Termination w.r.t. Q of the given QTRS could be proven:

0 QTRS
↳1 QTRSRRRProof (⇔)
↳2 QTRS
  ↳3 RisEmptyProof (⇔)
    ↳4 TRUE
  ↳5 RisEmptyProof (⇔)
    ↳6 TRUE
  ↳7 RisEmptyProof (⇔)
    ↳8 TRUE

(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:
Polynomial interpretation [POLO]:

POL(app(x1, x2)) = 1 + x1 + x2   
POL(cons(x1)) = x1   
POL(from(x1)) = 1 + x1   
POL(nil) = 0   
POL(prefix(x1)) = 1 + x1   
POL(zWadr(x1, x2)) = 2 + x1 + x2   
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

(5) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(6) TRUE

(7) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(8) TRUE