#6270 ⟨a, b | aaa=a, babab=a⟩

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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. a3 ⇒ a [1]
2. aba2 ⇒ ab [8]
3. a2b ⇒ ba2 [5]
4. ca2 ⇒ c [10]
5. a2c ⇒ c [4]
6. b2a ⇒ aca [13]
7. ab2 ⇒ c [3]
8. cb ⇒ abac [12]
9. b(ab)2 ⇒ a [2]
10. b2c ⇒ ac2 [14]
11. babc ⇒ ab [6]
12. c(ab)2 ⇒ aba [7]
13. cabc ⇒ (ab)2 [15]
# ab:aaa=a,babab=a a/bc abb=c morph:3/1
aaa=a
abaa=ab
aab=baa
caa=c
aac=c
bba=aca
abb=c
cb=abac
babab=a
bbc=acc
babc=ab
cabab=aba
cabc=abab