Certificate for #13011 ⟨a, b | abb=aab, bbaa=a⟩

Back:⟨a, b | abb=aab, bbaa=a⟩

Completion settings:

[1] abb=aab

Axiom: abb=aab.

Defines rule #2.

Referenced by [3], [4].

[2] bbaa=a

Axiom: bbaa=a.

Referenced by [3], [4], [6], [7].

[3] aabaa=aa

Overlap of [1] abb=aab with [2] bbaa=a:

a bb bbaa

Critical pair: aa=aabaa.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aba=aaa

Overlap of [1] abb=aab with [2] bbaa=a:

ab b bbaa

Critical pair: aba=aabbaa.

Reduce RHS:

[1]a(abb)aa
[3]⇒ a(aabaa)
⇒ aaa

Defines rule #1.

Referenced by [5].

[5] aaaaa=aa

Simplify [3] aabaa=aa.

Reduce LHS:

[4]a(aba)a
⇒ aaaaa

Referenced by [6].

[6] aaaa=a

Overlap of [2] bbaa=a with [5] aaaaa=aa:

bb aa aaaaa

Critical pair: bbaa=aaaa.

Reduce LHS:

[2](bbaa)
⇒ a

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

[7] bba=aaa

Overlap of [2] bbaa=a with [6] aaaa=a:

bb aa aaaa

Critical pair: bba=aaa.

Defines rule #3.