#2865 ⟨a, b | aaaababbaba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

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. ac ⇒ ca [5]
2. a5 ⇒ c [2]
3. dc ⇒ 1 [20]
4. cd ⇒ 1 [13]
5. ad ⇒ da [21]
6. cbab ⇒ babc [25]
7. c(ab)2 ⇒ (ab)2c [26]
8. ca(ab)2 ⇒ a(ab)2c [27]
9. ca3bab ⇒ a3babc [29]
10. ca4bab ⇒ a4babc [37]
11. dbab ⇒ babd [11]
12. d(ab)2 ⇒ (ab)2d [23]
13. da(ab)2 ⇒ a(ab)2d [28]
14. da3bab ⇒ a3babd [30]
15. da4bab ⇒ a4babd [38]
16. ab2ab ⇒ babcbda [31]
17. a4bab2 ⇒ b2aba4 [39]
18. a4babcb ⇒ cb2aba4 [41]
19. a4babc2b ⇒ c2b2aba4 [42]
20. a4babc3b ⇒ c3b2aba4 [43]
21. a4babc4b ⇒ c4b2aba4 [44]
22. c5b2ab ⇒ a4babc5bda [47]
23. db2ab ⇒ a4ba(bd)2a [40]
24. b2abcb ⇒ da4 [36]
# ab:aaaababbaba=1 ca/d/b aaaaa=c,babbab=d magic:0
ac=ca
aaaaa=c
dc=1
cd=1
ad=da
cbab=babc
cabab=ababc
caabab=aababc
caaabab=aaababc
caaaabab=aaaababc
dbab=babd
dabab=ababd
daabab=aababd
daaabab=aaababd
daaaabab=aaaababd
abbab=babcbda
aaaababb=bbabaaaa
aaaababcb=cbbabaaaa
aaaababccb=ccbbabaaaa
aaaababcccb=cccbbabaaaa
aaaababccccb=ccccbbabaaaa
cccccbbab=aaaababcccccbda
dbbab=aaaababdbda
bbabcb=daaaa

Isomorphic instances

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

3 total

Σ#PresentationMapping
112944⟨a, b | aaababbabaa=1⟩φ(a) = a, φ(b) = b
113267⟨a, b | ababbbbbaba=1⟩φ(a) = b, φ(b) = a
113284⟨a, b | abbabaaaaab=1⟩φ(a) = a, φ(b) = b