#2 ⟨a, b | aa=1, bb=1⟩

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Properties

Complete 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
  1. a2 ⇒ 1
  2. b2 ⇒ 1 
# ab:aa=1,bb=1 ab
aa=1
bb=1

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

110 total

Σ#PresentationMapping
667⟨a, b | aa=1, aabb=1⟩φ(a) = a, φ(b) = b
669⟨a, b | aa=1, abba=1⟩φ(a) = a, φ(b) = b
671⟨a, b | aa=1, baab=1⟩φ(a) = a, φ(b) = b
690⟨a, b | aa=1, abb=a⟩φ(a) = a, φ(b) = b
6105⟨a, b | aa=1, bb=aa⟩φ(a) = a, φ(b) = b
8494⟨a, b | aaa=a, aabb=1⟩φ(a) = a, φ(b) = b
8496⟨a, b | aaa=a, abba=1⟩φ(a) = a, φ(b) = b
8498⟨a, b | aaa=a, baab=1⟩φ(a) = a, φ(b) = b
8530⟨a, b | aab=b, aabb=1⟩φ(a) = a, φ(b) = b
8533⟨a, b | aab=b, abba=1⟩φ(a) = a, φ(b) = b
8536⟨a, b | aab=b, baab=1⟩φ(a) = a, φ(b) = b
8539⟨a, b | aab=b, bbaa=1⟩φ(a) = a, φ(b) = b
81027⟨a, b | aa=1, aaaabb=1⟩φ(a) = a, φ(b) = b
81030⟨a, b | aa=1, aaabba=1⟩φ(a) = a, φ(b) = b
81032⟨a, b | aa=1, aabaab=1⟩φ(a) = a, φ(b) = b
81035⟨a, b | aa=1, aabbaa=1⟩φ(a) = a, φ(b) = b
81040⟨a, b | aa=1, abaaba=1⟩φ(a) = a, φ(b) = b
81050⟨a, b | aa=1, baaaab=1⟩φ(a) = a, φ(b) = b
81102⟨a, b | aa=1, aaabb=a⟩φ(a) = a, φ(b) = b
81108⟨a, b | aa=1, aabba=a⟩φ(a) = a, φ(b) = b
81112⟨a, b | aa=1, abaab=a⟩φ(a) = a, φ(b) = b
81170⟨a, b | aa=1, aaaa=bb⟩φ(a) = a, φ(b) = b
81179⟨a, b | aa=1, aabb=aa⟩φ(a) = a, φ(b) = b
81187⟨a, b | aa=1, abba=aa⟩φ(a) = a, φ(b) = b
81194⟨a, b | aa=1, baab=aa⟩φ(a) = a, φ(b) = b
81243⟨a, b | aa=1, abb=aaa⟩φ(a) = a, φ(b) = b
103746⟨a, b | aaaa=aa, aabb=1⟩φ(a) = a, φ(b) = b
103748⟨a, b | aaaa=aa, abba=1⟩φ(a) = a, φ(b) = b
103750⟨a, b | aaaa=aa, baab=1⟩φ(a) = a, φ(b) = b
103792⟨a, b | aaab=ab, aabb=1⟩φ(a) = a, φ(b) = b
103795⟨a, b | aaab=ab, abba=1⟩φ(a) = a, φ(b) = b
103798⟨a, b | aaab=ab, baab=1⟩φ(a) = a, φ(b) = b
103801⟨a, b | aaab=ab, bbaa=1⟩φ(a) = a, φ(b) = b
103859⟨a, b | aaba=ba, aabb=1⟩φ(a) = a, φ(b) = b
103862⟨a, b | aaba=ba, abba=1⟩φ(a) = a, φ(b) = b
103865⟨a, b | aaba=ba, baab=1⟩φ(a) = a, φ(b) = b
103868⟨a, b | aaba=ba, bbaa=1⟩φ(a) = a, φ(b) = b
103887⟨a, b | aabb=aa, abba=1⟩φ(a) = a, φ(b) = b
103890⟨a, b | aabb=aa, baab=1⟩φ(a) = a, φ(b) = b
103893⟨a, b | aabb=aa, bbaa=1⟩φ(a) = a, φ(b) = b
103954⟨a, b | abba=aa, baab=1⟩φ(a) = a, φ(b) = b
103957⟨a, b | abba=aa, bbaa=1⟩φ(a) = a, φ(b) = b
103973⟨a, b | abba=bb, baab=1⟩φ(a) = a, φ(b) = b
103976⟨a, b | abba=bb, bbaa=1⟩φ(a) = a, φ(b) = b
105589⟨a, b | aabb=1, aaaabb=1⟩φ(a) = a, φ(b) = b
105592⟨a, b | aabb=1, aaabba=1⟩φ(a) = a, φ(b) = b
105595⟨a, b | aabb=1, aabaab=1⟩φ(a) = a, φ(b) = b
105598⟨a, b | aabb=1, aabbaa=1⟩φ(a) = a, φ(b) = b
105603⟨a, b | aabb=1, abaaba=1⟩φ(a) = a, φ(b) = b
105607⟨a, b | aabb=1, abbaaa=1⟩φ(a) = a, φ(b) = b
105611⟨a, b | aabb=1, abbbba=1⟩φ(a) = a, φ(b) = b
105614⟨a, b | aabb=1, baabaa=1⟩φ(a) = a, φ(b) = b
105619⟨a, b | aabb=1, bbaaaa=1⟩φ(a) = a, φ(b) = b
