Certificate for #5065 ⟨a, b | aaa=ab, babb=b⟩

Back:⟨a, b | aaa=ab, babb=b⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

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

[2] baaaaa=b

Axiom: babb=b.

Reduce LHS:

[1]b(ab)b
[1]⇒ baa(ab)
⇒ baaaaa

Defines rule #2.

Referenced by [3], [4].

[3] aaaaaaaa=aaa

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

a b baaaaa

Critical pair: ab=aaaaaaaa.

Reduce LHS:

[1](ab)
⇒ aaa

Flip LHS and RHS.

Defines rule #1.

[4] bb=baa

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

baaaa a ab

Critical pair: baaaaaaa=bb.

Reduce LHS:

[2](baaaaa)aa
⇒ baa

Flip LHS and RHS.

Defines rule #4.