Certificate for #1241 ⟨a, b | abaab=aaba⟩

Completion settings:

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

Axiom: abaab=aaba.

Referenced by [3].

Axiom: abaa=c.

Defines rule #14.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] abaab=aaba with [2] abaa=c:

Critical pair: cb=aaba.

Flip LHS and RHS.

Defines rule #13.

Referenced by [4], [5], [6], [7], [9], [15].

Overlap of [2] abaa=c with [3] aaba=cb:

Critical pair: abcb=cba.

Flip LHS and RHS.

Referenced by [6], [12].

Overlap of [2] abaa=c with [3] aaba=cb:

Critical pair: abacb=caba.

Flip LHS and RHS.

Defines rule #11.

Overlap of [3] aaba=cb with [2] abaa=c:

Critical pair: ac=cba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [10], [12], [13].

Overlap of [3] aaba=cb with [2] abaa=c:

Critical pair: aabc=cbbaa.

Flip LHS and RHS.

Defines rule #12.

Overlap of [2] abaa=c with [6] abcb=ac:

Critical pair: abaac=cbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [11], [14], [16].

Overlap of [3] aaba=cb with [6] abcb=ac:

Critical pair: aabac=cbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [16].

Overlap of [6] abcb=ac with [8] cbcb=cc:

Critical pair: abcc=accb.

Flip LHS and RHS.

Defines rule #6.

Overlap of [8] cbcb=cc with [8] cbcb=cc:

Critical pair: cbcc=cccb.

Flip LHS and RHS.

Defines rule #2.

Simplify [4] cba=abcb.

Reduce RHS:

Defines rule #7.

Referenced by [13], [14].

Overlap of [6] abcb=ac with [12] cba=ac:

Critical pair: abac=aca.

Flip LHS and RHS.

Defines rule #10.

Referenced by [15].

Overlap of [8] cbcb=cc with [12] cba=ac:

Critical pair: cbac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [3] aaba=cb with [13] aca=abac:

Critical pair: aababac=cbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [9] cbbcb=cbc with [8] cbcb=cc:

Critical pair: cbbcc=cbccb.

Flip LHS and RHS.

Defines rule #4.