Certificate for #3679 ⟨a, b | aabbbbaaab=a⟩

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: aabbbbaaab=a.

Referenced by [3].

Axiom: aaa=c.

Referenced by [3], [4], [5], [6], [8].

Overlap of [1] aabbbbaaab=a with [2] aaa=c:

Critical pair: aabbbbcb=a.

Referenced by [5], [6], [7], [9].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [2] aaa=c with [3] aabbbbcb=a:

Critical pair: aa=cbbbbcb.

Referenced by [6], [7], [8], [9].

Overlap of [2] aaa=c with [3] aabbbbcb=a:

Critical pair: aaa=cabbbbcb.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [4] ca=ac with [3] aabbbbcb=a:

Critical pair: ca=acabbbbcb.

Reduce LHS:

Reduce RHS:

Referenced by [8], [10].

Overlap of [2] aaa=c with [5] aa=cbbbbcb:

Critical pair: cbbbbcba=c.

Reduce LHS:

Referenced by [11].

Overlap of [3] aabbbbcb=a with [5] aa=cbbbbcb:

Critical pair: cbbbbcbbbbbcb=a.

Flip LHS and RHS.

Defines rule #12.

Referenced by [10].

Simplify [7] ac=cbbbbcbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [11], [12], [13].

Simplify [8] cbbbbcbcbbbbcbbbbbcb=c.

Reduce LHS:

Defines rule #11.

Referenced by [12], [13], [14], [15], [16], [17], [18], [19], [20].

Overlap of [10] cbbbbcbcbbbbcb=cbbbbcbbbbbcbc with [11] cbbbbcbbbbbcbcbbbbcb=c:

Critical pair: cbbbbcbc=cbbbbcbbbbbcbcbbbbcbcbbbbcb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [10] cbbbbcbcbbbbcb=cbbbbcbbbbbcbc:

Critical pair: cbbbbcbbbbbcbcbbbbcbbbbcbbbbbcbc=cbbbcbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [15].

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [11] cbbbbcbbbbbcbcbbbbcb=c:

Critical pair: cbbbbcbbbbbcbcbbbbc=cbbbcbbbbbcbcbbbbcb.

Flip LHS and RHS.

Defines rule #10.

Referenced by [18], [19].

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [13] cbbbcbcbbbbcb=cbbbcbbbbbcbc:

Critical pair: cbbbbcbbbbbcbcbbbbcbbbcbbbbbcbc=cbbcbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [16].

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [15] cbbcbcbbbbcb=cbbcbbbbbcbc:

Critical pair: cbbbbcbbbbbcbcbbbbcbbcbbbbbcbc=cbcbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [17].

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [16] cbcbcbbbbcb=cbcbbbbbcbc:

Critical pair: cbbbbcbbbbbcbcbbbbcbcbbbbbcbc=ccbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [14] cbbbcbbbbbcbcbbbbcb=cbbbbcbbbbbcbcbbbbc:

Critical pair: cbbbbcbbbbbcbcbbbbcbbbbcbbbbbcbcbbbbc=cbbcbbbbbcbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [14] cbbbcbbbbbcbcbbbbcb=cbbbbcbbbbbcbcbbbbc with [14] cbbbcbbbbbcbcbbbbcb=cbbbbcbbbbbcbcbbbbc:

Critical pair: cbbbcbbbbbcbcbbbbcbbbbcbbbbbcbcbbbbc=cbbbbcbbbbbcbcbbbbcbbcbbbbbcbcbbbbcb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [20].

Overlap of [11] cbbbbcbbbbbcbcbbbbcb=c with [19] cbcbbbbbcbcbbbbcb=cbbcbbbbbcbcbbbbc:

Critical pair: cbbbbcbbbbbcbcbbbbcbbcbbbbbcbcbbbbc=ccbbbbbcbcbbbbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.