Certificate for #5074 ⟨a, b | aaabbaa=abab⟩

Completion settings:

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

Axiom: aaabbaa=abab.

Referenced by [3].

Axiom: abba=c.

Defines rule #4.

Referenced by [3], [4], [5], [6], [8].

Overlap of [1] aaabbaa=abab with [2] abba=c:

Critical pair: aaca=abab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6], [7], [9], [10], [11], [12].

Overlap of [2] abba=c with [2] abba=c:

Critical pair: abbc=cbba.

Flip LHS and RHS.

Defines rule #10.

Overlap of [2] abba=c with [3] abab=aaca:

Critical pair: abbaaca=cbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9], [13].

Overlap of [3] abab=aaca with [2] abba=c:

Critical pair: abc=aacaba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [3] abab=aaca with [3] abab=aaca:

Critical pair: abaaca=aacaab.

Flip LHS and RHS.

Defines rule #1.

Overlap of [5] cbab=caca with [2] abba=c:

Critical pair: cbc=cacaba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [11].

Overlap of [5] cbab=caca with [3] abab=aaca:

Critical pair: cbaaca=cacaab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] aacaba=abc with [3] abab=aaca:

Critical pair: aacaaca=abcb.

Flip LHS and RHS.

Defines rule #8.

Referenced by [12], [13].

Overlap of [8] cacaba=cbc with [3] abab=aaca:

Critical pair: cacaaca=cbcb.

Flip LHS and RHS.

Defines rule #12.

Overlap of [3] abab=aaca with [10] abcb=aacaaca:

Critical pair: abaacaaca=aacacb.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] cbab=caca with [10] abcb=aacaaca:

Critical pair: cbaacaaca=cacacb.

Flip LHS and RHS.

Defines rule #11.