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

a__f(f(a)) → a__f(g(f(a)))
mark(f(X)) → a__f(X)
mark(a) → a
mark(g(X)) → g(mark(X))
a__f(X) → f(X)

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

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

a__f'(f'(a')) → a__f'(g'(f'(a')))
mark'(f'(X)) → a__f'(X)
mark'(a') → a'
mark'(g'(X)) → g'(mark'(X))
a__f'(X) → f'(X)

Rewrite Strategy: INNERMOST

Infered types.

Rules:
a__f'(f'(a')) → a__f'(g'(f'(a')))
mark'(f'(X)) → a__f'(X)
mark'(a') → a'
mark'(g'(X)) → g'(mark'(X))
a__f'(X) → f'(X)

Types:
a__f' :: a':f':g' → a':f':g'
f' :: a':f':g' → a':f':g'
a' :: a':f':g'
g' :: a':f':g' → a':f':g'
mark' :: a':f':g' → a':f':g'
_hole_a':f':g'1 :: a':f':g'
_gen_a':f':g'2 :: Nat → a':f':g'

Heuristically decided to analyse the following defined symbols:
a__f', mark'

They will be analysed ascendingly in the following order:
a__f' < mark'

Rules:
a__f'(f'(a')) → a__f'(g'(f'(a')))
mark'(f'(X)) → a__f'(X)
mark'(a') → a'
mark'(g'(X)) → g'(mark'(X))
a__f'(X) → f'(X)

Types:
a__f' :: a':f':g' → a':f':g'
f' :: a':f':g' → a':f':g'
a' :: a':f':g'
g' :: a':f':g' → a':f':g'
mark' :: a':f':g' → a':f':g'
_hole_a':f':g'1 :: a':f':g'
_gen_a':f':g'2 :: Nat → a':f':g'

Generator Equations:
_gen_a':f':g'2(0) ⇔ a'
_gen_a':f':g'2(+(x, 1)) ⇔ f'(_gen_a':f':g'2(x))

The following defined symbols remain to be analysed:
a__f', mark'

They will be analysed ascendingly in the following order:
a__f' < mark'

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

Rules:
a__f'(f'(a')) → a__f'(g'(f'(a')))
mark'(f'(X)) → a__f'(X)
mark'(a') → a'
mark'(g'(X)) → g'(mark'(X))
a__f'(X) → f'(X)

Types:
a__f' :: a':f':g' → a':f':g'
f' :: a':f':g' → a':f':g'
a' :: a':f':g'
g' :: a':f':g' → a':f':g'
mark' :: a':f':g' → a':f':g'
_hole_a':f':g'1 :: a':f':g'
_gen_a':f':g'2 :: Nat → a':f':g'

Generator Equations:
_gen_a':f':g'2(0) ⇔ a'
_gen_a':f':g'2(+(x, 1)) ⇔ f'(_gen_a':f':g'2(x))

The following defined symbols remain to be analysed:
mark'

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

Rules:
a__f'(f'(a')) → a__f'(g'(f'(a')))
mark'(f'(X)) → a__f'(X)
mark'(a') → a'
mark'(g'(X)) → g'(mark'(X))
a__f'(X) → f'(X)

Types:
a__f' :: a':f':g' → a':f':g'
f' :: a':f':g' → a':f':g'
a' :: a':f':g'
g' :: a':f':g' → a':f':g'
mark' :: a':f':g' → a':f':g'
_hole_a':f':g'1 :: a':f':g'
_gen_a':f':g'2 :: Nat → a':f':g'

Generator Equations:
_gen_a':f':g'2(0) ⇔ a'
_gen_a':f':g'2(+(x, 1)) ⇔ f'(_gen_a':f':g'2(x))

No more defined symbols left to analyse.