Certificate for #12181 ⟨a, b | aaaa=ab, baaa=b⟩

Back:⟨a, b | aaaa=ab, baaa=b⟩

Completion settings:

[1] ab=aaaa

Axiom: aaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[2] baaa=b

Axiom: baaa=b.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaaaa=aaaa

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

a b baaa

Critical pair: ab=aaaaaaa.

Reduce LHS:

[1](ab)
⇒ aaaa

Flip LHS and RHS.

Defines rule #1.

[4] bb=b

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

baa a ab

Critical pair: baaaaaa=bb.

Reduce LHS:

[2](baaa)aaa
[2]⇒ (baaa)
⇒ b

Flip LHS and RHS.

Defines rule #4.