#2084 ⟨a, b, c | aaab=1, bccc=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. ab ⇒ ba [11]
2. cb ⇒ bc [9]
3. c3 ⇒ a3 [3]
4. ba3 ⇒ 1 [12]
5. ca3 ⇒ a3c [5]
# abc:aaab=1,bccc=1 bac - -
ab=ba
cb=bc
ccc=aaa
baaa=1
caaa=aaac

Other submonoids of same group

4 unique, 5 total

Σ#PresentationPropertiesφ
82854⟨a, b, c | aaa=b, ccc=b⟩Can Inf1
82991⟨a, b, c | aab=c, bcc=a⟩Can Inf
83602⟨a, b, c | bb=ac, cb=aa⟩Can Inf
86089⟨a, b, c | ab=c, bcc=aa⟩Can Inf

Isomorphic instances

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

26 total

Σ#PresentationMapping
82101⟨a, b, c | aaab=1, cbcc=1⟩φ(a) = a, φ(b) = baabaabaa, φ(c) = c
82107⟨a, b, c | aaab=1, ccbc=1⟩φ(a) = a, φ(b) = baabaabaa, φ(c) = c
82157⟨a, b, c | aaba=1, cbcc=1⟩φ(a) = a, φ(b) = baabaabaa, φ(c) = c
82162⟨a, b, c | aaba=1, ccbc=1⟩φ(a) = a, φ(b) = baabaabaa, φ(c) = c
82346⟨a, b, c | aaa=b, cbcc=1⟩φ(a) = baa, φ(b) = baabaabaa, φ(c) = c
82512⟨a, b, c | aab=c, bacb=1⟩φ(a) = baa, φ(b) = acbaa, φ(c) = baacbaa
82516⟨a, b, c | aab=c, bbac=1⟩φ(a) = baa, φ(b) = acbaa, φ(c) = baacbaa
82544⟨a, b, c | aab=c, cbba=1⟩φ(a) = baa, φ(b) = acbaa, φ(c) = baacbaa
84282⟨a, b, c | aab=1, bccc=a⟩φ(a) = a, φ(b) = baabaa, φ(c) = c
84358⟨a, b, c | aab=1, ccca=b⟩φ(a) = baa, φ(b) = aa, φ(c) = c
84422⟨a, b, c | aba=1, accc=b⟩φ(a) = baa, φ(b) = aa, φ(c) = c
84460⟨a, b, c | aba=1, bccc=a⟩φ(a) = a, φ(b) = baabaa, φ(c) = c
84569⟨a, b, c | abc=1, bbaa=c⟩φ(a) = c, φ(b) = baa, φ(c) = abcc
84713⟨a, b, c | aa=b, acccb=1⟩φ(a) = baa, φ(b) = baabaa, φ(c) = c
84759⟨a, b, c | aa=b, cabcc=1⟩φ(a) = baa, φ(b) = baabaa, φ(c) = c
84764⟨a, b, c | aa=b, cbacc=1⟩φ(a) = baa, φ(b) = baabaa, φ(c) = c
85041⟨a, b, c | ab=c, acbba=1⟩φ(a) = c, φ(b) = baa, φ(c) = cbaa
85070⟨a, b, c | ab=c, bbaac=1⟩φ(a) = c, φ(b) = baa, φ(c) = cbaa
86333⟨a, b, c | ab=1, aaccca=1⟩φ(a) = baa, φ(b) = a, φ(c) = c
86447⟨a, b, c | ab=1, acccaa=1⟩φ(a) = baa, φ(b) = a, φ(c) = c
86523⟨a, b, c | ab=1, bbbccc=1⟩φ(a) = a, φ(b) = baa, φ(c) = c
86572⟨a, b, c | ab=1, caaacc=1⟩φ(a) = baa, φ(b) = a, φ(c) = c
86602⟨a, b, c | ab=1, cbbbcc=1⟩φ(a) = a, φ(b) = baa, φ(c) = c
86953⟨a, b, c | ab=1, accca=b⟩φ(a) = baa, φ(b) = a, φ(c) = c
87040⟨a, b, c | ab=1, bbccc=a⟩φ(a) = a, φ(b) = baa, φ(c) = c
87565⟨a, b, c | ab=1, bccc=aa⟩φ(a) = a, φ(b) = baa, φ(c) = c