f(S(x), x2) → f(x2, x)
f(0, x2) → 0
Renamed function symbols to avoid clashes with predefined symbol.
Runtime Complexity TRS:
The TRS R consists of the following rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'
Infered types.
Rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'
Types:
f' :: S':0' → S':0' → S':0'
S' :: S':0' → S':0'
0' :: S':0'
_hole_S':0'1 :: S':0'
_gen_S':0'2 :: Nat → S':0'
Heuristically decided to analyse the following defined symbols:
f'
Rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'
Types:
f' :: S':0' → S':0' → S':0'
S' :: S':0' → S':0'
0' :: S':0'
_hole_S':0'1 :: S':0'
_gen_S':0'2 :: Nat → S':0'
Generator Equations:
_gen_S':0'2(0) ⇔ 0'
_gen_S':0'2(+(x, 1)) ⇔ S'(_gen_S':0'2(x))
The following defined symbols remain to be analysed:
f'
Could not prove a rewrite lemma for the defined symbol f'.
Rules:
f'(S'(x), x2) → f'(x2, x)
f'(0', x2) → 0'
Types:
f' :: S':0' → S':0' → S':0'
S' :: S':0' → S':0'
0' :: S':0'
_hole_S':0'1 :: S':0'
_gen_S':0'2 :: Nat → S':0'
Generator Equations:
_gen_S':0'2(0) ⇔ 0'
_gen_S':0'2(+(x, 1)) ⇔ S'(_gen_S':0'2(x))
No more defined symbols left to analyse.