#3259 ⟨a, b | ababbabbbba=1⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
- a^-1 = (da)³d²c
- b^-1 = ad
- c^-1 = (ad)⁴d
- d^-1 = (ad)³dad³(ad)³dc

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

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

#	Rule	Proof
1.	a(ad)³dad² ⇒ d(ad)³(da)²	[25]
2.	(da)³d²ad² ⇒ a	[24]
3.	(ad)⁴dc ⇒ 1	[21]
4.	ca ⇒ ad³(ad)³dc	[22]
5.	cd ⇒ ad³a(d(ad²)²)²d²c	[28]
6.	b ⇒ (ad)³dc	[20]

# ab:ababbabbbba=1 reversed:ad/cb babbbb=c,bcaa=d morph:6/0,4/1
aadadaddadd=dadadaddada
dadadaddadd=a
adadadaddc=1
ca=adddadadaddc
cd=adddadaddadddaddaddddc
b=adadaddc

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