Certificate for #12294 ⟨a, b | aaab=ba, bbba=a⟩

Completion settings:

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

Axiom: aaab=ba.

Referenced by [3], [5], [7], [8], [10].

Axiom: bbba=a.

Defines rule #3.

Referenced by [3], [4], [6], [9], [11], [13].

Overlap of [1] aaab=ba with [2] bbba=a:

Critical pair: aaaa=babba.

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] bbba=a with [3] babba=aaaa:

Critical pair: bbaaaa=abba.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aaab=ba with [4] abba=bbaaaa:

Critical pair: aabbaaaa=baba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [8].

Overlap of [2] bbba=a with [5] baba=bbaaaaaaaaaa:

Critical pair: bbbbaaaaaaaaaa=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [10], [12].

Overlap of [1] aaab=ba with [6] aba=baaaaaaaaaa:

Critical pair: aabaaaaaaaaaa=baa.

Reduce LHS:

Referenced by [8].

Overlap of [7] baaaaaaaaaaaaaaaaaaaaaaaaaaaa=baa with [1] aaab=ba:

Critical pair: baaaaaaaaaaaaaaaaaaaaaaaaaba=baab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] bbba=a with [8] baab=bbaaaaaaaaaaaaaaaaaa:

Critical pair: bbbbaaaaaaaaaaaaaaaaaa=aab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [12].

Overlap of [1] aaab=ba with [9] aab=baaaaaaaaaaaaaaaaaa:

Critical pair: abaaaaaaaaaaaaaaaaaa=ba.

Reduce LHS:

Referenced by [11], [12].

Overlap of [2] bbba=a with [10] baaaaaaaaaaaaaaaaaaaaaaaaaaa=ba:

Critical pair: bbba=aaaaaaaaaaaaaaaaaaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [10] baaaaaaaaaaaaaaaaaaaaaaaaaaa=ba with [9] aab=baaaaaaaaaaaaaaaaaa:

Critical pair: baaaaaaaaaaaaaaaaaaaaaaaaabaaaaaaaaaaaaaaaaaa=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [2] bbba=a with [12] bab=bbaaaaaaaaa:

Critical pair: bbbbaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.