Certificate for #20052 ⟨a, b | aab=b, aaaa=baa⟩

Back:⟨a, b | aab=b, aaaa=baa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3], [4], [5].

[2] baa=aaaa

Axiom: aaaa=baa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4], [5].

[3] aaaaaa=aaaa

Overlap of [1] aab=b with [2] baa=aaaa:

aa b baa

Critical pair: aaaaaa=baa.

Reduce RHS:

[2](baa)
⇒ aaaa

Defines rule #1.

[4] bb=b

Overlap of [2] baa=aaaa with [1] aab=b:

b aa aab

Critical pair: bb=aaaab.

Reduce RHS:

[1]aa(aab)
[1]⇒ (aab)
⇒ b

Defines rule #4.

[5] bab=ab

Overlap of [2] baa=aaaa with [1] aab=b:

ba a aab

Critical pair: bab=aaaaab.

Reduce RHS:

[1]aaa(aab)
[1]⇒ a(aab)
⇒ ab

Defines rule #5.