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

not(true) → false
not(false) → true
evenodd(x, 0) → not(evenodd(x, s(0)))
evenodd(0, s(0)) → false
evenodd(s(x), s(0)) → evenodd(x, 0)

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

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

not'(true') → false'
not'(false') → true'
evenodd'(x, 0') → not'(evenodd'(x, s'(0')))
evenodd'(0', s'(0')) → false'
evenodd'(s'(x), s'(0')) → evenodd'(x, 0')

Rewrite Strategy: INNERMOST

Infered types.

Rules:
not'(true') → false'
not'(false') → true'
evenodd'(x, 0') → not'(evenodd'(x, s'(0')))
evenodd'(0', s'(0')) → false'
evenodd'(s'(x), s'(0')) → evenodd'(x, 0')

Types:
not' :: true':false' → true':false'
true' :: true':false'
false' :: true':false'
evenodd' :: 0':s' → 0':s' → true':false'
0' :: 0':s'
s' :: 0':s' → 0':s'
_hole_true':false'1 :: true':false'
_hole_0':s'2 :: 0':s'
_gen_0':s'3 :: Nat → 0':s'

Heuristically decided to analyse the following defined symbols:
evenodd'

Rules:
not'(true') → false'
not'(false') → true'
evenodd'(x, 0') → not'(evenodd'(x, s'(0')))
evenodd'(0', s'(0')) → false'
evenodd'(s'(x), s'(0')) → evenodd'(x, 0')

Types:
not' :: true':false' → true':false'
true' :: true':false'
false' :: true':false'
evenodd' :: 0':s' → 0':s' → true':false'
0' :: 0':s'
s' :: 0':s' → 0':s'
_hole_true':false'1 :: true':false'
_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:
evenodd'

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

Rules:
not'(true') → false'
not'(false') → true'
evenodd'(x, 0') → not'(evenodd'(x, s'(0')))
evenodd'(0', s'(0')) → false'
evenodd'(s'(x), s'(0')) → evenodd'(x, 0')

Types:
not' :: true':false' → true':false'
true' :: true':false'
false' :: true':false'
evenodd' :: 0':s' → 0':s' → true':false'
0' :: 0':s'
s' :: 0':s' → 0':s'
_hole_true':false'1 :: true':false'
_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.