Certificate for #5670 ⟨a, b | aabaab=bbaab⟩

Completion settings:

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

Axiom: aabaab=bbaab.

Referenced by [3].

Axiom: bbaab=c.

Defines rule #5.

Referenced by [3], [4], [6], [7], [9].

Simplify [1] aabaab=bbaab.

Reduce RHS:

Defines rule #10.

Referenced by [5], [6], [7], [8], [13].

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

Critical pair: bbaac=cbaab.

Defines rule #7.

Overlap of [3] aabaab=c with [3] aabaab=c:

Critical pair: aabc=caab.

Referenced by [12].

Overlap of [3] aabaab=c with [2] bbaab=c:

Critical pair: aabaac=cbaab.

Defines rule #11.

Overlap of [2] bbaab=c with [3] aabaab=c:

Critical pair: bbc=caab.

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [7] caab=bbc with [3] aabaab=c:

Critical pair: cc=bbcaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11].

Overlap of [7] caab=bbc with [2] bbaab=c:

Critical pair: caac=bbcbaab.

Defines rule #6.

Overlap of [8] bbbbc=cc with [7] caab=bbc:

Critical pair: bbbbbbc=ccaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [11].

Overlap of [8] bbbbc=cc with [10] bbcc=cbbc:

Critical pair: bbcbbc=ccc.

Defines rule #3.

Simplify [5] aabc=caab.

Reduce RHS:

Defines rule #8.

Referenced by [13].

Overlap of [3] aabaab=c with [12] aabc=bbc:

Critical pair: aabbbc=cc.

Defines rule #9.