Certificate for #2307 ⟨a, b | abaabab=aba⟩

Completion settings:

• Auxiliary generators:
  1. c = abaa
• Reduction order:
  • Right-to-left recursive path with deg(b) = 0; deg(c) = deg(a) = 1, c < a

Axiom: abaabab=aba.

Referenced by [3].

Axiom: abaa=c.

Referenced by [3], [4].

Overlap of [1] abaabab=aba with [2] abaa=c:

Critical pair: cbab=aba.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [2] abaa=c with [3] aba=cbab:

Critical pair: cbaba=c.

Reduce LHS:

Defines rule #4.

Referenced by [6], [8], [9].

Overlap of [3] aba=cbab with [3] aba=cbab:

Critical pair: abcbab=cbabba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [4] cbcbab=c with [3] aba=cbab:

Critical pair: cbcbcbab=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Overlap of [6] ca=cbc with [3] aba=cbab:

Critical pair: ccbab=cbcba.

Defines rule #3.

Overlap of [4] cbcbab=c with [5] cbabba=abcbab:

Critical pair: cbabcbab=cba.

Defines rule #8.

Referenced by [9], [10].

Overlap of [8] cbabcbab=cba with [3] aba=cbab:

Critical pair: cbabcbcbab=cbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [8] cbabcbab=cba with [8] cbabcbab=cba:

Critical pair: cbabcba=cbacbab.

Flip LHS and RHS.

Defines rule #7.