Certificate for #5349 ⟨a, b | ababaab=baba⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(d) = 0; deg(b) = deg(c) = 1, b < c; deg(a) = 2
• Auxiliary generators:
  1. abab=c
  2. aab=d

Axiom: ababaab=baba.

Referenced by [4].

Axiom: abab=c.

Defines rule #10.

Referenced by [4], [5], [6], [7], [8], [11].

Axiom: aab=d.

Defines rule #9.

Referenced by [4], [6], [9], [10], [12].

Overlap of [1] ababaab=baba with [2] abab=c:

Critical pair: caab=baba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

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

Overlap of [2] abab=c with [2] abab=c:

Critical pair: abc=cab.

Referenced by [10].

Overlap of [3] aab=d with [2] abab=c:

Critical pair: ac=dab.

Defines rule #6.

Referenced by [7].

Overlap of [2] abab=c with [4] baba=cd:

Critical pair: acd=ca.

Reduce LHS:

Defines rule #3.

Referenced by [10].

Overlap of [4] baba=cd with [2] abab=c:

Critical pair: bc=cdb.

Defines rule #1.

Overlap of [4] baba=cd with [3] aab=d:

Critical pair: babd=cdab.

Defines rule #4.

Overlap of [7] dabd=ca with [7] dabd=ca:

Critical pair: dabca=caabd.

Reduce LHS:

Reduce RHS:

Defines rule #8.

Referenced by [11], [12].

Overlap of [10] dcaba=cdd with [2] abab=c:

Critical pair: dcc=cddb.

Defines rule #2.

Overlap of [10] dcaba=cdd with [3] aab=d:

Critical pair: dcabd=cddab.

Defines rule #5.