#3626 ⟨a, b | aabbaaaaba=b⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element b has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabab^-1aabb⟩
- Embedding: φ(a) = a, φ(b) = 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

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

# ab:aabbaaaaba=b cb/a aa=c morph:2/0
cbbcccbbccbc=b
bbbcccbbccbc=cbbcccbbccbb
ca=ac
ba=cbbccbc
aa=c

1 unique, 1 total

Σ	#	Presentation	Properties
11	5276	⟨a, b \| aabbbba=babb⟩	Can Inf