#5773 ⟨a, b, c | aa=b, ccc=bb⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a²ca has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabbb⟩
- Embedding: φ(a) = a^-1, φ(b) = a^-1a^-1, φ(c) = b

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

# abc:aa=b,ccc=bb ac/b - -
aaaa=ccc
ccca=accc
b=aa

1 unique, 10 total

Σ	#	Presentation	Properties	φ
8	1578	⟨a, b, c \| aaa=bb, cbc=1⟩	Grp Inf	9