#3500 ⟨a, b, c | bb=ac, aaa=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 a is not injective:
- a ⋅ c = a⁶ and a ⋅ a⁵ = a⁶, however c ≠ a⁵

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) = 0; deg(b) = deg(c) = 1, b < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b ⇒ a³	[2]
2.	ac ⇒ a⁶	[3]

# abc:bb=ac,aaa=b a/bc - -
b=aaa
ac=aaaaaa

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

1 total

Σ	#	Presentation	Mapping
8	5731	⟨a, b, c \| aa=b, bbb=ac⟩	φ(a) = a, φ(b) = aa, φ(c) = c