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)
fib(N) → sel(N, fib1(s(0), s(0)))
fib1(X, Y) → cons(X)
add(0, X) → X
add(s(X), Y) → s(add(X, Y))
sel(0, cons(X)) → X
↳ 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)
fib(N) → sel(N, fib1(s(0), s(0)))
fib1(X, Y) → cons(X)
add(0, X) → X
add(s(X), Y) → s(add(X, Y))
sel(0, cons(X)) → X
The rule sel(s(N), cons(X)) → sel(N, XS) contains free variables in its right-hand side. Hence the TRS is not-terminating.