Termination proof of /tmp/tmpP63gry/Ex3_2_Luc97

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(0, cons) → X
sel(s, cons) → sel(X, Z)
dbl(0) → 0
dbl(s) → s
dbls(nil) → nil
dbls(cons) → cons
indx(nil) → nil
indx(cons) → cons
from → cons

↳ GTRS

  ↳ CritRuleProof

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

sel(0, cons) → X
sel(s, cons) → sel(X, Z)
dbl(0) → 0
dbl(s) → s
dbls(nil) → nil
dbls(cons) → cons
indx(nil) → nil
indx(cons) → cons
from → cons

The rule sel(0, cons) → X contains free variables in its right-hand side. Hence the TRS is not-terminating.