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

f(empty, l) → l
f(cons(x, k), l) → g(k, l, cons(x, k))
g(a, b, c) → f(a, cons(b, c))

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

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


f'(empty', l) → l
f'(cons'(x, k), l) → g'(k, l, cons'(x, k))
g'(a, b, c) → f'(a, cons'(b, c))

Rewrite Strategy: INNERMOST

Sliced the following arguments:
cons'/0
g'/1

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


f'(empty', l) → l
f'(cons'(k), l) → g'(k, cons'(k))
g'(a, c) → f'(a, cons'(c))

Rewrite Strategy: INNERMOST

Infered types.

Rules:
f'(empty', l) → l
f'(cons'(k), l) → g'(k, cons'(k))
g'(a, c) → f'(a, cons'(c))

Types:
f' :: empty':cons' → empty':cons' → empty':cons'
empty' :: empty':cons'
cons' :: empty':cons' → empty':cons'
g' :: empty':cons' → empty':cons' → empty':cons'
_hole_empty':cons'1 :: empty':cons'
_gen_empty':cons'2 :: Nat → empty':cons'

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

They will be analysed ascendingly in the following order:
f' = g'

Rules:
f'(empty', l) → l
f'(cons'(k), l) → g'(k, cons'(k))
g'(a, c) → f'(a, cons'(c))

Types:
f' :: empty':cons' → empty':cons' → empty':cons'
empty' :: empty':cons'
cons' :: empty':cons' → empty':cons'
g' :: empty':cons' → empty':cons' → empty':cons'
_hole_empty':cons'1 :: empty':cons'
_gen_empty':cons'2 :: Nat → empty':cons'

Generator Equations:
_gen_empty':cons'2(0) ⇔ empty'
_gen_empty':cons'2(+(x, 1)) ⇔ cons'(_gen_empty':cons'2(x))

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

They will be analysed ascendingly in the following order:
f' = g'

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

The following conjecture could not be proven:

g'(_gen_empty':cons'2(_n4), _gen_empty':cons'2(b)) →? _gen_empty':cons'2(2)

Rules:
f'(empty', l) → l
f'(cons'(k), l) → g'(k, cons'(k))
g'(a, c) → f'(a, cons'(c))

Types:
f' :: empty':cons' → empty':cons' → empty':cons'
empty' :: empty':cons'
cons' :: empty':cons' → empty':cons'
g' :: empty':cons' → empty':cons' → empty':cons'
_hole_empty':cons'1 :: empty':cons'
_gen_empty':cons'2 :: Nat → empty':cons'

Generator Equations:
_gen_empty':cons'2(0) ⇔ empty'
_gen_empty':cons'2(+(x, 1)) ⇔ cons'(_gen_empty':cons'2(x))

The following defined symbols remain to be analysed:
f'

They will be analysed ascendingly in the following order:
f' = g'

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

The following conjecture could not be proven:

f'(_gen_empty':cons'2(_n964), _gen_empty':cons'2(b)) →? _gen_empty':cons'2(2)

Rules:
f'(empty', l) → l
f'(cons'(k), l) → g'(k, cons'(k))
g'(a, c) → f'(a, cons'(c))

Types:
f' :: empty':cons' → empty':cons' → empty':cons'
empty' :: empty':cons'
cons' :: empty':cons' → empty':cons'
g' :: empty':cons' → empty':cons' → empty':cons'
_hole_empty':cons'1 :: empty':cons'
_gen_empty':cons'2 :: Nat → empty':cons'

Generator Equations:
_gen_empty':cons'2(0) ⇔ empty'
_gen_empty':cons'2(+(x, 1)) ⇔ cons'(_gen_empty':cons'2(x))

No more defined symbols left to analyse.