#2318 ⟨a, b | abaabba=bab⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabab^-1abb⟩
- Embedding: φ(a) = aab, φ(b) = b^-1a^-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 = ab
Reduction order:
- Right-to-left recursive path with deg(c) = deg(a) = 0, c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaabba=bab reversed:ca/b ab=c morph:2/0
ab=c
acacbc=ccb
cacba=bc
ccbb=acaccacbc
bcb=cacbc
ccbcacbc=acaccacbccb
bccacbc=cacbccb
ccbacba=acacbbc

1 unique, 1 total

Σ	#	Presentation	Properties
10	1782	⟨a, b \| ababaabba=b⟩	Can Inf

5 unique, 5 total

Σ	#	Presentation	Properties
9	838	⟨a, b \| abaaabba=b⟩	Can Inf
9	1100	⟨a, b \| aabbba=bab⟩	Can Inf
10	2758	⟨a, b \| baabb=ababa⟩	Can Inf
11	3708	⟨a, b \| abaaaababa=b⟩	Can Inf
11	4850	⟨a, b \| ababbbba=bab⟩	Can Inf