#2179 ⟨a, b, c | aabb=1, bacc=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. bd ⇒ db [10]
2. db2 ⇒ 1 [4]
3. ad ⇒ da [5]
4. ab2 ⇒ b2a [13]
5. a2 ⇒ d [3]
6. ac ⇒ dbcba [18]
7. abc ⇒ cab [16]
8. c2 ⇒ ab [14]
# abc:aabb=1,bacc=1 reversed:bd/ac aa=d morph:2/0
bd=db
dbb=1
ad=da
abb=bba
aa=d
ac=dbcba
abc=cab
cc=ab

Other submonoids of same group

2 unique, 6 total

Σ#PresentationPropertiesφ
7930⟨a, b, c | aa=b, bcb=c⟩Can Inf4
83490⟨a, b, c | bb=aa, acb=c⟩Can Inf

Isomorphic instances

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

15 total

Σ#PresentationMapping
82185⟨a, b, c | aabb=1, bcca=1⟩φ(a) = cbacbadb, φ(b) = b, φ(c) = c
82188⟨a, b, c | aabb=1, cbac=1⟩φ(a) = dbcbacba, φ(b) = b, φ(c) = c
82218⟨a, b, c | aabc=1, bccb=1⟩φ(a) = c, φ(b) = cbacbadb, φ(c) = b
82230⟨a, b, c | aabc=1, cbbc=1⟩φ(a) = c, φ(b) = cbacbadb, φ(c) = b
82282⟨a, b, c | abba=1, accb=1⟩φ(a) = dbcbacba, φ(b) = b, φ(c) = c
82286⟨a, b, c | abba=1, cabc=1⟩φ(a) = cbacbadb, φ(b) = b, φ(c) = c
82666⟨a, b, c | aba=c, bccb=1⟩φ(a) = db, φ(b) = cbab, φ(c) = dbcba
82671⟨a, b, c | aba=c, cbbc=1⟩φ(a) = db, φ(b) = cbab, φ(c) = dbcba
83284⟨a, b, c | bb=ac, acca=1⟩φ(a) = cbacbadb, φ(b) = cba, φ(c) = b
83296⟨a, b, c | bb=ac, bbca=1⟩φ(a) = cbacbadb, φ(b) = cba, φ(c) = b
83298⟨a, b, c | bb=ac, bcab=1⟩φ(a) = cbacbadb, φ(b) = cba, φ(c) = b
85086⟨a, b, c | ab=c, bcacc=1⟩φ(a) = cbadb, φ(b) = b, φ(c) = cba
85105⟨a, b, c | ab=c, cbcac=1⟩φ(a) = cbadb, φ(b) = b, φ(c) = cba
86562⟨a, b, c | ab=1, bccacc=1⟩φ(a) = db, φ(b) = b, φ(c) = cba
86607⟨a, b, c | ab=1, cbccac=1⟩φ(a) = db, φ(b) = b, φ(c) = cba