#4850 ⟨a, b | ababbbba=bab⟩

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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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. abbbba=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	a²bc⁴ ⇒ cb	[5]
2.	bab ⇒ abc	[3]
3.	abcab ⇒ ba²bc	[4]
4.	b²cb ⇒ (abc²)²c	[11]
5.	b²a²bc ⇒ abc²ab	[8]
6.	ab(cb)² ⇒ ba(abc²)²c	[13]
7.	abcba²bc ⇒ ba²bc²ab	[9]
8.	(abc²)²cab ⇒ b²cabc	[12]
9.	b³cabc ⇒ ab(c³ab)²	[18]
10.	ab⁴a ⇒ c	[2]
11.	abcb³a ⇒ bc	[6]
12.	abcb²cabc ⇒ ba²b(c³ab)²	[24]
13.	abc²b³a ⇒ b²c	[7]
14.	(abc²)²(cb)² ⇒ b²c(abc²)²c	[15]
15.	(abc²)²cba²bc ⇒ b²cabc²ab	[14]
16.	abc³b³a ⇒ b³c	[10]
17.	abc⁴b³a ⇒ b⁴c	[16]
18.	cb⁴a ⇒ ab⁴c	[22]
19.	b⁵c ⇒ abc⁵b³a	[20]
20.	abcb⁴c ⇒ (bc)²b³a	[21]
21.	(abc²)²cb²cabc ⇒ b²cab(c³ab)²	[25]
22.	a²bc³ab⁴c ⇒ cb⁵a	[23]
23.	abc²ab⁵a ⇒ b²a³bcb³c	[19]
24.	(abc²)²cb⁴c ⇒ b²cabc⁵b³a	[26]
25.	b³a³bcb³c ⇒ abc³ab⁵a	[28]
26.	abcb²a³bcb³c ⇒ ba²bc³ab⁵a	[29]
27.	a(bc³a)²b⁵a ⇒ b³ca²bcb³c	[27]
28.	b⁴ca²bcb³c ⇒ abc(c³ab)²b⁴a	[31]
29.	abcb³ca²bcb³c ⇒ bcabc⁴ab⁵a	[32]
30.	abc²b³ca²bcb³c ⇒ b²cabc⁴ab⁵a	[33]
31.	(abc²)²cb²a³bcb³c ⇒ b²cabc³ab⁵a	[30]
32.	(abc²)²cb³ca²bcb³c ⇒ b²(cabc³)²ab⁵a	[34]

# ab:ababbbba=bab ac/b abbbba=c morph:6/0
aabcccc=cb
bab=abc
abcab=baabc
bbcb=abccabccc
bbaabc=abccab
abcbcb=baabccabccc
abcbaabc=baabccab
abccabcccab=bbcabc
bbbcabc=abcccabcccab
abbbba=c
abcbbba=bc
abcbbcabc=baabcccabcccab
abccbbba=bbc
abccabcccbcb=bbcabccabccc
abccabcccbaabc=bbcabccab
abcccbbba=bbbc
abccccbbba=bbbbc
cbbbba=abbbbc
bbbbbc=abcccccbbba
abcbbbbc=bcbcbbba
abccabcccbbcabc=bbcabcccabcccab
aabcccabbbbc=cbbbbba
abccabbbbba=bbaaabcbbbc
abccabcccbbbbc=bbcabcccccbbba
bbbaaabcbbbc=abcccabbbbba
abcbbaaabcbbbc=baabcccabbbbba
abcccabcccabbbbba=bbbcaabcbbbc
bbbbcaabcbbbc=abccccabcccabbbbba
abcbbbcaabcbbbc=bcabccccabbbbba
abccbbbcaabcbbbc=bbcabccccabbbbba
abccabcccbbaaabcbbbc=bbcabcccabbbbba
abccabcccbbbcaabcbbbc=bbcabccccabcccabbbbba