Termination w.r.t. Q of the following Term Rewriting System could not be shown:

Q restricted rewrite system:
The TRS R consists of the following rules:

a__2nd1(cons2(X, cons2(Y, Z))) -> mark1(Y)
a__from1(X) -> cons2(mark1(X), from1(s1(X)))
mark1(2nd1(X)) -> a__2nd1(mark1(X))
mark1(from1(X)) -> a__from1(mark1(X))
mark1(cons2(X1, X2)) -> cons2(mark1(X1), X2)
mark1(s1(X)) -> s1(mark1(X))
a__2nd1(X) -> 2nd1(X)
a__from1(X) -> from1(X)

Q is empty.


QTRS
  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

a__2nd1(cons2(X, cons2(Y, Z))) -> mark1(Y)
a__from1(X) -> cons2(mark1(X), from1(s1(X)))
mark1(2nd1(X)) -> a__2nd1(mark1(X))
mark1(from1(X)) -> a__from1(mark1(X))
mark1(cons2(X1, X2)) -> cons2(mark1(X1), X2)
mark1(s1(X)) -> s1(mark1(X))
a__2nd1(X) -> 2nd1(X)
a__from1(X) -> from1(X)

Q is empty.

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

MARK1(s1(X)) -> MARK1(X)
MARK1(2nd1(X)) -> MARK1(X)
MARK1(from1(X)) -> MARK1(X)
A__2ND1(cons2(X, cons2(Y, Z))) -> MARK1(Y)
MARK1(from1(X)) -> A__FROM1(mark1(X))
MARK1(cons2(X1, X2)) -> MARK1(X1)
MARK1(2nd1(X)) -> A__2ND1(mark1(X))
A__FROM1(X) -> MARK1(X)

The TRS R consists of the following rules:

a__2nd1(cons2(X, cons2(Y, Z))) -> mark1(Y)
a__from1(X) -> cons2(mark1(X), from1(s1(X)))
mark1(2nd1(X)) -> a__2nd1(mark1(X))
mark1(from1(X)) -> a__from1(mark1(X))
mark1(cons2(X1, X2)) -> cons2(mark1(X1), X2)
mark1(s1(X)) -> s1(mark1(X))
a__2nd1(X) -> 2nd1(X)
a__from1(X) -> from1(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS
  ↳ DependencyPairsProof
QDP

Q DP problem:
The TRS P consists of the following rules:

MARK1(s1(X)) -> MARK1(X)
MARK1(2nd1(X)) -> MARK1(X)
MARK1(from1(X)) -> MARK1(X)
A__2ND1(cons2(X, cons2(Y, Z))) -> MARK1(Y)
MARK1(from1(X)) -> A__FROM1(mark1(X))
MARK1(cons2(X1, X2)) -> MARK1(X1)
MARK1(2nd1(X)) -> A__2ND1(mark1(X))
A__FROM1(X) -> MARK1(X)

The TRS R consists of the following rules:

a__2nd1(cons2(X, cons2(Y, Z))) -> mark1(Y)
a__from1(X) -> cons2(mark1(X), from1(s1(X)))
mark1(2nd1(X)) -> a__2nd1(mark1(X))
mark1(from1(X)) -> a__from1(mark1(X))
mark1(cons2(X1, X2)) -> cons2(mark1(X1), X2)
mark1(s1(X)) -> s1(mark1(X))
a__2nd1(X) -> 2nd1(X)
a__from1(X) -> from1(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.