Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
f1(a, x) → g1(x, x)
f1(x, a) → g2(x, x)
f2(a, x) → g1(x, x)
f2(x, a) → g2(x, x)
g1(a, x) → h1(x)
g1(x, a) → h2(x)
g2(a, x) → h1(x)
g2(x, a) → h2(x)
h1(a) → i
h2(a) → i
e1(h1(w), h2(w), x, y, z, w) → e2(x, x, y, z, z, w)
e1(x1, x1, x, y, z, a) → e5(x1, x, y, z)
e2(f1(w, w), x, y, z, f2(w, w), w) → e3(x, y, x, y, y, z, y, z, x, y, z, w)
e2(x, x, y, z, z, a) → e6(x, y, z)
e2(i, x, y, z, i, a) → e6(x, y, z)
e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) → e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w)
e3(x, y, x, y, y, z, y, z, x, y, z, a) → e6(x, y, z)
e4(g1(w, w), x1, g2(w, w), x1, g1(w, w), x1, g2(w, w), x1, x, y, z, w) → e1(x1, x1, x, y, z, w)
e4(i, x1, i, x1, i, x1, i, x1, x, y, z, a) → e5(x1, x, y, z)
e4(x, x, x, x, x, x, x, x, x, x, x, a) → e6(x, x, x)
e5(i, x, y, z) → e6(x, y, z)
Q is empty.
↳ QTRS
Q restricted rewrite system:
The TRS R consists of the following rules:
f1(a, x) → g1(x, x)
f1(x, a) → g2(x, x)
f2(a, x) → g1(x, x)
f2(x, a) → g2(x, x)
g1(a, x) → h1(x)
g1(x, a) → h2(x)
g2(a, x) → h1(x)
g2(x, a) → h2(x)
h1(a) → i
h2(a) → i
e1(h1(w), h2(w), x, y, z, w) → e2(x, x, y, z, z, w)
e1(x1, x1, x, y, z, a) → e5(x1, x, y, z)
e2(f1(w, w), x, y, z, f2(w, w), w) → e3(x, y, x, y, y, z, y, z, x, y, z, w)
e2(x, x, y, z, z, a) → e6(x, y, z)
e2(i, x, y, z, i, a) → e6(x, y, z)
e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) → e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w)
e3(x, y, x, y, y, z, y, z, x, y, z, a) → e6(x, y, z)
e4(g1(w, w), x1, g2(w, w), x1, g1(w, w), x1, g2(w, w), x1, x, y, z, w) → e1(x1, x1, x, y, z, w)
e4(i, x1, i, x1, i, x1, i, x1, x, y, z, a) → e5(x1, x, y, z)
e4(x, x, x, x, x, x, x, x, x, x, x, a) → e6(x, x, x)
e5(i, x, y, z) → e6(x, y, z)
Q is empty.