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

f(c(s(x), y)) → f(c(x, s(y)))
g(c(x, s(y))) → g(c(s(x), y))

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

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

f'(c'(s'(x), y)) → f'(c'(x, s'(y)))
g'(c'(x, s'(y))) → g'(c'(s'(x), y))

Rewrite Strategy: INNERMOST

Infered types.

Rules:
f'(c'(s'(x), y)) → f'(c'(x, s'(y)))
g'(c'(x, s'(y))) → g'(c'(s'(x), y))

Types:
f' :: c' → f'
c' :: s' → s' → c'
s' :: s' → s'
g' :: c' → g'
_hole_f'1 :: f'
_hole_c'2 :: c'
_hole_s'3 :: s'
_hole_g'4 :: g'
_gen_s'5 :: Nat → s'

Heuristically decided to analyse the following defined symbols:
f', g'

Rules:
f'(c'(s'(x), y)) → f'(c'(x, s'(y)))
g'(c'(x, s'(y))) → g'(c'(s'(x), y))

Types:
f' :: c' → f'
c' :: s' → s' → c'
s' :: s' → s'
g' :: c' → g'
_hole_f'1 :: f'
_hole_c'2 :: c'
_hole_s'3 :: s'
_hole_g'4 :: g'
_gen_s'5 :: Nat → s'

Generator Equations:
_gen_s'5(0) ⇔ _hole_s'3
_gen_s'5(+(x, 1)) ⇔ s'(_gen_s'5(x))

The following defined symbols remain to be analysed:
f', g'

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

Rules:
f'(c'(s'(x), y)) → f'(c'(x, s'(y)))
g'(c'(x, s'(y))) → g'(c'(s'(x), y))

Types:
f' :: c' → f'
c' :: s' → s' → c'
s' :: s' → s'
g' :: c' → g'
_hole_f'1 :: f'
_hole_c'2 :: c'
_hole_s'3 :: s'
_hole_g'4 :: g'
_gen_s'5 :: Nat → s'

Generator Equations:
_gen_s'5(0) ⇔ _hole_s'3
_gen_s'5(+(x, 1)) ⇔ s'(_gen_s'5(x))

The following defined symbols remain to be analysed:
g'

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

Rules:
f'(c'(s'(x), y)) → f'(c'(x, s'(y)))
g'(c'(x, s'(y))) → g'(c'(s'(x), y))

Types:
f' :: c' → f'
c' :: s' → s' → c'
s' :: s' → s'
g' :: c' → g'
_hole_f'1 :: f'
_hole_c'2 :: c'
_hole_s'3 :: s'
_hole_g'4 :: g'
_gen_s'5 :: Nat → s'

Generator Equations:
_gen_s'5(0) ⇔ _hole_s'3
_gen_s'5(+(x, 1)) ⇔ s'(_gen_s'5(x))

No more defined symbols left to analyse.