f(s(x), y) → f(x, s(s(x)))
f(x, s(s(y))) → f(y, x)
Renamed function symbols to avoid clashes with predefined symbol.
Runtime Complexity TRS:
The TRS R consists of the following rules:
f'(s'(x), y) → f'(x, s'(s'(x)))
f'(x, s'(s'(y))) → f'(y, x)
Infered types.
Rules:
f'(s'(x), y) → f'(x, s'(s'(x)))
f'(x, s'(s'(y))) → f'(y, x)
Types:
f' :: s' → s' → f'
s' :: s' → s'
_hole_f'1 :: f'
_hole_s'2 :: s'
_gen_s'3 :: Nat → s'
Heuristically decided to analyse the following defined symbols:
f'
Rules:
f'(s'(x), y) → f'(x, s'(s'(x)))
f'(x, s'(s'(y))) → f'(y, x)
Types:
f' :: s' → s' → f'
s' :: s' → s'
_hole_f'1 :: f'
_hole_s'2 :: s'
_gen_s'3 :: Nat → s'
Generator Equations:
_gen_s'3(0) ⇔ _hole_s'2
_gen_s'3(+(x, 1)) ⇔ s'(_gen_s'3(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_s'3(+(1, _n5)), _gen_s'3(b)) →? _*4
Rules:
f'(s'(x), y) → f'(x, s'(s'(x)))
f'(x, s'(s'(y))) → f'(y, x)
Types:
f' :: s' → s' → f'
s' :: s' → s'
_hole_f'1 :: f'
_hole_s'2 :: s'
_gen_s'3 :: Nat → s'
Generator Equations:
_gen_s'3(0) ⇔ _hole_s'2
_gen_s'3(+(x, 1)) ⇔ s'(_gen_s'3(x))
No more defined symbols left to analyse.