#7791 ⟨a, b | aaa=1, ababb=ba⟩

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Properties

Complete 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
  1. a3 ⇒ 1
  2. (ac)2 ⇒ c2a2
  3. abac ⇒ cba2
  4. a2c2 ⇒ (ca)2
  5. ac3 ⇒ c3a
  6. abc2 ⇒ cbca
  7. cabc ⇒ a2ba
  8. c2bc ⇒ acba
  9. cb2c ⇒ ab2a
  10. ca2b ⇒ ba2c
  11. ba2b ⇒ c
  12. a2cb ⇒ baca
  13. cacb ⇒ bac2
  14. bacb ⇒ (ca)2
  15. a2b2 ⇒ babc
  16. cab2 ⇒ (ba)2
  17. bab2 ⇒ a2ba
  18. (ab)2c ⇒ b2
  19. cbabc ⇒ b2aca
  20. b2abc ⇒ cb
  21. a(bc)2 ⇒ b2ca2
  22. c(bc)2 ⇒ b2c2a
  23. b(bc)2 ⇒ cbca2
  24. ab3c ⇒ b3ca
  25. cb3c ⇒ b3a2
  26. b4c ⇒ ab2a2
  27. ac(ab)2 ⇒ c2b2a2
  28. (ab)3 ⇒ cb3a2
  29. ac2bab ⇒ c2b2ac
  30. abcbab ⇒ cb3ac
  31. c2b2ab ⇒ ac2ba2
  32. cb3ab ⇒ abcba2
  33. ac2b3 ⇒ c2b3a
  34. abcb3 ⇒ cb4a
  35. c2b4 ⇒ (ab)2a2
  36. cb5 ⇒ ba2
  37. acaba2c ⇒ c2ab
  38. (ab)2a2c ⇒ cbab
  39. ac2ba2c ⇒ c3b
  40. abcba2c ⇒ (cb)2
  41. c2b2a2c ⇒ acb2
  42. cb3a2c ⇒ ab3
  43. ac2b2ac ⇒ c3b2a2
  44. abcb2ac ⇒ cbcb2a2
  45. c2b3ac ⇒ acb3a2
  46. cb4ac ⇒ ab4a2
  47. ac2bac2 ⇒ c3baca
  48. abcbac2 ⇒ (cb)2aca
  49. c2b2ac2 ⇒ acb2aca
  50. cb3ac2 ⇒ ab3aca
  51. abcb2ab ⇒ b2cb2a2
  52. cbcb2ab ⇒ b2cb2ac
  53. b2cb2ab ⇒ cbcb2a2
  54. ab4ab ⇒ b5ac
  55. cb4ab ⇒ b5a2
  56. b5ab ⇒ ab4a2
  57. cbcb4 ⇒ b2cb3a
  58. b2cb4 ⇒ cb4a2
  59. ab6 ⇒ b6a
  60. b7 ⇒ b
  61. abcb2a2c ⇒ b2cab
  62. cbcb2a2c ⇒ b2c2b
  63. b2cb2a2c ⇒ cbcab
  64. ab4a2c ⇒ b3cb
  65. cb4a2c ⇒ b3ab
  66. b5a2c ⇒ ab2ab
  67. cbcb3ac ⇒ b2c2b2a2
  68. b2cb3ac ⇒ cb2ab
  69. ab5ac ⇒ b3cb2a2
  70. b6ac ⇒ ac
  71. cbcb2ac2 ⇒ b2c2baca
  72. b2cb2ac2 ⇒ cbc2b
  73. ab4ac2 ⇒ b3cbaca
  74. b5ac2 ⇒ ab2cb 
# ab:aaa=1,ababb=ba reversed:acb baab=c frequency:4/0
aaa=1
acac=ccaa
abac=cbaa
aacc=caca
accc=ccca
abcc=cbca
cabc=aaba
ccbc=acba
cbbc=abba
caab=baac
baab=c
aacb=baca
cacb=bacc
bacb=caca
aabb=babc
cabb=baba
babb=aaba
ababc=bb
cbabc=bbaca
bbabc=cb
abcbc=bbcaa
cbcbc=bbcca
bbcbc=cbcaa
abbbc=bbbca
cbbbc=bbbaa
bbbbc=abbaa
acabab=ccbbaa
ababab=cbbbaa
accbab=ccbbac
abcbab=cbbbac
ccbbab=accbaa
cbbbab=abcbaa
accbbb=ccbbba
abcbbb=cbbbba
ccbbbb=ababaa
cbbbbb=baa
acabaac=ccab
ababaac=cbab
accbaac=cccb
abcbaac=cbcb
ccbbaac=acbb
cbbbaac=abbb
accbbac=cccbbaa
abcbbac=cbcbbaa
ccbbbac=acbbbaa
cbbbbac=abbbbaa
accbacc=cccbaca
abcbacc=cbcbaca
ccbbacc=acbbaca
cbbbacc=abbbaca
abcbbab=bbcbbaa
cbcbbab=bbcbbac
bbcbbab=cbcbbaa
abbbbab=bbbbbac
cbbbbab=bbbbbaa
bbbbbab=abbbbaa
cbcbbbb=bbcbbba
bbcbbbb=cbbbbaa
abbbbbb=bbbbbba
bbbbbbb=b
abcbbaac=bbcab
cbcbbaac=bbccb
bbcbbaac=cbcab
abbbbaac=bbbcb
cbbbbaac=bbbab
bbbbbaac=abbab
cbcbbbac=bbccbbaa
bbcbbbac=cbbab
abbbbbac=bbbcbbaa
bbbbbbac=ac
cbcbbacc=bbccbaca
bbcbbacc=cbccb
abbbbacc=bbbcbaca
bbbbbacc=abbcb

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1123306⟨a, b | aaa=1, babb=aaba⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1121697⟨a, b | aaa=1, aabbaba=b⟩φ(a) = a, φ(b) = b