105661⟨a, b | abba=1, aaaabb=1⟩φ(a) = a, φ(b) = b
105664⟨a, b | abba=1, aaabba=1⟩φ(a) = a, φ(b) = b
105666⟨a, b | abba=1, aabaab=1⟩φ(a) = a, φ(b) = b
105669⟨a, b | abba=1, aabbaa=1⟩φ(a) = a, φ(b) = b
105672⟨a, b | abba=1, aabbbb=1⟩φ(a) = a, φ(b) = b
105674⟨a, b | abba=1, abaaba=1⟩φ(a) = a, φ(b) = b
105680⟨a, b | abba=1, abbabb=1⟩φ(a) = a, φ(b) = b
105682⟨a, b | abba=1, abbbba=1⟩φ(a) = a, φ(b) = b
105684⟨a, b | abba=1, baaaab=1⟩φ(a) = a, φ(b) = b
105687⟨a, b | abba=1, baabbb=1⟩φ(a) = a, φ(b) = b
105689⟨a, b | abba=1, babbab=1⟩φ(a) = a, φ(b) = b
105691⟨a, b | abba=1, bbaabb=1⟩φ(a) = a, φ(b) = b
105969⟨a, b | aaa=a, aaaabb=1⟩φ(a) = a, φ(b) = b
105972⟨a, b | aaa=a, aaabba=1⟩φ(a) = a, φ(b) = b
105974⟨a, b | aaa=a, aabaab=1⟩φ(a) = a, φ(b) = b
105977⟨a, b | aaa=a, aabbaa=1⟩φ(a) = a, φ(b) = b
105982⟨a, b | aaa=a, abaaba=1⟩φ(a) = a, φ(b) = b
105992⟨a, b | aaa=a, baaaab=1⟩φ(a) = a, φ(b) = b
106105⟨a, b | aab=b, aaaabb=1⟩φ(a) = a, φ(b) = b
106108⟨a, b | aab=b, aaabba=1⟩φ(a) = a, φ(b) = b
106111⟨a, b | aab=b, aabaab=1⟩φ(a) = a, φ(b) = b
106114⟨a, b | aab=b, aabbaa=1⟩φ(a) = a, φ(b) = b
106120⟨a, b | aab=b, abaaba=1⟩φ(a) = a, φ(b) = b
106126⟨a, b | aab=b, abbaaa=1⟩φ(a) = a, φ(b) = b
106135⟨a, b | aab=b, baaaab=1⟩φ(a) = a, φ(b) = b
106138⟨a, b | aab=b, baabaa=1⟩φ(a) = a, φ(b) = b
106150⟨a, b | aab=b, bbaaaa=1⟩φ(a) = a, φ(b) = b
109387⟨a, b | aa=1, aaaaaabb=1⟩φ(a) = a, φ(b) = b
109390⟨a, b | aa=1, aaaaabba=1⟩φ(a) = a, φ(b) = b
109393⟨a, b | aa=1, aaaabaab=1⟩φ(a) = a, φ(b) = b
109396⟨a, b | aa=1, aaaabbaa=1⟩φ(a) = a, φ(b) = b
109401⟨a, b | aa=1, aaabaaba=1⟩φ(a) = a, φ(b) = b
109407⟨a, b | aa=1, aaabbaaa=1⟩φ(a) = a, φ(b) = b
109415⟨a, b | aa=1, aabaaaab=1⟩φ(a) = a, φ(b) = b
109418⟨a, b | aa=1, aabaabaa=1⟩φ(a) = a, φ(b) = b
109443⟨a, b | aa=1, abaaaaba=1⟩φ(a) = a, φ(b) = b
109484⟨a, b | aa=1, baaaaaab=1⟩φ(a) = a, φ(b) = b
109662⟨a, b | aa=1, aaaaabb=a⟩φ(a) = a, φ(b) = b
109668⟨a, b | aa=1, aaaabba=a⟩φ(a) = a, φ(b) = b
109674⟨a, b | aa=1, aaabaab=a⟩φ(a) = a, φ(b) = b
109680⟨a, b | aa=1, aaabbaa=a⟩φ(a) = a, φ(b) = b
109690⟨a, b | aa=1, aabaaba=a⟩φ(a) = a, φ(b) = b
109716⟨a, b | aa=1, abaaaab=a⟩φ(a) = a, φ(b) = b
109930⟨a, b | aa=1, aaaaaa=bb⟩φ(a) = a, φ(b) = b
109939⟨a, b | aa=1, aaaabb=aa⟩φ(a) = a, φ(b) = b
109951⟨a, b | aa=1, aaabba=aa⟩φ(a) = a, φ(b) = b
109959⟨a, b | aa=1, aabaab=aa⟩φ(a) = a, φ(b) = b
109971⟨a, b | aa=1, aabbaa=aa⟩φ(a) = a, φ(b) = b
109990⟨a, b | aa=1, abaaba=aa⟩φ(a) = a, φ(b) = b
1010028⟨a, b | aa=1, baaaab=aa⟩φ(a) = a, φ(b) = b
1010203⟨a, b | aa=1, aaaaa=abb⟩φ(a) = a, φ(b) = b
1010222⟨a, b | aa=1, aaabb=aaa⟩φ(a) = a, φ(b) = b
1010244⟨a, b | aa=1, aabba=aaa⟩φ(a) = a, φ(b) = b
1010260⟨a, b | aa=1, abaab=aaa⟩φ(a) = a, φ(b) = b
1010475⟨a, b | aa=1, aabb=aaaa⟩φ(a) = a, φ(b) = b
1010486⟨a, b | aa=1, abba=aaaa⟩φ(a) = a, φ(b) = b
1010502⟨a, b | aa=1, baab=aaaa⟩φ(a) = a, φ(b) = b