Certificate for #20686 ⟨a, b | bb=aa, aaaaab=a⟩

Back:⟨a, b | bb=aa, aaaaab=a⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #4.

Referenced by [3], [5].

[2] aaaaab=a

Axiom: aaaaab=a.

Referenced by [4].

[3] aab=baa

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

b b bb

Critical pair: baa=aab.

Flip LHS and RHS.

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

[4] abaaaa=a

Simplify [2] aaaaab=a.

Reduce LHS:

[3]aaa(aab)
[3]⇒ a(aab)aa
⇒ abaaaa

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

[5] ab=aaaaaaa

Overlap of [4] abaaaa=a with [3] aab=baa:

abaa aa aab

Critical pair: abaabaa=ab.

Reduce LHS:

[3]ab(aab)aa
[1]⇒ a(bb)aaaa
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[6] baaaaaa=aa

Overlap of [3] aab=baa with [4] abaaaa=a:

a ab abaaaa

Critical pair: aa=baaaaaa.

Flip LHS and RHS.

Referenced by [8].

[7] aaaaaaaaaaa=a

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

abaaaa ab

Critical pair: aaaaaaaaaaa=a.

Defines rule #1.

Referenced by [8].

[8] ba=aaaaaaa

Overlap of [6] baaaaaa=aa with [7] aaaaaaaaaaa=a:

b aaaaaa aaaaaaaaaaa

Critical pair: ba=aaaaaaa.

Defines rule #2.