Certificate for #20885 ⟨a, b | bb=aa, aaaaa=ab⟩

Back:⟨a, b | bb=aa, aaaaa=ab⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [4].

[2] ab=bbbba

Axiom: aaaaa=ab.

Reduce LHS:

[1](aa)aaa
[1]⇒ bb(aa)a
⇒ bbbba

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] bbbbbbbba=bba

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

a a aa

Critical pair: abb=bba.

Reduce LHS:

[2](ab)b
[2]⇒ bbbb(ab)
⇒ bbbbbbbba

Referenced by [4], [5].

[4] bbbbbb=bbb

Overlap of [1] aa=bb with [2] ab=bbbba:

a a ab

Critical pair: abbbba=bbb.

Reduce LHS:

[2](ab)bbba
[2]⇒ bbbb(ab)bba
[3]⇒ (bbbbbbbba)bba
[2]⇒ bb(ab)ba
[2]⇒ bbbbbb(ab)a
[3]⇒ bb(bbbbbbbba)a
[1]⇒ bbbb(aa)
⇒ bbbbbb

Defines rule #1.

Referenced by [5].

[5] bbbbba=bba

Simplify [3] bbbbbbbba=bba.

Reduce LHS:

[4](bbbbbb)bba
⇒ bbbbba

Defines rule #2.