Certificate for #3119 ⟨a, b | aabbabaabba=1⟩

Completion settings:

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

Axiom: aabbabaabba=1.

Referenced by [3].

Axiom: aabba=c.

Referenced by [3], [5], [8], [11], [13].

Overlap of [1] aabbabaabba=1 with [2] aabba=c:

Critical pair: cbaabba=1.

Reduce LHS:

Referenced by [4], [6], [7], [10], [11], [12].

Overlap of [3] cbc=1 with [3] cbc=1:

Critical pair: cb=bc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [6], [9], [14], [16], [17], [19], [20], [23].

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

Critical pair: aabbc=cabba.

Reduce LHS:

Defines rule #6.

Referenced by [6], [11], [23].

Overlap of [5] aacbb=cabba with [4] bc=cb:

Critical pair: aacbcb=cabbac.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] cbc=1 with [6] cabbac=aab:

Critical pair: cbaab=abbac.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [15].

Overlap of [2] aabba=c with [7] abbac=cbaab:

Critical pair: acbaab=cc.

Referenced by [9].

Overlap of [8] acbaab=cc with [4] bc=cb:

Critical pair: acbaacb=ccc.

Referenced by [10], [11].

Overlap of [9] acbaacb=ccc with [3] cbc=1:

Critical pair: acbaa=cccc.

Defines rule #7.

Referenced by [13], [14], [21].

Overlap of [9] acbaacb=ccc with [5] aacbb=cabba:

Critical pair: acbcabba=cccb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [3] cbc=1 with [11] cccb=c:

Critical pair: cbc=ccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [14], [15], [16], [18], [19], [20], [21], [22], [23].

Overlap of [10] acbaa=cccc with [2] aabba=c:

Critical pair: acbac=ccccabba.

Defines rule #4.

Referenced by [14], [15].

Overlap of [13] acbac=ccccabba with [10] acbaa=cccc:

Critical pair: acbcccc=ccccabbabaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [19].

Overlap of [13] acbac=ccccabba with [12] ccb=1:

Critical pair: acba=ccccabbacb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [16].

Overlap of [4] bc=cb with [15] cccaabb=acba:

Critical pair: bacba=cbccaabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [17].

Overlap of [4] bc=cb with [16] caabb=bacba:

Critical pair: bbacba=cbaabb.

Flip LHS and RHS.

Referenced by [18].

Overlap of [12] ccb=1 with [17] cbaabb=bbacba:

Critical pair: cbbacba=aabb.

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] bc=cb with [14] ccccabbabaa=accc:

Critical pair: baccc=cbcccabbabaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [20].

Overlap of [4] bc=cb with [19] ccabbabaa=baccc:

Critical pair: bbaccc=cbcabbabaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [21].

Overlap of [20] abbabaa=bbaccc with [10] acbaa=cccc:

Critical pair: abbabacccc=bbaccccbaa.

Reduce RHS:

Referenced by [22].

Overlap of [21] abbabacccc=bbaccaa with [12] ccb=1:

Critical pair: abbabacc=bbaccaab.

Referenced by [23].

Overlap of [22] abbabacc=bbaccaab with [12] ccb=1:

Critical pair: abbabac=bbaccaabcb.

Reduce RHS:

Defines rule #8.