Certificate for #1916 ⟨a, b | aaabbaba=ab⟩

Completion settings:

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

Axiom: aaabbaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

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

Simplify [1] aaabbaba=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabbaba=c with [2] ab=c:

Critical pair: aacbaba=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6], [7], [8].

Overlap of [4] aacbca=c with [2] ab=c:

Critical pair: aacbcc=cb.

Defines rule #3.

Referenced by [6], [7], [9], [10], [13].

Overlap of [4] aacbca=c with [4] aacbca=c:

Critical pair: aacbcc=cacbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [11], [12].

Overlap of [4] aacbca=c with [5] aacbcc=cb:

Critical pair: aacbccb=cacbcc.

Reduce LHS:

Defines rule #5.

Referenced by [9].

Overlap of [4] aacbca=c with [6] cacbca=cb:

Critical pair: aacbcb=ccbca.

Defines rule #7.

Referenced by [12].

Overlap of [5] aacbcc=cb with [6] cacbca=cb:

Critical pair: aacbccb=cbacbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [13].

Overlap of [6] cacbca=cb with [5] aacbcc=cb:

Critical pair: cacbccb=cbacbcc.

Defines rule #9.

Overlap of [6] cacbca=cb with [6] cacbca=cb:

Critical pair: cacbcb=cbcbca.

Defines rule #8.

Overlap of [6] cacbca=cb with [8] aacbcb=ccbca:

Critical pair: cacbcccbca=cbacbcb.

Flip LHS and RHS.

Defines rule #10.

Overlap of [9] cbacbca=cacbcc with [5] aacbcc=cb:

Critical pair: cbacbccb=cacbccacbcc.

Defines rule #11.