(0) Obligation:

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

from(X) → cons(X)
length0
lengths(length1)
length1length

Q is empty.

(1) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(2) Obligation:

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

LENGTHLENGTH1
LENGTH1LENGTH

The TRS R consists of the following rules:

from(X) → cons(X)
length0
lengths(length1)
length1length

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