Certificate for #15733 ⟨a, b | aab=ba, bbbba=a⟩

Completion settings:

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

Axiom: aab=ba.

Referenced by [3], [5], [7], [9], [11], [13].

Axiom: bbbba=a.

Defines rule #3.

Referenced by [3], [4], [6], [8], [10], [12], [14].

Overlap of [1] aab=ba with [2] bbbba=a:

Critical pair: aaa=babbba.

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] bbbba=a with [3] babbba=aaa:

Critical pair: bbbaaa=abbba.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=ba with [4] abbba=bbbaaa:

Critical pair: abbbaaa=babba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] bbbba=a with [5] babba=bbbaaaaa:

Critical pair: bbbbbbaaaaa=abba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aab=ba with [6] abba=bbaaaaa:

Critical pair: abbaaaaa=baba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] bbbba=a with [7] baba=bbaaaaaaaaa:

Critical pair: bbbbbaaaaaaaaa=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9], [11].

Overlap of [1] aab=ba with [8] aba=baaaaaaaaa:

Critical pair: abaaaaaaaaa=baa.

Reduce LHS:

Referenced by [10].

Overlap of [2] bbbba=a with [9] baaaaaaaaaaaaaaaaa=baa:

Critical pair: bbbbaa=aaaaaaaaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [10] aaaaaaaaaaaaaaaaa=aa with [1] aab=ba:

Critical pair: aaaaaaaaaaaaaaaba=aab.

Reduce LHS:

Reduce RHS:

Referenced by [12], [13].

Overlap of [2] bbbba=a with [11] baaaaaaaaaaaaaaaa=ba:

Critical pair: bbbba=aaaaaaaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [11] baaaaaaaaaaaaaaaa=ba with [1] aab=ba:

Critical pair: baaaaaaaaaaaaaaba=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [2] bbbba=a with [13] bab=bbaaaaaaaa:

Critical pair: bbbbbaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.