#4285 ⟨a, b | ababaaaab=ba⟩

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  2. Rewriting system

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. a(dc)2 ⇒ d [5]
2. cadc2dc ⇒ ad [10]
3. dad(c2d)2c ⇒ adcd2 [14]
4. c2adc3(dc2)2 ⇒ acd [20]
5. a2d ⇒ cadc [9]
6. adcdad ⇒ dadc2dc [11]
7. adcdacd ⇒ dcadc3(dc2)2 [22]
8. acad2 ⇒ c2ad(c3d)2c2dc [29]
9. acadc2 ⇒ ca [17]
10. acadcd ⇒ c2adc(c2d)2c [18]
11. (adc)2d2 ⇒ da(dc2)2(cdc)2 [16]
12. (ad)2c2dc ⇒ cadc2dad [13]
13. acdadc2dc ⇒ c2adc(c2d)2cad [21]
14. adcd2adc2dc ⇒ dad(c2d)2ad [15]
15. ac2adc2d2 ⇒ c2ad(c3d)3c2dc [32]
16. (adc)2c2(dc2)2 ⇒ cadc2dacd [23]
17. acdadc3(dc2)2 ⇒ c2adc(c2d)2acd [27]
18. acdcadc3(dc2)2 ⇒ c2adc(c2d)2cacd [28]
19. adcd2cadc3(dc2)2 ⇒ dad(c2d)2acd [24]
20. ac(ad)2 ⇒ c2ad(c3d)2c [19]
21. a(cad)2 ⇒ c2adc3dc [12]
22. ac2adc2dad ⇒ c2ad(c3d)3c [30]
23. acadacd ⇒ c2adc4(dc2)2 [25]
24. acadcacd ⇒ c2ac(dc2)2 [26]
25. ac2adc2dacd ⇒ c2adc3dc4(dc2)2 [31]
26. a(c2ad)2cd2 ⇒ c2ad(c3d)4c2dc [33]
27. a3b ⇒ c [2]
28. bc ⇒ dca2b [7]
29. bd ⇒ (dc)3 [8]
30. ba ⇒ dc [4]
# ab:ababaaaab=ba reversed:cd/a/b aaab=c,ababa=d morph:4/0,5/0
adcdc=d
cadccdc=ad
dadccdccdc=adcdd
ccadcccdccdcc=acd
aad=cadc
adcdad=dadccdc
adcdacd=dcadcccdccdcc
acadd=ccadcccdcccdccdc
acadcc=ca
acadcd=ccadcccdccdc
adcadcdd=dadccdcccdccdc
adadccdc=cadccdad
acdadccdc=ccadcccdccdcad
adcddadccdc=dadccdccdad
accadccdd=ccadcccdcccdcccdccdc
adcadcccdccdcc=cadccdacd
acdadcccdccdcc=ccadcccdccdacd
acdcadcccdccdcc=ccadcccdccdcacd
adcddcadcccdccdcc=dadccdccdacd
acadad=ccadcccdcccdc
acadcad=ccadcccdc
accadccdad=ccadcccdcccdcccdc
acadacd=ccadccccdccdcc
acadcacd=ccacdccdcc
accadccdacd=ccadcccdccccdccdcc
accadccadcdd=ccadcccdcccdcccdcccdccdc
aaab=c
bc=dcaab
bd=dcdcdc
ba=dc