Certificate for #1515 ⟨a, b | abababbaba=1⟩

Completion settings:

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

Axiom: abababbaba=1.

Referenced by [4].

Axiom: ba=c.

Defines rule #8.

Referenced by [4], [5], [6], [9], [10].

Axiom: accb=d.

Defines rule #7.

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

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

Critical pair: acbabbaba=1.

Reduce LHS:

Referenced by [7], [8], [10], [11].

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

Critical pair: bd=cccb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [7], [10].

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

Critical pair: accc=da.

Flip LHS and RHS.

Defines rule #3.

Referenced by [14].

Overlap of [4] dcc=1 with [5] cccb=bd:

Critical pair: dbd=cb.

Referenced by [8].

Overlap of [7] dbd=cb with [4] dcc=1:

Critical pair: db=cbcc.

Defines rule #5.

Referenced by [9].

Overlap of [8] db=cbcc with [2] ba=c:

Critical pair: dc=cbcca.

Flip LHS and RHS.

Referenced by [10].

Overlap of [5] cccb=bd with [9] cbcca=dc:

Critical pair: ccdc=bdcca.

Reduce RHS:

Referenced by [11], [12].

Overlap of [4] dcc=1 with [10] ccdc=c:

Critical pair: dcc=cdc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12], [13], [16].

Overlap of [10] ccdc=c with [11] cdc=1:

Critical pair: ccd=cdc.

Reduce RHS:

Defines rule #2.

Referenced by [14], [15].

Overlap of [11] cdc=1 with [11] cdc=1:

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [16].

Overlap of [12] ccd=1 with [6] da=accc:

Critical pair: ccaccc=a.

Referenced by [15].

Overlap of [14] ccaccc=a with [12] ccd=1:

Critical pair: ccac=ad.

Referenced by [16].

Overlap of [15] ccac=ad with [11] cdc=1:

Critical pair: cca=addc.

Reduce RHS:

Defines rule #4.