Certificate for #5322 ⟨a, b | aaa=ab, abb=bb⟩

Back:⟨a, b | aaa=ab, abb=bb⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

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

[2] bb=aaaaa

Axiom: abb=bb.

Reduce LHS:

[1](ab)b
[1]⇒ aa(ab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaaa=aaaaa

Overlap of [1] ab=aaa with [2] bb=aaaaa:

a b bb

Critical pair: aaaaaa=aaab.

Reduce RHS:

[1]aa(ab)
⇒ aaaaa

Defines rule #1.

Referenced by [4].

[4] baaaaa=aaaaa

Overlap of [2] bb=aaaaa with [2] bb=aaaaa:

b b bb

Critical pair: baaaaa=aaaaab.

Reduce RHS:

[1]aaaa(ab)
[3]⇒ (aaaaaa)a
[3]⇒ (aaaaaa)
⇒ aaaaa

Defines rule #2.