Certificate for #12190 ⟨a, b | aaaa=ab, bbab=a⟩

Back:⟨a, b | aaaa=ab, bbab=a⟩

Completion settings:

[1] ab=aaaa

Axiom: aaaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bbaaaa=a

Axiom: bbab=a.

Reduce LHS:

[1]bb(ab)
⇒ bbaaaa

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

[3] aaaaaaaaaaa=aa

Overlap of [1] ab=aaaa with [2] bbaaaa=a:

a b bbaaaa

Critical pair: aa=aaaabaaaa.

Reduce RHS:

[1]aaa(ab)aaaa
⇒ aaaaaaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] bbaa=aaaaaaaa

Overlap of [2] bbaaaa=a with [3] aaaaaaaaaaa=aa:

bb aaaa aaaaaaaaaaa

Critical pair: bbaa=aaaaaaaa.

Referenced by [5].

[5] aaaaaaaaaa=a

Overlap of [2] bbaaaa=a with [4] bbaa=aaaaaaaa:

bbaaaa bbaa

Critical pair: aaaaaaaaaa=a.

Defines rule #1.

Referenced by [6].

[6] bba=aaaaaaa

Overlap of [2] bbaaaa=a with [5] aaaaaaaaaa=a:

bb aaaa aaaaaaaaaa

Critical pair: bba=aaaaaaa.

Defines rule #3.