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

f(s(x1), x2, x3, x4, x5) → f(x1, x2, x3, x4, x5)
f(0, s(x2), x3, x4, x5) → f(x2, x2, x3, x4, x5)
f(0, 0, s(x3), x4, x5) → f(x3, x3, x3, x4, x5)
f(0, 0, 0, s(x4), x5) → f(x4, x4, x4, x4, x5)
f(0, 0, 0, 0, s(x5)) → f(x5, x5, x5, x5, x5)
f(0, 0, 0, 0, 0) → 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'(x1), x2, x3, x4, x5) → f'(x1, x2, x3, x4, x5)
f'(0', s'(x2), x3, x4, x5) → f'(x2, x2, x3, x4, x5)
f'(0', 0', s'(x3), x4, x5) → f'(x3, x3, x3, x4, x5)
f'(0', 0', 0', s'(x4), x5) → f'(x4, x4, x4, x4, x5)
f'(0', 0', 0', 0', s'(x5)) → f'(x5, x5, x5, x5, x5)
f'(0', 0', 0', 0', 0') → 0'

Rewrite Strategy: INNERMOST

Infered types.

Rules:
f'(s'(x1), x2, x3, x4, x5) → f'(x1, x2, x3, x4, x5)
f'(0', s'(x2), x3, x4, x5) → f'(x2, x2, x3, x4, x5)
f'(0', 0', s'(x3), x4, x5) → f'(x3, x3, x3, x4, x5)
f'(0', 0', 0', s'(x4), x5) → f'(x4, x4, x4, x4, x5)
f'(0', 0', 0', 0', s'(x5)) → f'(x5, x5, x5, x5, x5)
f'(0', 0', 0', 0', 0') → 0'

Types:
f' :: s':0' → s':0' → s':0' → 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'(x1), x2, x3, x4, x5) → f'(x1, x2, x3, x4, x5)
f'(0', s'(x2), x3, x4, x5) → f'(x2, x2, x3, x4, x5)
f'(0', 0', s'(x3), x4, x5) → f'(x3, x3, x3, x4, x5)
f'(0', 0', 0', s'(x4), x5) → f'(x4, x4, x4, x4, x5)
f'(0', 0', 0', 0', s'(x5)) → f'(x5, x5, x5, x5, x5)
f'(0', 0', 0', 0', 0') → 0'

Types:
f' :: s':0' → s':0' → s':0' → 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'(x1), x2, x3, x4, x5) → f'(x1, x2, x3, x4, x5)
f'(0', s'(x2), x3, x4, x5) → f'(x2, x2, x3, x4, x5)
f'(0', 0', s'(x3), x4, x5) → f'(x3, x3, x3, x4, x5)
f'(0', 0', 0', s'(x4), x5) → f'(x4, x4, x4, x4, x5)
f'(0', 0', 0', 0', s'(x5)) → f'(x5, x5, x5, x5, x5)
f'(0', 0', 0', 0', 0') → 0'

Types:
f' :: s':0' → s':0' → s':0' → 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.