#4727 ⟨a, b | aabbbaba=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. abbbab=c
2. ccca=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	(a²d)²(da)²(ada(ad²)²)² ⇒ da	[28]
2.	((a²d)²dad)²dada²d²adcd ⇒ dca	[32]
3.	ca² ⇒ a²dca	[17]
4.	cda ⇒ dadca	[24]
5.	cad ⇒ a²dcd	[11]
6.	cd² ⇒ dadcd	[14]
7.	cac ⇒ a²dc²	[9]
8.	cdc ⇒ dadc²	[15]
9.	((a²d)²dad)²dada²d²adc²d ⇒ dc²a	[27]
10.	c³a ⇒ d	[3]
11.	((a²d)²dad)²dada²d²adc³d ⇒ d²	[25]
12.	((a²d)²dad)²dada²d²adc⁴ ⇒ dc	[26]
13.	ba² ⇒ aca	[4]
14.	bda ⇒ a³d(da)²(ada(ad²)²)²dca	[33]
15.	bad ⇒ acd	[10]
16.	bd² ⇒ a³d(da)²(ada(ad²)²)²dcd	[30]
17.	bac ⇒ ac²	[8]
18.	bdc ⇒ a³d(da)²(ada(ad²)²)²dc²	[31]
19.	ab³c ⇒ cb²ab	[5]
20.	db³c ⇒ c⁴b²ab	[22]
21.	cb²abc²a ⇒ ab³d	[23]
22.	ab³ab ⇒ c	[2]
23.	db³ab ⇒ c⁴	[7]

# ab:aabbbaba=baa reversed:ad/c/b abbbab=c,ccca=d morph:6/1,4/3
aadaaddadaadaaddaddadaaddadd=da
aadaaddadaadaaddaddadaaddadcd=dca
caa=aadca
cda=dadca
cad=aadcd
cdd=dadcd
cac=aadcc
cdc=dadcc
aadaaddadaadaaddaddadaaddadccd=dcca
ccca=d
aadaaddadaadaaddaddadaaddadcccd=dd
aadaaddadaadaaddaddadaaddadcccc=dc
baa=aca
bda=aaaddadaadaaddaddadaaddadddca
bad=acd
bdd=aaaddadaadaaddaddadaaddadddcd
bac=acc
bdc=aaaddadaadaaddaddadaaddadddcc
abbbc=cbbab
dbbbc=ccccbbab
cbbabcca=abbbd
abbbab=c
dbbbab=cccc