Runtime Complexity TRS:
The TRS R consists of the following rules:

f(S(x), x2) → f(x2, x)
f(0, x2) → 0

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

Runtime Complexity TRS:
The TRS R consists of the following rules:

f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'

Rewrite Strategy: INNERMOST

Infered types.

Rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'

Types:
f' :: S':0' → S':0' → S':0'
S' :: S':0' → S':0'
0' :: S':0'
_hole_S':0'1 :: S':0'
_gen_S':0'2 :: Nat → S':0'

Heuristically decided to analyse the following defined symbols:
f'

Rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'

Types:
f' :: S':0' → S':0' → S':0'
S' :: S':0' → S':0'
0' :: S':0'
_hole_S':0'1 :: S':0'
_gen_S':0'2 :: Nat → S':0'

Generator Equations:
_gen_S':0'2(0) ⇔ 0'
_gen_S':0'2(+(x, 1)) ⇔ S'(_gen_S':0'2(x))

The following defined symbols remain to be analysed:
f'

Could not prove a rewrite lemma for the defined symbol f'.

Rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'

Types:
f' :: S':0' → S':0' → S':0'
S' :: S':0' → S':0'
0' :: S':0'
_hole_S':0'1 :: S':0'
_gen_S':0'2 :: Nat → S':0'

Generator Equations:
_gen_S':0'2(0) ⇔ 0'
_gen_S':0'2(+(x, 1)) ⇔ S'(_gen_S':0'2(x))

No more defined symbols left to analyse.