Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__zeros
activate(n__zeros) → zeros
activate(X) → X
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__zeros
activate(n__zeros) → zeros
activate(X) → X
Q is empty.
We use [23] with the following order to prove termination.
Recursive path order with status [2].
Precedence:
tail1 > activate1 > zeros > cons2
tail1 > activate1 > zeros > 0
tail1 > activate1 > zeros > nzeros
Status:
zeros: multiset
0: multiset
tail1: multiset
cons2: multiset
nzeros: multiset
activate1: multiset