Certificate for #19684 ⟨a, b | aba=a, baaab=aa⟩

Back:⟨a, b | aba=a, baaab=aa⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #3.

Referenced by [3], [4].

[2] baaab=aa

Axiom: baaab=aa.

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

[3] aaab=aaa

Overlap of [1] aba=a with [2] baaab=aa:

a ba baaab

Critical pair: aaa=aaab.

Flip LHS and RHS.

Referenced by [5], [6].

[4] baaa=aaa

Overlap of [2] baaab=aa with [1] aba=a:

baa ab aba

Critical pair: baaa=aaa.

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

[5] aaa=aa

Overlap of [2] baaab=aa with [4] baaa=aaa:

baaab baaa

Critical pair: aaab=aa.

Reduce LHS:

[3](aaab)
⇒ aaa

Defines rule #1.

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

[6] aab=aa

Overlap of [4] baaa=aaa with [3] aaab=aaa:

b aaa aaab

Critical pair: baaa=aaab.

Reduce LHS:

[4](baaa)
[5]⇒ (aaa)
⇒ aa

Reduce RHS:

[5](aaa)b
⇒ aab

Flip LHS and RHS.

Defines rule #2.

[7] baaa=aa

Simplify [4] baaa=aaa.

Reduce RHS:

[5](aaa)
⇒ aa

Referenced by [8].

[8] baa=aa

Overlap of [7] baaa=aa with [5] aaa=aa:

b aaa aaa

Critical pair: baa=aa.

Defines rule #4.