Certificate for #13091 ⟨a, b | bab=aaa, abba=b⟩

Completion settings:

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

Axiom: bab=aaa.

Defines rule #5.

Referenced by [3], [4], [5], [7], [16].

Axiom: abba=b.

Referenced by [4], [5], [11], [12], [13], [15].

Overlap of [1] bab=aaa with [1] bab=aaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [8], [11].

Overlap of [1] bab=aaa with [2] abba=b:

Critical pair: bb=aaaba.

Referenced by [5], [6].

Overlap of [2] abba=b with [1] bab=aaa:

Critical pair: abaaa=bb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [6], [8], [10].

Simplify [4] bb=aaaba.

Reduce RHS:

Defines rule #4.

Referenced by [7], [9], [15].

Overlap of [1] bab=aaa with [6] bb=abaaa:

Critical pair: baabaaa=aaab.

Referenced by [9].

Overlap of [3] aaaab=baaaa with [5] aaaba=abaaa:

Critical pair: aabaaa=baaaaa.

Referenced by [9], [11], [14].

Simplify [7] baabaaa=aaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [5] aaaba=abaaa with [9] aaab=abaaaaaaaa:

Critical pair: abaaaaaaaaa=abaaa.

Referenced by [11].

Overlap of [10] abaaaaaaaaa=abaaa with [3] aaaab=baaaa:

Critical pair: abaaaaaabaaaa=abaaaab.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [2] abba=b with [11] baaaaaaaaa=baaa:

Critical pair: abbaaa=baaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13], [14].

Overlap of [2] abba=b with [12] baaaaaaaa=baa:

Critical pair: abbaa=baaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [8] aabaaa=baaaaa with [12] baaaaaaaa=baa:

Critical pair: aabaa=baaaaaaaaaa.

Reduce RHS:

Referenced by [15], [17].

Overlap of [2] abba=b with [6] bb=abaaa:

Critical pair: aabaaaa=b.

Reduce LHS:

Defines rule #2.

Referenced by [16], [17].

Overlap of [1] bab=aaa with [15] baaaaaa=b:

Critical pair: bab=aaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [14] aabaa=baaaa with [15] baaaaaa=b:

Critical pair: aab=baaaaaaaa.

Reduce RHS:

Defines rule #3.