(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(nil, YS) → YS
app(cons(X), YS) → cons(X)
from(X) → cons(X)
zWadr(nil, YS) → nil
zWadr(XS, nil) → nil
zWadr(cons(X), cons(Y)) → cons(app(Y, cons(X)))
prefix(L) → cons(nil)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Precedence:
from1 > cons1 > app2 > nil
zWadr2 > cons1 > app2 > nil
prefix1 > cons1 > app2 > nil
Status:
app2: multiset
nil: multiset
cons1: multiset
from1: multiset
zWadr2: multiset
prefix1: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
app(nil, YS) → YS
app(cons(X), YS) → cons(X)
from(X) → cons(X)
zWadr(nil, YS) → nil
zWadr(XS, nil) → nil
zWadr(cons(X), cons(Y)) → cons(app(Y, cons(X)))
prefix(L) → cons(nil)
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) TRUE