#3046 ⟨a, b | aabaabbabba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group
  5. Isomorphic instances
  6. Anti-isomorphic instances

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. bd ⇒ 1 [36]
2. db ⇒ 1 [8]
3. cacbc ⇒ acb2 [49]
4. dacbc ⇒ ba [13]
5. b2a ⇒ acbc [12]
6. cacbac ⇒ a2cb(bc)2d2 [59]
7. ba2 ⇒ ca2c [40]
8. bad2ac ⇒ ca2d [47]
9. dacbac ⇒ ca2c2bcd2 [55]
10. bca2 ⇒ acbcd2acb [53]
11. dca2 ⇒ ad2acb [48]
12. a3c ⇒ d2 [37]
13. ca(ac)2 ⇒ d [41]
14. cac2a2c2 ⇒ a2cb(bc)2ad2 [63]
15. bad2a2c ⇒ ca2bad2 [52]
16. da(ac)2 ⇒ ca2cad [44]
17. dac2a2c2 ⇒ ca2c2bcad2 [61]
18. c(a2c)2 ⇒ bad2 [42]
19. d(a2c)2 ⇒ ca2cabad2 [51]
# ab:aabaabbabba=1 cbd/a baabba=c,aaacb=d morph:6/0,5/0
bd=1
db=1
cacbc=acbb
dacbc=ba
bba=acbc
cacbac=aacbbcbcdd
baa=caac
baddac=caad
dacbac=caaccbcdd
bcaa=acbcddacb
dcaa=addacb
aaac=dd
caacac=d
caccaacc=aacbbcbcadd
baddaac=caabadd
daacac=caacad
daccaacc=caaccbcadd
caacaac=badd
daacaac=caacabadd

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
113651⟨a, b | aabbababba=b⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
115305⟨a, b | abaaaba=babb⟩Can Inf

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ#PresentationMapping
113125⟨a, b | aabbabbaaab=1⟩φ(a) = a, φ(b) = aacbbab
113147⟨a, b | aabbbabbaab=1⟩φ(a) = aacbbab, φ(b) = a
113223⟨a, b | abaabbbabba=1⟩φ(a) = aacbbab, φ(b) = a

Anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

4 total

Σ#PresentationMapping
113126⟨a, b | aabbabbaaba=1⟩φ(a) = a, φ(b) = abaacbb
113129⟨a, b | aabbabbbaab=1⟩φ(a) = abaacbb, φ(b) = a
113196⟨a, b | abaaabbabba=1⟩φ(a) = a, φ(b) = abaacbb
113219⟨a, b | abaabbabbba=1⟩φ(a) = abaacbb, φ(b) = a