Certificate for #1513 ⟨a, b | ababababba=1⟩

Completion settings:

• Auxiliary generators:
  1. c = ba
  2. d = acccb
• Reduction order:
  • Left-to-right recursive path with deg(d) = 0; deg(c) = 1; deg(a) = deg(b) = 2, a < b

Axiom: ababababba=1.

Referenced by [4].

Axiom: ba=c.

Defines rule #8.

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

Axiom: acccb=d.

Referenced by [4], [5], [6], [14].

Overlap of [1] ababababba=1 with [2] ba=c:

Critical pair: acbababba=1.

Reduce LHS:

Defines rule #2.

Referenced by [7], [8], [9], [10], [11], [13], [15].

Overlap of [2] ba=c with [3] acccb=d:

Critical pair: bd=ccccb.

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] acccb=d with [2] ba=c:

Critical pair: acccc=da.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] dc=1 with [5] ccccb=bd:

Critical pair: dbd=cccb.

Flip LHS and RHS.

Referenced by [8], [14].

Overlap of [4] dc=1 with [7] cccb=dbd:

Critical pair: ddbd=ccb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] dc=1 with [8] ccb=ddbd:

Critical pair: dddbd=cb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10].

Overlap of [4] dc=1 with [9] cb=dddbd:

Critical pair: ddddbd=b.

Referenced by [11], [12].

Overlap of [10] ddddbd=b with [4] dc=1:

Critical pair: ddddb=bc.

Defines rule #5.

Referenced by [12], [13].

Overlap of [10] ddddbd=b with [11] ddddb=bc:

Critical pair: bcd=b.

Referenced by [16].

Overlap of [11] ddddb=bc with [2] ba=c:

Critical pair: ddddc=bca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [17].

Overlap of [3] acccb=d with [7] cccb=dbd:

Critical pair: adbd=d.

Referenced by [15].

Overlap of [14] adbd=d with [4] dc=1:

Critical pair: adb=dc.

Reduce RHS:

Defines rule #7.

Referenced by [16], [17].

Overlap of [15] adb=1 with [12] bcd=b:

Critical pair: adb=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [15] adb=1 with [13] bca=ddd:

Critical pair: adddd=ca.

Flip LHS and RHS.

Defines rule #4.