#1577 ⟨a, b, c | aaa=bb, cac=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. ac ⇒ ca [3]
2. c2a ⇒ 1 [5]
3. a3b ⇒ ba3 [4]
4. c2b ⇒ a2bc6 [12]
5. b2 ⇒ a3 [1]
# abc:aaa=bb,cac=1 a/c/b - -
ac=ca
cca=1
aaab=baaa
ccb=aabcccccc
bb=aaa

Other submonoids of same group

5 unique, 5 total

Σ#PresentationProperties
82852⟨a, b, c | aaa=b, cbc=b⟩Can Inf
83497⟨a, b, c | bb=aa, ccc=a⟩Can Inf
85266⟨a, b, c | aa=b, cbbc=b⟩Can Inf
85733⟨a, b, c | aa=b, bbb=cc⟩Can Inf
85767⟨a, b, c | aa=b, cbc=bb⟩Can Inf

Isomorphic instances

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

22 total

Σ#PresentationMapping
81859⟨a, b, c | aba=bb, cbc=1⟩φ(a) = cacabcccccc, φ(b) = cc, φ(c) = ca
82075⟨a, b, c | aaab=1, bbcc=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82083⟨a, b, c | aaab=1, bccb=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82098⟨a, b, c | aaab=1, cbbc=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82134⟨a, b, c | aaba=1, bbcc=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82142⟨a, b, c | aaba=1, bccb=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82154⟨a, b, c | aaba=1, cbbc=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82161⟨a, b, c | aaba=1, ccbb=1⟩φ(a) = c, φ(b) = cacaca, φ(c) = bcccccc
82340⟨a, b, c | aaa=b, bccb=1⟩φ(a) = ca, φ(b) = cacaca, φ(c) = bcccccc
82345⟨a, b, c | aaa=b, cbbc=1⟩φ(a) = ca, φ(b) = cacaca, φ(c) = bcccccc
82627⟨a, b, c | aba=b, cbcc=1⟩φ(a) = cacacabcccccc, φ(b) = ccc, φ(c) = ca
83260⟨a, b, c | bb=aa, cacc=1⟩φ(a) = ccc, φ(b) = bcccccc, φ(c) = ca
83746⟨a, b, c | aab=1, bbbcc=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
83754⟨a, b, c | aab=1, bbccb=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
83778⟨a, b, c | aab=1, bccbb=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
83824⟨a, b, c | aab=1, cbbbc=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
83943⟨a, b, c | aba=1, bbbcc=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
83947⟨a, b, c | aba=1, bbccb=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
83972⟨a, b, c | aba=1, cbbbc=1⟩φ(a) = c, φ(b) = caca, φ(c) = bcccccc
84473⟨a, b, c | aba=1, cbbc=b⟩φ(a) = c, φ(b) = caca, φ(c) = cacabcccccc
84740⟨a, b, c | aa=b, bbccb=1⟩φ(a) = ca, φ(b) = caca, φ(c) = bcccccc
84765⟨a, b, c | aa=b, cbbbc=1⟩φ(a) = ca, φ(b) = caca, φ(c) = bcccccc