f(h(x), y) → h(f(y, f(x, h(f(a, a)))))
Renamed function symbols to avoid clashes with predefined symbol.
Runtime Complexity TRS:
The TRS R consists of the following rules:
f'(h'(x), y) → h'(f'(y, f'(x, h'(f'(a', a')))))
Infered types.
Rules:
f'(h'(x), y) → h'(f'(y, f'(x, h'(f'(a', a')))))
Types:
f' :: h':a' → h':a' → h':a'
h' :: h':a' → h':a'
a' :: h':a'
_hole_h':a'1 :: h':a'
_gen_h':a'2 :: Nat → h':a'
Heuristically decided to analyse the following defined symbols:
f'
Rules:
f'(h'(x), y) → h'(f'(y, f'(x, h'(f'(a', a')))))
Types:
f' :: h':a' → h':a' → h':a'
h' :: h':a' → h':a'
a' :: h':a'
_hole_h':a'1 :: h':a'
_gen_h':a'2 :: Nat → h':a'
Generator Equations:
_gen_h':a'2(0) ⇔ a'
_gen_h':a'2(+(x, 1)) ⇔ h'(_gen_h':a'2(x))
The following defined symbols remain to be analysed:
f'
Could not prove a rewrite lemma for the defined symbol f'.
The following conjecture could not be proven:
f'(_gen_h':a'2(+(1, _n4)), _gen_h':a'2(b)) →? _*3
Rules:
f'(h'(x), y) → h'(f'(y, f'(x, h'(f'(a', a')))))
Types:
f' :: h':a' → h':a' → h':a'
h' :: h':a' → h':a'
a' :: h':a'
_hole_h':a'1 :: h':a'
_gen_h':a'2 :: Nat → h':a'
Generator Equations:
_gen_h':a'2(0) ⇔ a'
_gen_h':a'2(+(x, 1)) ⇔ h'(_gen_h':a'2(x))
No more defined symbols left to analyse.