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:
merge(x, nil) → x
merge(nil, y) → y
merge(++(x, y), ++(u, v)) → ++(x, merge(y, ++(u, v)))
merge(++(x, y), ++(u, v)) → ++(u, merge(++(x, y), v))
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
merge(x, nil) → x
merge(nil, y) → y
merge(++(x, y), ++(u, v)) → ++(x, merge(y, ++(u, v)))
merge(++(x, y), ++(u, v)) → ++(u, merge(++(x, y), v))
Q is empty.
We use [23] with the following order to prove termination.
Recursive path order with status [2].
Precedence:
merge2 > u > ++2
merge2 > v > ++2
nil > ++2
Status:
v: multiset
++2: [1,2]
u: multiset
merge2: multiset
nil: multiset