#3623 ⟨a, b | aabbaaaaab=a⟩

Up:Monoids with two generators and one relation
Prev:#3622 ⟨a, b | aababbbbba=b⟩
Next:#3624 ⟨a, b | aabbaaaaab=b⟩

Quick links

  1. Properties
  2. Rewriting system

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. c2b2cb ⇒ cb(bc)2 [8]
2. c2(bcb)2 ⇒ c2b3cbc [37]
3. (cb)3bcb ⇒ cbcb3cbc [17]
4. (cb2cb)2 ⇒ c(b2cb)2c [11]
5. c2b3c(bcb)2 ⇒ c2(b3c)2bc [38]
6. cbcb3c(bcb)2 ⇒ cbc(b3c)2bc [21]
7. cb2cb3c(bcb)2 ⇒ c(b2cb)3c [20]
8. c2(b3c)2(bcb)2 ⇒ c2(b3c)3bc [39]
9. cbc(b3c)2(bcb)2 ⇒ cbc(b3c)3bc [36]
10. c(b2cb)3cb2cb ⇒ c(b2cb)4c [26]
11. c2(b3c)3(bcb)2 ⇒ cbc(b3c)3bcb2c [35]
12. cbc(b3c)3(bcb)2 ⇒ c(b2cb)4cb2c [32]
13. c(b2cb)4cb2cb ⇒ c [28]
14. a ⇒ c(b2cb)4 [25]
# ab:aabbaaaaab=a bc/a aaaaa=c morph:5/0
ccbbcb=cbbcbc
ccbcbbcb=ccbbbcbc
cbcbcbbcb=cbcbbbcbc
cbbcbcbbcb=cbbcbbbcbc
ccbbbcbcbbcb=ccbbbcbbbcbc
cbcbbbcbcbbcb=cbcbbbcbbbcbc
cbbcbbbcbcbbcb=cbbcbbbcbbbcbc
ccbbbcbbbcbcbbcb=ccbbbcbbbcbbbcbc
cbcbbbcbbbcbcbbcb=cbcbbbcbbbcbbbcbc
cbbcbbbcbbbcbcbbcb=cbbcbbbcbbbcbbbcbc
ccbbbcbbbcbbbcbcbbcb=cbcbbbcbbbcbbbcbcbbc
cbcbbbcbbbcbbbcbcbbcb=cbbcbbbcbbbcbbbcbcbbc
cbbcbbbcbbbcbbbcbcbbcb=c
a=cbbcbbbcbbbcbbbcb