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:
f(x, y, w, w, a) → g1(x, x, y, w)
f(x, y, w, a, a) → g1(y, x, x, w)
f(x, y, a, a, w) → g2(x, y, y, w)
f(x, y, a, w, w) → g2(y, y, x, w)
g1(x, x, y, a) → h(x, y)
g1(y, x, x, a) → h(x, y)
g2(x, y, y, a) → h(x, y)
g2(y, y, x, a) → h(x, y)
h(x, x) → x
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y, w, w, a) → g1(x, x, y, w)
f(x, y, w, a, a) → g1(y, x, x, w)
f(x, y, a, a, w) → g2(x, y, y, w)
f(x, y, a, w, w) → g2(y, y, x, w)
g1(x, x, y, a) → h(x, y)
g1(y, x, x, a) → h(x, y)
g2(x, y, y, a) → h(x, y)
g2(y, y, x, a) → h(x, y)
h(x, x) → x
Q is empty.
We use [23] with the following order to prove termination.
Lexicographic path order with status [19].
Quasi-Precedence:
f5 > g14 > h2
f5 > g24 > h2
a > g14 > h2
a > g24 > h2
Status: g24: [4,2,3,1]
a: multiset
f5: [5,4,3,1,2]
g14: [4,2,3,1]
h2: [2,1]