Certificate for #16025 ⟨a, b | aaa=ab, babb=aa⟩

Back:⟨a, b | aaa=ab, babb=aa⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaaaa=aa

Axiom: babb=aa.

Reduce LHS:

[1]b(ab)b
[1]⇒ baa(ab)
⇒ baaaaa

Referenced by [3], [4], [5], [6].

[3] aaaaaaaa=aaa

Overlap of [1] ab=aaa with [2] baaaaa=aa:

a b baaaaa

Critical pair: aaa=aaaaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baaa=aaaaa

Overlap of [2] baaaaa=aa with [3] aaaaaaaa=aaa:

b aaaaa aaaaaaaa

Critical pair: baaa=aaaaa.

Referenced by [5].

[5] aaaaaaa=aa

Overlap of [2] baaaaa=aa with [4] baaa=aaaaa:

baaaaa baaa

Critical pair: aaaaaaa=aa.

Defines rule #1.

Referenced by [6].

[6] baa=aaaa

Overlap of [2] baaaaa=aa with [5] aaaaaaa=aa:

b aaaaa aaaaaaa

Critical pair: baa=aaaa.

Defines rule #2.