#2986 ⟨a, b, c | aab=c, bca=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ a²ba = b and b ⋅ 1 = b, however a²ba ≠ 1

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Reduction order:
- Left-to-right recursive path with deg(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aab=c,bca=b ab/c - -
bba=bab
baba=baab
baaba=b
c=aab

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ	#	Presentation	Mapping
8	3053	⟨a, b, c \| aba=c, bac=b⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	5566	⟨a, b, c \| ab=c, baca=b⟩	φ(a) = a, φ(b) = b, φ(c) = ab