#2987 ⟨a, b, c | aab=c, bca=c⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

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. a2c ⇒ c2a [3]
2. a2b ⇒ c [1]
3. bc2 ⇒ cab [4]
4. bca ⇒ c [2]
# abc:aab=c,bca=c cab - -
aac=cca
aab=c
bcc=cab
bca=c

Other submonoids of same group

8 unique, 25 total

Σ#PresentationPropertiesφ
82228⟨a, b, c | aabc=1, cbac=1⟩Grp Inf11
82983⟨a, b, c | aab=c, bba=c⟩Can Inf
83448⟨a, b, c | ba=ac, abb=c⟩Can Inf3
83537⟨a, b, c | bb=ac, caa=b⟩Can Inf
83593⟨a, b, c | ba=ac, ca=bb⟩Can Inf
85581⟨a, b, c | ab=c, bbca=c⟩Can Inf1
85717⟨a, b, c | aa=b, acc=cb⟩Can Inf1
86064⟨a, b, c | ab=c, baa=cc⟩Can Inf1