Certificate for #4084 ⟨a, b | baa=aab, abab=1⟩

Completion settings:

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

Axiom: baa=aab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6].

Axiom: abab=1.

Referenced by [4].

Axiom: bab=c.

Defines rule #5.

Referenced by [4], [5].

Overlap of [2] abab=1 with [3] bab=c:

Critical pair: ac=1.

Defines rule #1.

Referenced by [5], [7], [8], [9].

Overlap of [1] aab=baa with [3] bab=c:

Critical pair: aac=baaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [5] caa=a with [1] aab=baa:

Critical pair: cbaa=ab.

Referenced by [8].

Overlap of [5] caa=a with [4] ac=1:

Critical pair: ca=ac.

Reduce RHS:

Defines rule #2.

Overlap of [6] cbaa=ab with [4] ac=1:

Critical pair: cba=abc.

Referenced by [9].

Overlap of [8] cba=abc with [4] ac=1:

Critical pair: cb=abcc.

Defines rule #3.