Certificate for #3802 ⟨a, b | abbaaabaab=b⟩

Completion settings:

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

Axiom: abbaaabaab=b.

Referenced by [3].

Axiom: aaab=c.

Defines rule #11.

Referenced by [3], [4].

Overlap of [1] abbaaabaab=b with [2] aaab=c:

Critical pair: abbcaab=b.

Defines rule #13.

Referenced by [4], [5], [6], [7], [11].

Overlap of [2] aaab=c with [3] abbcaab=b:

Critical pair: aab=cbcaab.

Flip LHS and RHS.

Defines rule #8.

Referenced by [6], [8], [12].

Overlap of [3] abbcaab=b with [3] abbcaab=b:

Critical pair: abbcab=bbcaab.

Defines rule #10.

Referenced by [11].

Overlap of [4] cbcaab=aab with [3] abbcaab=b:

Critical pair: cbcab=aabbcaab.

Reduce RHS:

Defines rule #4.

Referenced by [7], [9], [13].

Overlap of [6] cbcab=ab with [3] abbcaab=b:

Critical pair: cbcb=abbcaab.

Reduce RHS:

Defines rule #2.

Referenced by [8], [9], [10], [14].

Overlap of [7] cbcb=b with [4] cbcaab=aab:

Critical pair: cbaab=bcaab.

Defines rule #7.

Overlap of [7] cbcb=b with [6] cbcab=ab:

Critical pair: cbab=bcab.

Defines rule #3.

Overlap of [7] cbcb=b with [7] cbcb=b:

Critical pair: cbb=bcb.

Defines rule #1.

Overlap of [5] abbcab=bbcaab with [3] abbcaab=b:

Critical pair: abbcb=bbcaabbcaab.

Reduce RHS:

Defines rule #6.

Referenced by [12], [13], [14].

Overlap of [11] abbcb=bbcab with [4] cbcaab=aab:

Critical pair: abbaab=bbcabcaab.

Defines rule #12.

Overlap of [11] abbcb=bbcab with [6] cbcab=ab:

Critical pair: abbab=bbcabcab.

Defines rule #9.

Overlap of [11] abbcb=bbcab with [7] cbcb=b:

Critical pair: abbb=bbcabcb.

Defines rule #5.