(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, empty) → x
f(empty, cons(a, k)) → f(cons(a, k), k)
f(cons(a, k), y) → f(y, k)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(cons(x1, x2)) = 2·x1 + 2·x2
POL(empty) = 2
POL(f(x1, x2)) = 2 + x1 + 2·x2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(x, empty) → x
f(empty, cons(a, k)) → f(cons(a, k), k)
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(cons(a, k), y) → f(y, k)
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Knuth-Bendix order [KBO] with precedence:
cons2 > f2
and weight map:
cons_2=0
f_2=0
The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(cons(a, k), y) → f(y, k)
(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) YES