#4887 ⟨a, b | abbbbbba=bab⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ab ⇒ c [2]
2. cb ⇒ d [3]
3. db ⇒ e [4]
4. eb ⇒ f [5]
5. fb ⇒ g [6]
6. gb ⇒ h [7]
7. ha ⇒ bc [9]
8. hc ⇒ bd [10]
9. hd ⇒ be [11]
10. he ⇒ bf [12]
11. hf ⇒ bg [13]
12. hg ⇒ bh [14]
13. bhb ⇒ h2 [15]
14. chb ⇒ ah2 [16]
15. dhb ⇒ ch2 [17]
16. ehb ⇒ dh2 [18]
17. fhb ⇒ eh2 [19]
18. ghb ⇒ fh2 [20]
19. h2b ⇒ gh2 [21]
# ab:abbbbbba=bab bacdefgh ab=c,cb=d,db=e,eb=f,fb=g,gb=h morph:2/1,2/1,2/1,2/1,2/1,2/0
ab=c
cb=d
db=e
eb=f
fb=g
gb=h
ha=bc
hc=bd
hd=be
he=bf
hf=bg
hg=bh
bhb=hh
chb=ahh
dhb=chh
ehb=dhh
fhb=ehh
ghb=fhh
hhb=ghh

Other submonoids of same group

12 unique, 57 total

Σ#PresentationPropertiesφ
530⟨a, b | aabba=1⟩Grp Inf40
543⟨a, b | abba=b⟩Can Inf
546⟨a, b | aaa=bb⟩Can Inf
553⟨a, b | aba=bb⟩Can Inf
691⟨a, b | ababa=b⟩Can Inf5
6123⟨a, b | bab=aba⟩Can Inf
7267⟨a, b | abba=bab⟩Can Inf
8555⟨a, b | abbba=bab⟩Can Inf
91137⟨a, b | abbbba=bab⟩Can Inf
91262⟨a, b | ababa=baab⟩Can Inf
102361⟨a, b | abbbbba=bab⟩Can Inf
115855⟨a, b | abaaba=baaab⟩Can Inf