Certificate for #21086 ⟨a, b | bb=aa, aaaa=aba⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3].

[2] aaaa=aba

Axiom: aaaa=aba.

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 [4], [5].

[4] aaba=aaab

Overlap of [2] aaaa=aba with [2] aaaa=aba:

a aaa aaaa

Critical pair: aaba=abaa.

Reduce RHS:

[3]a(baa)
⇒ aaab

Defines rule #4.

Referenced by [5].

[5] baba=abab

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

b aa aaaa

Critical pair: baba=aabaa.

Reduce RHS:

[4](aaba)a
[4]⇒ a(aaba)
[2]⇒ (aaaa)b
⇒ abab

Defines rule #5.