Certificate for #3421 ⟨a, b | aaaabbbbaa=a⟩

Back:⟨a, b | aaaabbbbaa=a⟩

Completion settings:

[1] aaaabbbbaa=a

Axiom: aaaabbbbaa=a.

Referenced by [2], [3], [4].

[2] aaabbbbaa=aaaabbbba

Overlap of [1] aaaabbbbaa=a with [1] aaaabbbbaa=a:

aaaabbbb aa aaaabbbbaa

Critical pair: aaaabbbba=aaabbbbaa.

Flip LHS and RHS.

Referenced by [3], [4].

[3] abbbbaa=aabbbba

Overlap of [2] aaabbbbaa=aaaabbbba with [2] aaabbbbaa=aaaabbbba:

aaabbbb aa aaabbbbaa

Critical pair: aaabbbbaaaabbbba=aaaabbbbaabbbbaa.

Reduce LHS:

[2](aaabbbbaa)aabbbba
[1]⇒ (aaaabbbbaa)abbbba
⇒ aabbbba

Reduce RHS:

[1](aaaabbbbaa)bbbbaa
⇒ abbbbaa

Flip LHS and RHS.

Defines rule #1.

[4] aaaaabbbba=a

Overlap of [1] aaaabbbbaa=a with [2] aaabbbbaa=aaaabbbba:

a aaabbbbaa aaabbbbaa

Critical pair: aaaaabbbba=a.

Defines rule #2.