Certificate for #4343 ⟨a, b | abbabaaab=bb⟩

Completion settings:

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

Axiom: abbabaaab=bb.

Referenced by [3].

Axiom: babaa=c.

Defines rule #9.

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

Overlap of [1] abbabaaab=bb with [2] babaa=c:

Critical pair: abcab=bb.

Defines rule #5.

Referenced by [4], [5], [6], [8], [9], [13].

Overlap of [2] babaa=c with [3] abcab=bb:

Critical pair: bababb=cbcab.

Defines rule #11.

Referenced by [11], [12].

Overlap of [3] abcab=bb with [2] babaa=c:

Critical pair: abcac=bbabaa.

Reduce RHS:

Defines rule #2.

Referenced by [7], [8], [10], [14].

Overlap of [3] abcab=bb with [3] abcab=bb:

Critical pair: abcbb=bbcab.

Defines rule #4.

Overlap of [2] babaa=c with [5] abcac=bc:

Critical pair: bababc=cbcac.

Defines rule #7.

Referenced by [9], [10].

Overlap of [3] abcab=bb with [5] abcac=bc:

Critical pair: abcbc=bbcac.

Defines rule #1.

Overlap of [7] bababc=cbcac with [3] abcab=bb:

Critical pair: babbb=cbcacab.

Defines rule #6.

Referenced by [12].

Overlap of [7] bababc=cbcac with [5] abcac=bc:

Critical pair: babbc=cbcacac.

Defines rule #3.

Referenced by [11].

Overlap of [4] bababb=cbcab with [10] babbc=cbcacac:

Critical pair: bacbcacac=cbcabc.

Defines rule #10.

Overlap of [4] bababb=cbcab with [9] babbb=cbcacab:

Critical pair: bacbcacab=cbcabb.

Defines rule #13.

Referenced by [13], [14].

Overlap of [12] bacbcacab=cbcabb with [3] abcab=bb:

Critical pair: bacbcacbb=cbcabbcab.

Defines rule #12.

Overlap of [12] bacbcacab=cbcabb with [5] abcac=bc:

Critical pair: bacbcacbc=cbcabbcac.

Defines rule #8.