Certificate for #4010 ⟨a, b | aaabbaaab=aa⟩

Completion settings:

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

Axiom: aaabbaaab=aa.

Referenced by [3].

Axiom: aaa=c.

Referenced by [3], [4].

Overlap of [1] aaabbaaab=aa with [2] aaa=c:

Critical pair: cbbaaab=aa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

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

Overlap of [2] aaa=c with [3] aa=cbbcb:

Critical pair: cbbcba=c.

Defines rule #12.

Referenced by [5], [6], [8], [9], [10].

Overlap of [3] aa=cbbcb with [3] aa=cbbcb:

Critical pair: acbbcb=cbbcba.

Reduce RHS:

Referenced by [7], [8], [9], [11], [12], [13], [14].

Overlap of [4] cbbcba=c with [3] aa=cbbcb:

Critical pair: cbbcbcbbcb=ca.

Flip LHS and RHS.

Defines rule #9.

Referenced by [10].

Overlap of [3] aa=cbbcb with [5] acbbcb=c:

Critical pair: ac=cbbcbcbbcb.

Defines rule #8.

Referenced by [9], [11], [12], [13], [14], [15].

Overlap of [4] cbbcba=c with [5] acbbcb=c:

Critical pair: cbbcbc=ccbbcb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Overlap of [5] acbbcb=c with [4] cbbcba=c:

Critical pair: acbbc=cbcba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [14].

Overlap of [8] ccbbcb=cbbcbc with [4] cbbcba=c:

Critical pair: cc=cbbcbca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [13].

Overlap of [5] acbbcb=c with [7] ac=cbbcbcbbcb:

Critical pair: cbbcbcbbcbbbcb=c.

Defines rule #5.

Referenced by [12], [14], [16].

Overlap of [5] acbbcb=c with [11] cbbcbcbbcbbbcb=c:

Critical pair: acbbc=cbcbcbbcbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [16].

Overlap of [5] acbbcb=c with [10] cbbcbcbbcbcbbcb=cc:

Critical pair: acbbcc=cbcbcbbcbcbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] acbbcb=c with [9] cbcba=cbbcbcbbcbbbc:

Critical pair: acbbcbbcbcbbcbbbc=ccba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [15].

Overlap of [14] ccba=cbcbcbbcbbbc with [7] ac=cbbcbcbbcb:

Critical pair: ccbcbbcbcbbcb=cbcbcbbcbbbcc.

Defines rule #4.

Overlap of [11] cbbcbcbbcbbbcb=c with [12] cbcbcbbcbbbcb=cbbcbcbbcbbbc:

Critical pair: cbbcbcbbcbbbcbbcbcbbcbbbc=ccbcbbcbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.