Certificate for #1595 ⟨a, b | aaa=ab, bab=b⟩

Back:⟨a, b | aaa=ab, bab=b⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

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

[2] baaa=b

Axiom: bab=b.

Reduce LHS:

[1]b(ab)
⇒ baaa

Defines rule #2.

Referenced by [3], [4].

[3] aaaaaa=aaa

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

a b baaa

Critical pair: ab=aaaaaa.

Reduce LHS:

[1](ab)
⇒ aaa

Flip LHS and RHS.

Defines rule #1.

[4] bb=baa

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

baa a ab

Critical pair: baaaaa=bb.

Reduce LHS:

[2](baaa)aa
⇒ baa

Flip LHS and RHS.

Defines rule #4.