Certificate for #2277 ⟨a, b | bb=aa, aba=aa⟩

Back:⟨a, b | bb=aa, aba=aa⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3], [5].

[2] aba=aa

Axiom: aba=aa.

Defines rule #2.

Referenced by [4], [5].

[3] baa=aab

Overlap of [1] bb=aa with [1] bb=aa:

b b bb

Critical pair: baa=aab.

Defines rule #3.

Referenced by [4], [5].

[4] aaab=aaa

Overlap of [2] aba=aa with [3] baa=aab:

a ba baa

Critical pair: aaab=aaa.

Defines rule #4.

[5] aaaaa=aaa

Overlap of [3] baa=aab with [2] aba=aa:

ba a aba

Critical pair: baaa=aabba.

Reduce LHS:

[3](baa)a
[2]⇒ a(aba)
⇒ aaa

Reduce RHS:

[1]aa(bb)a
⇒ aaaaa

Flip LHS and RHS.

Defines rule #5.