Certificate for #2220 ⟨a, b | bb=aa, aaab=a⟩

Back:⟨a, b | bb=aa, aaab=a⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #4.

Referenced by [3], [5].

[2] aaab=a

Axiom: aaab=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] abaa=a

Simplify [2] aaab=a.

Reduce LHS:

[3]a(aab)
⇒ abaa

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

[5] ab=aaaaa

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

ab aa aab

Critical pair: abbaa=ab.

Reduce LHS:

[1]a(bb)aa
⇒ aaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[6] baaaa=aa

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

a ab abaa

Critical pair: aa=baaaa.

Flip LHS and RHS.

Referenced by [8].

[7] aaaaaaa=a

Overlap of [4] abaa=a with [5] ab=aaaaa:

abaa ab

Critical pair: aaaaaaa=a.

Defines rule #1.

Referenced by [8].

[8] ba=aaaaa

Overlap of [6] baaaa=aa with [7] aaaaaaa=a:

b aaaa aaaaaaa

Critical pair: ba=aaaaa.

Defines rule #2.