⟨a, b | aababaabba=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:
- Left-to-right recursive path with deg(a) = deg(d) = 0, a < d; deg(b) = deg(c) = 1, b < c
Auxiliary generator: baabb=c
Auxiliary generator: bac=d

da ⇒ ad
a³d ⇒ 1
bac ⇒ d
ca³b ⇒ a²d
cac ⇒ ba²bd
ca²c ⇒ a²dba³bad
ca³c ⇒ ab²
ca⁴c ⇒ a(ab)²a²d
b²a³b ⇒ a²dca²
baba²b ⇒ adca³
ba²b² ⇒ c
ba³bab ⇒ aca
cba³b ⇒ (ba²)²dca²
caba²b ⇒ ba²badca³
caba³b ⇒ a²dba³bca²
ca²b² ⇒ ba²bc
c(a²b)² ⇒ a²dba³ba²dca³
ca²ba³b ⇒ ab²a²ca²
ca⁴b² ⇒ ab²a³c
ca⁴bab ⇒ a²dba³ba²ca
ca⁴ba²b ⇒ a(ab)²ca³
ca⁵b² ⇒ a(ab)²a²c
ca⁵bab ⇒ ab²a⁴ca
ca⁶bab ⇒ a(ab)²a³ca

# ab:aababaabba=1 ad/bc baabb=c,bac=d frequency:5/0,3/0 da=ad aaad=1 bac=d caaab=aad cac=baabd caac=aadbaaabad caaac=abb caaaac=aababaad bbaaab=aadcaa babaab=adcaaa baabb=c baaabab=aca cbaaab=baabaadcaa cabaab=baabadcaaa cabaaab=aadbaaabcaa caabb=baabc caabaab=aadbaaabaadcaaa caabaaab=abbaacaa caaaabb=abbaaac caaaabab=aadbaaabaaca caaaabaab=aababcaaa caaaaabb=aababaac caaaaabab=abbaaaaca caaaaaabab=aababaaaca

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#1419 ⟨a, b | aababaabba=1⟩

Properties

Complete rewriting system

Right Cayley graph (truncated)

Left Cayley graph (truncated)