f(x, h(y)) → h(f(f(h(a), y), x))
Renamed function symbols to avoid clashes with predefined symbol.
Runtime Complexity TRS:
The TRS R consists of the following rules:
f'(x, h'(y)) → h'(f'(f'(h'(a'), y), x))
Infered types.
Rules:
f'(x, h'(y)) → h'(f'(f'(h'(a'), y), x))
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'(x, h'(y)) → h'(f'(f'(h'(a'), y), x))
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(a), _gen_h':a'2(+(1, _n4))) →? _*3
Rules:
f'(x, h'(y)) → h'(f'(f'(h'(a'), y), x))
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.