#860 ⟨a, b | abbaabba=b⟩

Properties

Sum of relation sides is 9
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbaabb⟩
- Embedding: φ(a) = aba, φ(b) = a^-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

Auxiliary generators:
1. c = bba
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.
Morphocompletion: how the auxiliary generators were found.

# ab:abbaabba=b ac/b bba=c morph:3/0
cca=acc
acacacaca=c
b=acac

2 unique, 14 total

Σ	#	Presentation	Properties	φ
9	678	⟨a, b \| aabbaaabb=1⟩	Grp Inf	12
11	4865	⟨a, b \| abbaabba=bab⟩	Can Inf

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

1 total

Σ	#	Presentation	Mapping
10	1786	⟨a, b \| ababababa=b⟩	φ(a) = a, φ(b) = c