⟨a, b | abaaabbaab=1⟩

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Monoids with two generators and one relation

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:
- Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(b) = deg(c) = 1, b < c
Auxiliary generator: bbaab=c
Auxiliary generator: baaac=d

da ⇒ 1
ad ⇒ 1
cab ⇒ d³
ba³c ⇒ d
cac ⇒ d³ba²b
ca²c ⇒ d²ba³bd
ca³c ⇒ b²a
ca⁴c ⇒ dbaba²
ba³b² ⇒ a²cd
ba(ab)² ⇒ a³cd²
b²a²b ⇒ c
baba³b ⇒ aca
ba³bc ⇒ a²cdba²b
ba²bac ⇒ a³cd²ba²b
ba³bac ⇒ a²cba³bd
b²a²c ⇒ cba²b
(ba²)²c ⇒ a³cdba³bd
ba³ba²c ⇒ a²ca²b²a
b²a⁴c ⇒ ca³b²a
baba⁴c ⇒ aca²ba³bd
ba²ba⁴c ⇒ a³cbaba²
b²a⁵c ⇒ ca(ab)²a²
baba⁵c ⇒ aca⁴b²a
baba⁶c ⇒ aca³baba²

# ab:abaaabbaab=1 reversed:ad/bc bbaab=c,baaac=d frequency:5/3,5/0 da=1 ad=1 cab=ddd baaac=d cac=dddbaab caac=ddbaaabd caaac=bba caaaac=dbabaa baaabb=aacd baabab=aaacdd bbaab=c babaaab=aca baaabc=aacdbaab baabac=aaacddbaab baaabac=aacbaaabd bbaac=cbaab baabaac=aaacdbaaabd baaabaac=aacaabba bbaaaac=caaabba babaaaac=acaabaaabd baabaaaac=aaacbabaa bbaaaaac=caababaa babaaaaac=acaaaabba babaaaaaac=acaaababaa

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#1487 ⟨a, b | abaaabbaab=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)