Certificate for #16272 ⟨a, b | aab=ba, bbbb=bb⟩

Completion settings:

[1] ba=aab

Axiom: aab=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3].

[2] bbbb=bb

Axiom: bbbb=bb.

Defines rule #3.

Referenced by [3].

[3] aaaaaaaaaaaaaaaabb=aaaabb

Overlap of [2] bbbb=bb with [1] ba=aab:

bbb b ba

Critical pair: bbbaab=bba.

Reduce LHS:

[1]bb(ba)ab
[1]⇒ b(ba)abab
[1]⇒ (ba)ababab
[1]⇒ aa(ba)babab
[1]⇒ aaaab(ba)bab
[1]⇒ aaaa(ba)abbab
[1]⇒ aaaaaa(ba)bbab
[1]⇒ aaaaaaaabb(ba)b
[1]⇒ aaaaaaaab(ba)abb
[1]⇒ aaaaaaaa(ba)ababb
[1]⇒ aaaaaaaaaa(ba)babb
[1]⇒ aaaaaaaaaaaab(ba)bb
[1]⇒ aaaaaaaaaaaa(ba)abbb
[1]⇒ aaaaaaaaaaaaaa(ba)bbb
[2]⇒ aaaaaaaaaaaaaaaa(bbbb)
⇒ aaaaaaaaaaaaaaaabb

Reduce RHS:

[1]b(ba)
[1]⇒ (ba)ab
[1]⇒ aa(ba)b
⇒ aaaabb

Defines rule #2.