__inf1(X)
take2(X1, X2) -> n__take2(X1, X2)
length1(X) -> n__length1(X)
activate1(n__0) -> 0
activate1(n__s1(X)) -> s1(X)
activate1(n__inf1(X)) -> inf1(X)
activate1(n__take2(X1, X2)) -> take2(X1, X2)
activate1(n__length1(X)) -> length1(X)
activate1(X) -> X