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:
fac(0) → 1
fac(s(x)) → *(s(x), fac(x))
floop(0, y) → y
floop(s(x), y) → floop(x, *(s(x), y))
*(x, 0) → 0
*(x, s(y)) → +(*(x, y), x)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
1 → s(0)
fac(0) → s(0)
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
fac(0) → 1
fac(s(x)) → *(s(x), fac(x))
floop(0, y) → y
floop(s(x), y) → floop(x, *(s(x), y))
*(x, 0) → 0
*(x, s(y)) → +(*(x, y), x)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
1 → s(0)
fac(0) → s(0)
Q is empty.
We use [23] with the following order to prove termination.
Recursive path order with status [2].
Precedence:
fac1 > 1 > 0 > s1
fac1 > *2 > 0 > s1
fac1 > *2 > +2 > s1
floop2 > *2 > 0 > s1
floop2 > *2 > +2 > s1
Status:
fac1: multiset
+2: multiset
1: multiset
s1: multiset
0: multiset
floop2: [1,2]
*2: multiset