Certificate for #14789 ⟨a, b | abab=a, bbbba=a⟩

Back:⟨a, b | abab=a, bbbba=a⟩

Completion settings:

[1] abab=a

Axiom: abab=a.

Referenced by [3], [4].

[2] bbbba=a

Axiom: bbbba=a.

Defines rule #4.

Referenced by [5].

[3] aba=aab

Overlap of [1] abab=a with [1] abab=a:

ab ab abab

Critical pair: aba=aab.

Defines rule #2.

Referenced by [4].

[4] aabb=a

Overlap of [1] abab=a with [3] aba=aab:

abab aba

Critical pair: aabb=a.

Referenced by [5], [6], [7], [8].

[5] abba=aaa

Overlap of [4] aabb=a with [2] bbbba=a:

aa bb bbbba

Critical pair: aaa=abba.

Flip LHS and RHS.

Referenced by [6], [7].

[6] aaaa=aa

Overlap of [4] aabb=a with [5] abba=aaa:

a abb abba

Critical pair: aaaa=aa.

Referenced by [7].

[7] aaa=a

Overlap of [5] abba=aaa with [4] aabb=a:

abb a aabb

Critical pair: abba=aaaabb.

Reduce LHS:

[5](abba)
⇒ aaa

Reduce RHS:

[6](aaaa)bb
[4]⇒ (aabb)
⇒ a

Defines rule #1.

Referenced by [8].

[8] abb=aa

Overlap of [7] aaa=a with [4] aabb=a:

a aa aabb

Critical pair: aa=abb.

Flip LHS and RHS.

Defines rule #3.