#14 ⟨a, b | abba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. 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. a2 ⇒ c [2]
2. b2 ⇒ d [3]
3. ca ⇒ ac [5]
4. cb ⇒ bc [13]
5. cd ⇒ 1 [11]
6. da ⇒ ad [8]
7. db ⇒ bd [6]
8. dc ⇒ 1 [9]
# ab:abba=1 abcd aa=c,bb=d magic:0
aa=c
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
420⟨a, b | aba=b⟩Can Inf
423⟨a, b | bb=aa⟩Can Inf

Isomorphic instances

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

14 total

Σ#PresentationMapping
663⟨a, b | aababa=1⟩φ(a) = a, φ(b) = adb
668⟨a, b | abaaab=1⟩φ(a) = a, φ(b) = adb
8286⟨a, b | aaabaaba=1⟩φ(a) = a, φ(b) = adadb
8299⟨a, b | aabaaaab=1⟩φ(a) = a, φ(b) = adadb
8302⟨a, b | aabaabaa=1⟩φ(a) = a, φ(b) = adadb
8322⟨a, b | abaaaaba=1⟩φ(a) = a, φ(b) = adadb
101308⟨a, b | aaaabaaaba=1⟩φ(a) = a, φ(b) = adadadb
101337⟨a, b | aaabaaaaab=1⟩φ(a) = a, φ(b) = adadadb
101340⟨a, b | aaabaaabaa=1⟩φ(a) = a, φ(b) = adadadb
101392⟨a, b | aabaaaaaba=1⟩φ(a) = a, φ(b) = adadadb
101420⟨a, b | aabababaab=1⟩φ(a) = adb, φ(b) = bcaa
101492⟨a, b | abaabaabab=1⟩φ(a) = adb, φ(b) = bcaa
101495⟨a, b | abaabababa=1⟩φ(a) = adb, φ(b) = bcaa
101508⟨a, b | ababaabaab=1⟩φ(a) = adb, φ(b) = bcaa