Certificate for #12280 ⟨a, b | aaab=ba, abbb=a⟩

Completion settings:

[1] ba=aaab

Axiom: aaab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[2] abbb=a

Axiom: abbb=a.

Defines rule #3.

Referenced by [3].

[3] aaaaaaaaaaaaaaaaaaaaaaaaaaaa=aa

Overlap of [2] abbb=a with [1] ba=aaab:

abb b ba

Critical pair: abbaaab=aa.

Reduce LHS:

[1]ab(ba)aab
[1]⇒ a(ba)aabaab
[1]⇒ aaaa(ba)abaab
[1]⇒ aaaaaaa(ba)baab
[1]⇒ aaaaaaaaaab(ba)ab
[1]⇒ aaaaaaaaaa(ba)aabab
[1]⇒ aaaaaaaaaaaaa(ba)abab
[1]⇒ aaaaaaaaaaaaaaaa(ba)bab
[1]⇒ aaaaaaaaaaaaaaaaaaab(ba)b
[1]⇒ aaaaaaaaaaaaaaaaaaa(ba)aabb
[1]⇒ aaaaaaaaaaaaaaaaaaaaaa(ba)abb
[1]⇒ aaaaaaaaaaaaaaaaaaaaaaaaa(ba)bb
[2]⇒ aaaaaaaaaaaaaaaaaaaaaaaaaaa(abbb)
⇒ aaaaaaaaaaaaaaaaaaaaaaaaaaaa

Defines rule #1.