f(x, a) → x
f(x, g(y)) → f(g(x), y)
Renamed function symbols to avoid clashes with predefined symbol.
Runtime Complexity TRS:
The TRS R consists of the following rules:
f'(x, a') → x
f'(x, g'(y)) → f'(g'(x), y)
Infered types.
Rules:
f'(x, a') → x
f'(x, g'(y)) → f'(g'(x), y)
Types:
f' :: a':g' → a':g' → a':g'
a' :: a':g'
g' :: a':g' → a':g'
_hole_a':g'1 :: a':g'
_gen_a':g'2 :: Nat → a':g'
Heuristically decided to analyse the following defined symbols:
f'
Rules:
f'(x, a') → x
f'(x, g'(y)) → f'(g'(x), y)
Types:
f' :: a':g' → a':g' → a':g'
a' :: a':g'
g' :: a':g' → a':g'
_hole_a':g'1 :: a':g'
_gen_a':g'2 :: Nat → a':g'
Generator Equations:
_gen_a':g'2(0) ⇔ a'
_gen_a':g'2(+(x, 1)) ⇔ g'(_gen_a':g'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_a':g'2(a), _gen_a':g'2(_n4)) →? _gen_a':g'2(+(_n4, a))
Rules:
f'(x, a') → x
f'(x, g'(y)) → f'(g'(x), y)
Types:
f' :: a':g' → a':g' → a':g'
a' :: a':g'
g' :: a':g' → a':g'
_hole_a':g'1 :: a':g'
_gen_a':g'2 :: Nat → a':g'
Generator Equations:
_gen_a':g'2(0) ⇔ a'
_gen_a':g'2(+(x, 1)) ⇔ g'(_gen_a':g'2(x))
No more defined symbols left to analyse.