#145 ⟨a, b | aababba=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. dc ⇒ 1 [11]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [10]
5. a3 ⇒ c [2]
6. b2c ⇒ a(ab)2 [15]
7. babd ⇒ adb2 [12]
8. bcba ⇒ cbab [18]
9. b2ac ⇒ a2(ba)2 [17]
10. (ba)2d ⇒ adb2a [13]
11. b2a2 ⇒ a2dbcb [23]
12. baba2 ⇒ d(bc)2 [21]
13. bab2 ⇒ d [3]
# ab:aababba=1 reversed:cda/b aaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bbc=aabab
babd=adbb
bcba=cbab
bbac=aababa
babad=adbba
bbaa=aadbcb
babaa=dbcbc
babb=d

Other submonoids of same group

11 unique, 11 total

Σ#PresentationProperties
6104⟨a, b | aaba=bb⟩Can Inf
7193⟨a, b | ababba=b⟩Can Inf
7252⟨a, b | aaba=bab⟩Can Inf
9842⟨a, b | abaababa=b⟩Can Inf
91126⟨a, b | ababba=bab⟩Can Inf
91273⟨a, b | abbba=babb⟩Can Inf
102633⟨a, b | abbbba=babb⟩Can Inf
113716⟨a, b | abaaabaaba=b⟩Can Inf
114876⟨a, b | abbabbba=bab⟩Can Inf
115415⟨a, b | abbbbba=babb⟩Can Inf
115898⟨a, b | ababba=babab⟩Can Inf

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationProperties
687⟨a, b | aabba=b⟩Can Inf
7179⟨a, b | aababa=b⟩Can Inf
8374⟨a, b | aabaaba=b⟩Can Inf
8586⟨a, b | baab=aaba⟩Can Inf
9792⟨a, b | aabaaaba=b⟩Can Inf
101666⟨a, b | aabaaaaba=b⟩Can Inf
113536⟨a, b | aabaaaaaba=b⟩Can Inf

Isomorphic instances

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

22 total

Σ#PresentationMapping
7158⟨a, b | abbaaab=1⟩φ(a) = a, φ(b) = aadab
8312⟨a, b | aabbaaba=1⟩φ(a) = aad, φ(b) = aaab
8324⟨a, b | abaaabba=1⟩φ(a) = aad, φ(b) = aaab
8338⟨a, b | abbabbba=1⟩φ(a) = aaab, φ(b) = aad
9671⟨a, b | aababbaab=1⟩φ(a) = cbabaada, φ(b) = aadabab
9706⟨a, b | abaababba=1⟩φ(a) = cbabaada, φ(b) = aadabab
9723⟨a, b | abbaabaab=1⟩φ(a) = cbabaada, φ(b) = aadabab
101346⟨a, b | aaabaababa=1⟩φ(a) = a, φ(b) = aadaadab
101406⟨a, b | aabaababaa=1⟩φ(a) = a, φ(b) = aadaadab
101415⟨a, b | aababaaaab=1⟩φ(a) = a, φ(b) = aadaadab
101479⟨a, b | abaaaabaab=1⟩φ(a) = a, φ(b) = aadaadab
112928⟨a, b | aaababaaaba=1⟩φ(a) = aad, φ(b) = aaaab
113012⟨a, b | aabaaaababa=1⟩φ(a) = aad, φ(b) = aaaab
113064⟨a, b | aabababaaba=1⟩φ(a) = aadab, φ(b) = cbabaadaa
113077⟨a, b | aababbaabab=1⟩φ(a) = cbabaadcbabaada, φ(b) = aadababab
113185⟨a, b | abaaabaaaab=1⟩φ(a) = aad, φ(b) = aaaab
113190⟨a, b | abaaabababa=1⟩φ(a) = aadab, φ(b) = cbabaadaa
113201⟨a, b | abaabaaabab=1⟩φ(a) = aadab, φ(b) = cbabaadaa
113211⟨a, b | abaababbaab=1⟩φ(a) = cbabaadcbabaada, φ(b) = aadababab
113233⟨a, b | ababaabaaab=1⟩φ(a) = aadab, φ(b) = cbabaadaa
113235⟨a, b | ababaababba=1⟩φ(a) = cbabaadcbabaada, φ(b) = aadababab
113279⟨a, b | abbaababaab=1⟩φ(a) = cbabaadcbabaada, φ(b) = aadababab

Anti-isomorphic instances

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

22 total

Σ#PresentationMapping
7147⟨a, b | aabbaba=1⟩φ(a) = a, φ(b) = abaad
7157⟨a, b | ababbba=1⟩φ(a) = abaad, φ(b) = a
8304⟨a, b | aabaabba=1⟩φ(a) = aad, φ(b) = abaa
8311⟨a, b | aabbaaab=1⟩φ(a) = aad, φ(b) = abaa
9681⟨a, b | aabbabaab=1⟩φ(a) = acbabaad, φ(b) = ababaad
9708⟨a, b | abaabbaba=1⟩φ(a) = acbabaad, φ(b) = ababaad
9717⟨a, b | ababbabba=1⟩φ(a) = ababaad, φ(b) = acbabaad
101352⟨a, b | aaababaaba=1⟩φ(a) = a, φ(b) = abaadaad
101480⟨a, b | abaaaababa=1⟩φ(a) = a, φ(b) = abaadaad
101491⟨a, b | abaabaaaab=1⟩φ(a) = a, φ(b) = abaadaad
112908⟨a, b | aaabaaababa=1⟩φ(a) = aad, φ(b) = abaaa
112927⟨a, b | aaababaaaab=1⟩φ(a) = aad, φ(b) = abaaa
113020⟨a, b | aabaaababaa=1⟩φ(a) = aad, φ(b) = abaaa
113036⟨a, b | aabaabababa=1⟩φ(a) = abaad, φ(b) = aacbabaad
113053⟨a, b | aababaaaaba=1⟩φ(a) = aad, φ(b) = abaaa
113063⟨a, b | aabababaaab=1⟩φ(a) = abaad, φ(b) = aacbabaad
113177⟨a, b | abaaaabaaab=1⟩φ(a) = aad, φ(b) = abaaa
113187⟨a, b | abaaabaabab=1⟩φ(a) = abaad, φ(b) = aacbabaad
113217⟨a, b | abaabbabaab=1⟩φ(a) = acbabaadcbabaad, φ(b) = abababaad
113230⟨a, b | ababaaabaab=1⟩φ(a) = abaad, φ(b) = aacbabaad
113237⟨a, b | ababaabbaba=1⟩φ(a) = acbabaadcbabaad, φ(b) = abababaad
113256⟨a, b | ababbababba=1⟩φ(a) = abababaad, φ(b) = acbabaadcbabaad