#672 ⟨a, b | aababbaba=1⟩

Properties

Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
- a^-1 = a²d
- b^-1 = babcba
- c^-1 = d
- d^-1 = c

Complete 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:
- Left-to-right recursive path with deg(a) = deg(c) = deg(d) = 0, a < c < d; deg(b) = 1
Auxiliary generator: aaa=c
Auxiliary generator: babbab=d

ca ⇒ ac
cd ⇒ 1
da ⇒ ad
dc ⇒ 1
a³ ⇒ c
cbab ⇒ babc
dbab ⇒ babd
ab²ab ⇒ babcbad
a²bab² ⇒ b²aba²
a(ab)²cb ⇒ cb²aba²
a(ab)²db ⇒ db²aba²
acb²ab ⇒ babc²bad
adb²ab ⇒ bab²ad
c²b²ab ⇒ a(ab)²c²bad
d²b²ab ⇒ a(ab)²d²bad
b²abcb ⇒ a²d

# ab:aababbaba=1 acd/b aaa=c,babbab=d magic:0
ca=ac
cd=1
da=ad
dc=1
aaa=c
cbab=babc
dbab=babd
abbab=babcbad
aababb=bbabaa
aababcb=cbbabaa
aababdb=dbbabaa
acbbab=babccbad
adbbab=babbad
ccbbab=aababccbad
ddbbab=aababddbad
bbabcb=aad

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

2 total

Σ	#	Presentation	Mapping
9	719	⟨a, b \| ababbbaba=1⟩	φ(a) = b, φ(b) = a
9	725	⟨a, b \| abbabaaab=1⟩	φ(a) = a, φ(b) = b

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