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

f(0) → cons(0)
f(s(0)) → f(p(s(0)))
p(s(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'(0') → cons'(0')
f'(s'(0')) → f'(p'(s'(0')))
p'(s'(0')) → 0'

Rewrite Strategy: INNERMOST

Sliced the following arguments:
cons'/0

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


f'(0') → cons'
f'(s'(0')) → f'(p'(s'(0')))
p'(s'(0')) → 0'

Rewrite Strategy: INNERMOST

Infered types.

Rules:
f'(0') → cons'
f'(s'(0')) → f'(p'(s'(0')))
p'(s'(0')) → 0'

Types:
f' :: 0':s' → cons'
0' :: 0':s'
cons' :: cons'
s' :: 0':s' → 0':s'
p' :: 0':s' → 0':s'
_hole_cons'1 :: cons'
_hole_0':s'2 :: 0':s'
_gen_0':s'3 :: Nat → 0':s'

Heuristically decided to analyse the following defined symbols:
f'

Rules:
f'(0') → cons'
f'(s'(0')) → f'(p'(s'(0')))
p'(s'(0')) → 0'

Types:
f' :: 0':s' → cons'
0' :: 0':s'
cons' :: cons'
s' :: 0':s' → 0':s'
p' :: 0':s' → 0':s'
_hole_cons'1 :: cons'
_hole_0':s'2 :: 0':s'
_gen_0':s'3 :: Nat → 0':s'

Generator Equations:
_gen_0':s'3(0) ⇔ 0'
_gen_0':s'3(+(x, 1)) ⇔ s'(_gen_0':s'3(x))

The following defined symbols remain to be analysed:
f'

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

Rules:
f'(0') → cons'
f'(s'(0')) → f'(p'(s'(0')))
p'(s'(0')) → 0'

Types:
f' :: 0':s' → cons'
0' :: 0':s'
cons' :: cons'
s' :: 0':s' → 0':s'
p' :: 0':s' → 0':s'
_hole_cons'1 :: cons'
_hole_0':s'2 :: 0':s'
_gen_0':s'3 :: Nat → 0':s'

Generator Equations:
_gen_0':s'3(0) ⇔ 0'
_gen_0':s'3(+(x, 1)) ⇔ s'(_gen_0':s'3(x))

No more defined symbols left to analyse.