#2228 ⟨a, b, c | aabc=1, cbac=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. cf ⇒ 1 [15]
2. fc ⇒ 1 [6]
3. fd ⇒ cb [7]
4. a2 ⇒ fe [8]
5. ad ⇒ 1 [25]
6. ba ⇒ f2 [11]
7. be ⇒ 1 [24]
8. ef ⇒ ac [19]
9. eb ⇒ 1 [17]
10. ed ⇒ ca [28]
11. df ⇒ ab [38]
12. da ⇒ 1 [27]
13. de ⇒ c2 [23]
14. d2 ⇒ bc [33]
15. c2b ⇒ d [3]
16. fab ⇒ cbf [39]
17. fbc ⇒ cbd [34]
18. ac2 ⇒ e [21]
19. afe ⇒ fea [9]
20. abc ⇒ d [35]
21. bca ⇒ d [30]
22. bfe ⇒ f2a [12]
23. ec2 ⇒ cae [31]
24. ecb ⇒ acd [22]
25. eab ⇒ caf [40]
26. dc2 ⇒ bce [32]
27. dca ⇒ c2d [29]
28. dcb ⇒ abd [37]
29. dbc ⇒ bcd [36]
30. faf2 ⇒ cbfa [41]
31. afac ⇒ feaf [20]
32. bfac ⇒ f2af [42]
33. eaf2 ⇒ cafa [43]
# abc:aabc=1,cbac=1 cfabed ccb=d,caa=e,cba=f morph:3/0,3/0,3/0
cf=1
fc=1
fd=cb
aa=fe
ad=1
ba=ff
be=1
ef=ac
eb=1
ed=ca
df=ab
da=1
de=cc
dd=bc
ccb=d
fab=cbf
fbc=cbd
acc=e
afe=fea
abc=d
bca=d
bfe=ffa
ecc=cae
ecb=acd
eab=caf
dcc=bce
dca=ccd
dcb=abd
dbc=bcd
faff=cbfa
afac=feaf
bfac=ffaf
eaff=cafa

Other submonoids of same group

8 unique, 14 total

Σ#PresentationPropertiesφ
82983⟨a, b, c | aab=c, bba=c⟩Can Inf
82987⟨a, b, c | aab=c, bca=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

Isomorphic instances

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

11 total

Σ#PresentationMapping
82229⟨a, b, c | aabc=1, cbba=1⟩φ(a) = f, φ(b) = d, φ(c) = acc
82233⟨a, b, c | aabc=1, ccba=1⟩φ(a) = a, φ(b) = ddf, φ(c) = c
82289⟨a, b, c | abbc=1, acba=1⟩φ(a) = aacdd, φ(b) = a, φ(c) = fdd
82296⟨a, b, c | abca=1, bacb=1⟩φ(a) = f, φ(b) = d, φ(c) = acc
82775⟨a, b, c | abc=b, acba=1⟩φ(a) = cdf, φ(b) = c, φ(c) = a
82797⟨a, b, c | abc=b, cbaa=1⟩φ(a) = cdf, φ(b) = c, φ(c) = a
84038⟨a, b, c | abc=1, acbba=1⟩φ(a) = d, φ(b) = c, φ(c) = fa
84044⟨a, b, c | abc=1, accba=1⟩φ(a) = acd, φ(b) = af, φ(c) = d
84100⟨a, b, c | abc=1, cbbaa=1⟩φ(a) = d, φ(b) = c, φ(c) = fa
84104⟨a, b, c | abc=1, ccbaa=1⟩φ(a) = acd, φ(b) = af, φ(c) = d
84601⟨a, b, c | abc=1, cbaa=b⟩φ(a) = acd, φ(b) = a, φ(c) = fd