Certificate for #12206 ⟨a, b | aaaa=bb, abbb=a⟩

Back:⟨a, b | aaaa=bb, abbb=a⟩

Completion settings:

[1] bb=aaaa

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5].

[2] aaaaab=a

Axiom: abbb=a.

Reduce LHS:

[1]a(bb)b
⇒ aaaaab

Referenced by [4].

[3] aaaab=baaaa

Overlap of [1] bb=aaaa with [1] bb=aaaa:

b b bb

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

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

[4] abaaaa=a

Simplify [2] aaaaab=a.

Reduce LHS:

[3]a(aaaab)
⇒ abaaaa

Referenced by [5], [6], [7].

[5] ab=aaaaaaaaa

Overlap of [4] abaaaa=a with [3] aaaab=baaaa:

ab aaaa aaaab

Critical pair: abbaaaa=ab.

Reduce LHS:

[1]a(bb)aaaa
⇒ aaaaaaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[6] baaaaaaaa=aaaa

Overlap of [3] aaaab=baaaa with [4] abaaaa=a:

aaa ab abaaaa

Critical pair: aaaa=baaaaaaaa.

Flip LHS and RHS.

Referenced by [8].

[7] aaaaaaaaaaaaa=a

Overlap of [4] abaaaa=a with [5] ab=aaaaaaaaa:

abaaaa ab

Critical pair: aaaaaaaaaaaaa=a.

Defines rule #1.

Referenced by [8].

[8] ba=aaaaaaaaa

Overlap of [6] baaaaaaaa=aaaa with [7] aaaaaaaaaaaaa=a:

b aaaaaaaa aaaaaaaaaaaaa

Critical pair: ba=aaaaaaaaa.

Defines rule #2.