Certificate for #12183 ⟨a, b | aaaa=ab, baab=b⟩

Back:⟨a, b | aaaa=ab, baab=b⟩

Completion settings:

[1] ab=aaaa

Axiom: aaaa=ab.

Flip LHS and RHS.

Defines rule #3.

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

[2] baaaaa=b

Axiom: baab=b.

Reduce LHS:

[1]ba(ab)
⇒ baaaaa

Defines rule #2.

Referenced by [3], [4].

[3] aaaaaaaaa=aaaa

Overlap of [1] ab=aaaa with [2] baaaaa=b:

a b baaaaa

Critical pair: ab=aaaaaaaaa.

Reduce LHS:

[1](ab)
⇒ aaaa

Flip LHS and RHS.

Defines rule #1.

[4] bb=baaa

Overlap of [2] baaaaa=b with [1] ab=aaaa:

baaaa a ab

Critical pair: baaaaaaaa=bb.

Reduce LHS:

[2](baaaaa)aaa
⇒ baaa

Flip LHS and RHS.

Defines rule #4.