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:
app(app(apply, f_1), x) → app(f_1, x)
app(id, x) → x
app(app(app(uncurry, f_2), x), y) → app(app(f_2, x), y)
app(app(app(swap, f_2), y), x) → app(app(f_2, x), y)
app(app(app(compose, g_1), f_1), x) → app(g_1, app(f_1, x))
app(app(const, x), y) → x
app(listify, x) → app(app(cons, x), nil)
app(app(app(app(fold, f_3), g_2), x), nil) → x
app(app(app(app(fold, f_3), g_2), x), app(app(cons, z), t)) → app(app(f_3, app(g_2, z)), app(app(app(app(fold, f_3), g_2), x), t))
app(sum, l) → app(app(app(app(fold, add), id), 0), l)
app(app(uncurry, app(app(fold, cons), id)), nil) → id
append → app(app(compose, app(app(swap, fold), cons)), id)
reverse → app(app(uncurry, app(app(fold, app(swap, append)), listify)), nil)
length → app(app(uncurry, app(app(fold, add), app(cons, 1))), 0)
Q is empty.
↳ QTRS
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(apply, f_1), x) → app(f_1, x)
app(id, x) → x
app(app(app(uncurry, f_2), x), y) → app(app(f_2, x), y)
app(app(app(swap, f_2), y), x) → app(app(f_2, x), y)
app(app(app(compose, g_1), f_1), x) → app(g_1, app(f_1, x))
app(app(const, x), y) → x
app(listify, x) → app(app(cons, x), nil)
app(app(app(app(fold, f_3), g_2), x), nil) → x
app(app(app(app(fold, f_3), g_2), x), app(app(cons, z), t)) → app(app(f_3, app(g_2, z)), app(app(app(app(fold, f_3), g_2), x), t))
app(sum, l) → app(app(app(app(fold, add), id), 0), l)
app(app(uncurry, app(app(fold, cons), id)), nil) → id
append → app(app(compose, app(app(swap, fold), cons)), id)
reverse → app(app(uncurry, app(app(fold, app(swap, append)), listify)), nil)
length → app(app(uncurry, app(app(fold, add), app(cons, 1))), 0)
Q is empty.