Certificate for #16026 ⟨a, b | aaa=ab, babb=ab⟩

Back:⟨a, b | aaa=ab, babb=ab⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] baaaaa=aaa

Axiom: babb=ab.

Reduce LHS:

[1]b(ab)b
[1]⇒ baa(ab)
⇒ baaaaa

Reduce RHS:

[1](ab)
⇒ aaa

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

[3] aaaaaaaa=aaaa

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

a b baaaaa

Critical pair: aaaa=aaaaaaaa.

Flip LHS and RHS.

Referenced by [4].

[4] baaaa=aaaaaa

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

b aaaaa aaaaaaaa

Critical pair: baaaa=aaaaaa.

Referenced by [5].

[5] aaaaaaa=aaa

Overlap of [2] baaaaa=aaa with [4] baaaa=aaaaaa:

baaaaa baaaa

Critical pair: aaaaaaa=aaa.

Defines rule #1.

Referenced by [6].

[6] baaa=aaaaa

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

b aaaaa aaaaaaa

Critical pair: baaa=aaaaa.

Defines rule #2.