Certificate for #656 ⟨a, b | bb=aa, aba=a⟩

Back:⟨a, b | bb=aa, aba=a⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3], [5].

[2] aba=a

Axiom: aba=a.

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=aa

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

a ba baa

Critical pair: aaab=aa.

Defines rule #4.

[5] aaaaa=aab

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

ba a aba

Critical pair: baa=aabba.

Reduce LHS:

[3](baa)
⇒ aab

Reduce RHS:

[1]aa(bb)a
⇒ aaaaa

Flip LHS and RHS.

Defines rule #5.