Certificate for #2171 ⟨a, b | aaababa=baa⟩

Completion settings:

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

Axiom: aaababa=baa.

Referenced by [3].

Axiom: aaabab=c.

Defines rule #10.

Referenced by [3], [4], [5], [6], [7], [11], [12].

Overlap of [1] aaababa=baa with [2] aaabab=c:

Critical pair: ca=baa.

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [2] aaabab=c with [3] baa=ca:

Critical pair: aaabaca=caa.

Referenced by [17].

Overlap of [3] baa=ca with [2] aaabab=c:

Critical pair: bc=caabab.

Flip LHS and RHS.

Defines rule #11.

Referenced by [8], [9], [10], [13], [14], [15], [16].

Overlap of [3] baa=ca with [2] aaabab=c:

Critical pair: bac=caaabab.

Reduce RHS:

Defines rule #6.

Referenced by [7], [8], [9], [10], [12], [14], [17].

Overlap of [2] aaabab=c with [6] bac=cc:

Critical pair: aaabacc=cac.

Reduce LHS:

Defines rule #2.

Overlap of [5] caabab=bc with [3] baa=ca:

Critical pair: caabaca=bcaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [15], [16].

Overlap of [5] caabab=bc with [6] bac=cc:

Critical pair: caabacc=bcac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [6] bac=cc with [5] caabab=bc:

Critical pair: babc=ccaabab.

Reduce RHS:

Defines rule #13.

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

Overlap of [2] aaabab=c with [10] babc=cbc:

Critical pair: aaacbc=cc.

Defines rule #3.

Overlap of [2] aaabab=c with [10] babc=cbc:

Critical pair: aaabacbc=cabc.

Reduce LHS:

Defines rule #4.

Overlap of [5] caabab=bc with [10] babc=cbc:

Critical pair: caacbc=bcc.

Flip LHS and RHS.

Defines rule #7.

Referenced by [15].

Overlap of [5] caabab=bc with [10] babc=cbc:

Critical pair: caabacbc=bcabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [13] bcc=caacbc with [5] caabab=bc:

Critical pair: bcbc=caacbcaabab.

Reduce RHS:

Defines rule #14.

Overlap of [8] bcaa=caacca with [5] caabab=bc:

Critical pair: bbc=caaccabab.

Defines rule #12.

Simplify [4] aaabaca=caa.

Reduce LHS:

Defines rule #1.