Certificate for #5068 ⟨a, b | aaa=ab, bbab=a⟩

Back:⟨a, b | aaa=ab, bbab=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bbaaa=a

Axiom: bbab=a.

Reduce LHS:

[1]bb(ab)
⇒ bbaaa

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

[3] aaaaaaaa=aa

Overlap of [1] ab=aaa with [2] bbaaa=a:

a b bbaaa

Critical pair: aa=aaabaaa.

Reduce RHS:

[1]aa(ab)aaa
⇒ aaaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbaa=aaaaaa

Overlap of [2] bbaaa=a with [3] aaaaaaaa=aa:

bb aaa aaaaaaaa

Critical pair: bbaa=aaaaaa.

Referenced by [5].

[5] aaaaaaa=a

Overlap of [2] bbaaa=a with [4] bbaa=aaaaaa:

bbaaa bbaa

Critical pair: aaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] bba=aaaaa

Overlap of [2] bbaaa=a with [5] aaaaaaa=a:

bb aaa aaaaaaa

Critical pair: bba=aaaaa.

Defines rule #3.