#4527 ⟨a, b | aaababba=baa⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

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) = 1; deg(b) = 2
Auxiliary generators:
1. babb=c
2. caa=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a³dad² ⇒ da	[11]
2.	a³dadca ⇒ d	[6]
3.	cd ⇒ d(ad)²ca	[7]
4.	ca² ⇒ d	[3]
5.	cad ⇒ da(ad)²ca	[8]
6.	bd ⇒ a³d²adca	[9]
7.	ba² ⇒ a³ca	[4]
8.	bad ⇒ a²(ad)³ca	[10]
9.	babc ⇒ cab²	[5]
10.	bab² ⇒ c	[2]

# ab:aaababba=baa reversed:ad/c/b babb=c,caa=d morph:4/1,3/0
aaadadd=da
aaadadca=d
cd=dadadca
caa=d
cad=daadadca
bd=aaaddadca
baa=aaaca
bad=aaadadadca
babc=cabb
babb=c