(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
rev(ls) → r1(ls, empty)
r1(empty, a) → a
r1(cons(x, k), a) → r1(k, cons(x, a))
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:
rev(ls) → r1(ls, empty)
r1(empty, a) → a
r1(cons(x, k), a) → r1(k, cons(x, a))
The set Q consists of the following terms:
rev(x0)
r1(empty, x0)
r1(cons(x0, x1), x2)
(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:
REV(ls) → R1(ls, empty)
R1(cons(x, k), a) → R1(k, cons(x, a))
The TRS R consists of the following rules:
rev(ls) → r1(ls, empty)
r1(empty, a) → a
r1(cons(x, k), a) → r1(k, cons(x, a))
The set Q consists of the following terms:
rev(x0)
r1(empty, x0)
r1(cons(x0, x1), x2)
We have to consider all minimal (P,Q,R)-chains.
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
(6) Obligation:
Q DP problem:
The TRS P consists of the following rules:
R1(cons(x, k), a) → R1(k, cons(x, a))
The TRS R consists of the following rules:
rev(ls) → r1(ls, empty)
r1(empty, a) → a
r1(cons(x, k), a) → r1(k, cons(x, a))
The set Q consists of the following terms:
rev(x0)
r1(empty, x0)
r1(cons(x0, x1), x2)
We have to consider all minimal (P,Q,R)-chains.