Certificate for #16262 ⟨a, b | aab=ba, bbab=ab⟩

Completion settings:

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

Axiom: aab=ba.

Referenced by [3], [4], [5], [6], [7], [9].

Axiom: bbab=ab.

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

Overlap of [2] bbab=ab with [2] bbab=ab:

Critical pair: bbaab=abbab.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [4], [8], [9].

Overlap of [1] aab=ba with [3] bbba=ba:

Critical pair: aaba=babba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=ba with [4] babba=baa:

Critical pair: aabaa=baabba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aab=ba with [5] aba=baaa:

Critical pair: abaaa=baa.

Reduce LHS:

Referenced by [7].

Overlap of [6] baaaaa=baa with [1] aab=ba:

Critical pair: baaaba=baab.

Reduce LHS:

Reduce RHS:

Referenced by [8], [9].

Overlap of [3] bbba=ba with [7] bbaaaa=bba:

Critical pair: bbba=baaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [7] bbaaaa=bba with [1] aab=ba:

Critical pair: bbaaba=bbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.