Certificate for #15532 ⟨a, b | aaa=bb, abbbb=b⟩

Back:⟨a, b | aaa=bb, abbbb=b⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Referenced by [2], [3].

[2] b=aaaaaaa

Axiom: abbbb=b.

Reduce LHS:

[1]a(bb)bb
[1]⇒ aaaa(bb)
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] aaaaaaaaaaaaaa=aaa

Overlap of [1] bb=aaa with [2] b=aaaaaaa:

bb b

Critical pair: aaaaaaab=aaa.

Reduce LHS:

[2]aaaaaaa(b)
⇒ aaaaaaaaaaaaaa

Defines rule #1.