Innermost Termination of the following Term Rewriting System could be disproven:

Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

sel(s(N), cons(X)) → sel(N, XS)
from(X) → cons(X)
sel(0, cons(X)) → X
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X), cons(Y)) → cons(quot(X, Y))

Innermost Strategy.


↳ GTRS
  ↳ CritRuleProof

Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

sel(s(N), cons(X)) → sel(N, XS)
from(X) → cons(X)
sel(0, cons(X)) → X
minus(X, 0) → 0
minus(s(X), s(Y)) → minus(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(minus(X, Y), s(Y)))
zWquot(XS, nil) → nil
zWquot(nil, XS) → nil
zWquot(cons(X), cons(Y)) → cons(quot(X, Y))

Innermost Strategy.

The rule sel(s(N), cons(X)) → sel(N, XS) contains free variables in its right-hand side. Hence the TRS is not-terminating.