#4176 ⟨a, b | aabbababa=ab⟩

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  1. Properties
  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. ab2 ⇒ c [2]
2. aca(ba)2 ⇒ ab [3]
3. ac(ab)2c ⇒ cb [4]
4. c2a(ba)2 ⇒ cb [7]
5. abca(ba)2 ⇒ c [5]
6. abc(ab)2c ⇒ cb2 [6]
7. cb3 ⇒ c2(ab)2c [9]
8. c(ba)3 ⇒ acabc [8]
9. cbca(ba)2 ⇒ cb2 [10]
10. acabcb2 ⇒ cb(ab)2c [13]
11. c2(ab)2cb ⇒ cbc(ab)2c [11]
12. cb(ba)3 ⇒ (abc)2 [14]
13. cb2(ab)2c ⇒ (abc)2b2 [15]
14. cb2ca(ba)2 ⇒ c2(ab)2c [12]
15. cb(ab)2cb ⇒ acabc2(ab)2c [18]
16. cbc(ab)2cb ⇒ cb2c(ab)2c [16]
17. cb2c(ab)2cb ⇒ (c2(ab)2)2c [17]
# ab:aabbababa=ab ac/b abb=c morph:3/1
abb=c
acababa=ab
acababc=cb
ccababa=cb
abcababa=c
abcababc=cbb
cbbb=ccababc
cbababa=acabc
cbcababa=cbb
acabcbb=cbababc
ccababcb=cbcababc
cbbababa=abcabc
cbbababc=abcabcbb
cbbcababa=ccababc
cbababcb=acabccababc
cbcababcb=cbbcababc
cbbcababcb=ccababccababc