(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
2nd(cons(X, cons(Y, Z))) → Y
from(X) → cons(X, from(s(X)))
Q is empty.
(1) Overlay + Local Confluence (EQUIVALENT transformation)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
2nd(cons(X, cons(Y, Z))) → Y
from(X) → cons(X, from(s(X)))
The set Q consists of the following terms:
2nd(cons(x0, cons(x1, x2)))
from(x0)
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
FROM(X) → FROM(s(X))
The TRS R consists of the following rules:
2nd(cons(X, cons(Y, Z))) → Y
from(X) → cons(X, from(s(X)))
The set Q consists of the following terms:
2nd(cons(x0, cons(x1, x2)))
from(x0)
We have to consider all minimal (P,Q,R)-chains.