Certificate for #5277 ⟨a, b | aba=bb, aaab=b⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aba=bb.

Defines rule #5.

Referenced by [3], [4], [5], [6], [9].

Axiom: aaab=b.

Defines rule #8.

Referenced by [4], [5].

Overlap of [1] aba=bb with [1] aba=bb:

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [1] aba=bb with [2] aaab=b:

Critical pair: abb=bbaab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] aaab=b with [1] aba=bb:

Critical pair: aabb=ba.

Defines rule #4.

Referenced by [6], [7], [8].

Overlap of [1] aba=bb with [5] aabb=ba:

Critical pair: abba=bbabb.

Defines rule #6.

Referenced by [7], [8].

Overlap of [5] aabb=ba with [6] abba=bbabb:

Critical pair: abbabb=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [6] abba=bbabb with [4] bbaab=abb:

Critical pair: aabb=bbabbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [1] aba=bb with [8] babbbbbb=ba:

Critical pair: aba=bbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.