Certificate for #14725 ⟨a, b | aabb=a, bbbba=a⟩

Back:⟨a, b | aabb=a, bbbba=a⟩

Completion settings:

[1] aabb=a

Axiom: aabb=a.

Referenced by [3], [4], [5], [6].

[2] bbbba=a

Axiom: bbbba=a.

Defines rule #3.

Referenced by [3].

[3] abba=aaa

Overlap of [1] aabb=a with [2] bbbba=a:

aa bb bbbba

Critical pair: aaa=abba.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aaaa=aa

Overlap of [1] aabb=a with [3] abba=aaa:

a abb abba

Critical pair: aaaa=aa.

Referenced by [5].

[5] aaa=a

Overlap of [3] abba=aaa with [1] aabb=a:

abb a aabb

Critical pair: abba=aaaabb.

Reduce LHS:

[3](abba)
⇒ aaa

Reduce RHS:

[4](aaaa)bb
[1]⇒ (aabb)
⇒ a

Defines rule #1.

Referenced by [6].

[6] abb=aa

Overlap of [5] aaa=a with [1] aabb=a:

a aa aabb

Critical pair: aa=abb.

Flip LHS and RHS.

Defines rule #2.