Certificate for #4165 ⟨a, b | abb=aba, baa=b⟩

Back:⟨a, b | abb=aba, baa=b⟩

Completion settings:

[1] aba=abb

Axiom: abb=aba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[2] baa=b

Axiom: baa=b.

Defines rule #2.

Referenced by [3], [4], [5].

[3] abba=ab

Overlap of [1] aba=abb with [2] baa=b:

a ba baa

Critical pair: ab=abba.

Flip LHS and RHS.

Referenced by [6].

[4] bba=bbb

Overlap of [2] baa=b with [1] aba=abb:

ba a aba

Critical pair: baabb=bba.

Reduce LHS:

[2](baa)bb
⇒ bbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [6].

[5] bbbb=bb

Overlap of [4] bba=bbb with [2] baa=b:

b ba baa

Critical pair: bb=bbba.

Reduce RHS:

[4]b(bba)
⇒ bbbb

Flip LHS and RHS.

Defines rule #4.

[6] abbb=ab

Simplify [3] abba=ab.

Reduce LHS:

[4]a(bba)
⇒ abbb

Defines rule #5.