Certificate for #5341 ⟨a, b | aaa=bb, aab=bb⟩

Back:⟨a, b | aaa=bb, aab=bb⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

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

[2] aab=aaa

Axiom: aab=bb.

Reduce RHS:

[1](bb)
⇒ aaa

Defines rule #3.

Referenced by [3], [4].

[3] baaa=aaaa

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

b b bb

Critical pair: baaa=aaab.

Reduce RHS:

[2]a(aab)
⇒ aaaa

Defines rule #2.

[4] aaaaa=aaaa

Overlap of [2] aab=aaa with [1] bb=aaa:

aa b bb

Critical pair: aaaaa=aaab.

Reduce RHS:

[2]a(aab)
⇒ aaaa

Defines rule #1.