Certificate for #5201 ⟨a, b | aab=bb, abab=b⟩

Back:⟨a, b | aab=bb, abab=b⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #1.

Referenced by [3], [5].

[2] abab=b

Axiom: abab=b.

Referenced by [3], [4], [6].

[3] bbab=ab

Overlap of [1] aab=bb with [2] abab=b:

a ab abab

Critical pair: ab=bbab.

Flip LHS and RHS.

Referenced by [5].

[4] bab=abb

Overlap of [2] abab=b with [2] abab=b:

ab ab abab

Critical pair: abb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbb=ab

Overlap of [1] aab=bb with [4] bab=abb:

aa b bab

Critical pair: aaabb=bbab.

Reduce LHS:

[1]a(aab)b
⇒ abbb

Reduce RHS:

[3](bbab)
⇒ ab

Referenced by [6].

[6] bbb=b

Overlap of [2] abab=b with [5] abbb=ab:

ab ab abbb

Critical pair: abab=bbb.

Reduce LHS:

[2](abab)
⇒ b

Flip LHS and RHS.

Defines rule #3.