Certificate for #21090 ⟨a, b | bb=aa, aaab=aaa⟩

Back:⟨a, b | bb=aa, aaab=aaa⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3], [4].

[2] aaab=aaa

Axiom: aaab=aaa.

Defines rule #3.

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 #2.

Referenced by [5].

[4] aaaaa=aaa

Overlap of [2] aaab=aaa with [1] bb=aa:

aaa b bb

Critical pair: aaaaa=aaab.

Reduce RHS:

[2](aaab)
⇒ aaa

Defines rule #5.

Referenced by [5].

[5] aaba=aaa

Overlap of [3] baa=aab with [4] aaaaa=aaa:

b aa aaaaa

Critical pair: baaa=aabaaa.

Reduce LHS:

[3](baa)a
⇒ aaba

Reduce RHS:

[3]aa(baa)a
[2]⇒ a(aaab)a
[4]⇒ (aaaaa)
⇒ aaa

Defines rule #4.