(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) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(cons(x1, x2)) = 1 + x1 + x2
POL(empty) = 2
POL(r1(x1, x2)) = 2·x1 + x2
POL(rev(x1)) = 2 + 2·x1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
r1(empty, a) → a
r1(cons(x, k), a) → r1(k, cons(x, a))
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
rev(ls) → r1(ls, empty)
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(empty) = 0
POL(r1(x1, x2)) = x1 + x2
POL(rev(x1)) = 1 + x1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
rev(ls) → r1(ls, empty)
(4) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(5) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(6) TRUE