#3749 ⟨a, b, c | aab=1, bbcac=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. ba ⇒ ab [7]
2. a2b ⇒ 1 [1]
3. b2c ⇒ acab3 [11]
4. a3c ⇒ bca5 [5]
5. cac ⇒ a4 [4]
# abc:aab=1,bbcac=1 ab/c - -
ba=ab
aab=1
bbc=acabbb
aaac=bcaaaaa
cac=aaaa

Other submonoids of same group

5 unique, 6 total

Σ#PresentationPropertiesφ
85260⟨a, b, c | aa=b, cabc=b⟩Can Inf
85265⟨a, b, c | aa=b, cbbc=a⟩Can Inf
85685⟨a, b, c | aa=b, abb=cc⟩Can Inf1
85761⟨a, b, c | aa=b, cac=bb⟩Can Inf
85765⟨a, b, c | aa=b, cbc=ab⟩Can Inf

Isomorphic instances

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

16 total

Σ#PresentationMapping
83763⟨a, b, c | aab=1, bcacb=1⟩φ(a) = a, φ(b) = abab, φ(c) = abac
83825⟨a, b, c | aab=1, cbbca=1⟩φ(a) = a, φ(b) = abab, φ(c) = abac
83911⟨a, b, c | aba=1, acbbc=1⟩φ(a) = a, φ(b) = abab, φ(c) = abac
83944⟨a, b, c | aba=1, bbcac=1⟩φ(a) = a, φ(b) = abab, φ(c) = abac
83951⟨a, b, c | aba=1, bcacb=1⟩φ(a) = a, φ(b) = abab, φ(c) = abac
84255⟨a, b, c | aab=1, bbcc=a⟩φ(a) = a, φ(b) = abab, φ(c) = ac
84279⟨a, b, c | aab=1, bccb=a⟩φ(a) = a, φ(b) = abab, φ(c) = ac
84331⟨a, b, c | aab=1, cbca=b⟩φ(a) = ab, φ(b) = aa, φ(c) = ababac
84413⟨a, b, c | aba=1, acbc=b⟩φ(a) = ab, φ(b) = aa, φ(c) = ababac
84448⟨a, b, c | aba=1, bbcc=a⟩φ(a) = a, φ(b) = abab, φ(c) = ac
84457⟨a, b, c | aba=1, bccb=a⟩φ(a) = a, φ(b) = abab, φ(c) = ac
84692⟨a, b, c | aa=b, abccb=1⟩φ(a) = ab, φ(b) = abab, φ(c) = ac
84710⟨a, b, c | aa=b, accbb=1⟩φ(a) = ab, φ(b) = abab, φ(c) = ac
84727⟨a, b, c | aa=b, baccb=1⟩φ(a) = ab, φ(b) = abab, φ(c) = ac
84758⟨a, b, c | aa=b, cabbc=1⟩φ(a) = ab, φ(b) = abab, φ(c) = ac
84763⟨a, b, c | aa=b, cbabc=1⟩φ(a) = ab, φ(b) = abab, φ(c) = ac