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 #2.

Referenced by [3], [4].

[2] aaaaab=a

Axiom: aaaaab=a.

Defines rule #3.

Referenced by [4], [5], [7].

[3] baa=aab

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

b b bb

Critical pair: baa=aab.

Referenced by [5].

[4] aaaaaaa=ab

Overlap of [2] aaaaab=a with [1] bb=aa:

aaaaa b bb

Critical pair: aaaaaaa=ab.

Defines rule #4.

Referenced by [6].

[5] aaaabab=ba

Overlap of [3] baa=aab with [2] aaaaab=a:

b aa aaaaab

Critical pair: ba=aabaaab.

Reduce RHS:

[3]aa(baa)ab
⇒ aaaabab

Flip LHS and RHS.

Referenced by [7].

[6] aba=aab

Overlap of [4] aaaaaaa=ab with [4] aaaaaaa=ab:

a aaaaaa aaaaaaa

Critical pair: aab=aba.

Flip LHS and RHS.

Referenced by [7].

[7] ba=ab

Simplify [5] aaaabab=ba.

Reduce LHS:

[6]aaa(aba)b
[2]⇒ (aaaaab)b
⇒ ab

Flip LHS and RHS.

Defines rule #1.