Certificate for #20087 ⟨a, b | aab=b, abaa=bbb⟩

Back:⟨a, b | aab=b, abaa=bbb⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #4.

Referenced by [3], [4], [5], [6], [8].

[2] abaa=bbb

Axiom: abaa=bbb.

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

[3] baa=abbb

Overlap of [1] aab=b with [2] abaa=bbb:

a ab abaa

Critical pair: abbb=baa.

Flip LHS and RHS.

Referenced by [7].

[4] abb=bbbb

Overlap of [2] abaa=bbb with [1] aab=b:

ab aa aab

Critical pair: abb=bbbb.

Defines rule #2.

Referenced by [6], [7].

[5] abab=bbbab

Overlap of [2] abaa=bbb with [1] aab=b:

aba a aab

Critical pair: abab=bbbab.

Defines rule #5.

[6] bbbbbb=bb

Overlap of [1] aab=b with [4] abb=bbbb:

a ab abb

Critical pair: abbbb=bb.

Reduce LHS:

[4](abb)bb
⇒ bbbbbb

Defines rule #1.

[7] baa=bbbbb

Simplify [3] baa=abbb.

Reduce RHS:

[4](abb)b
⇒ bbbbb

Defines rule #6.

Referenced by [8].

[8] bbbbbab=bab

Overlap of [7] baa=bbbbb with [1] aab=b:

ba a aab

Critical pair: bab=bbbbbab.

Flip LHS and RHS.

Defines rule #3.