Certificate for #984 ⟨a, b | ababaab=ba⟩

Completion settings:

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

Axiom: ababaab=ba.

Referenced by [3].

Axiom: ababa=c.

Referenced by [3], [4].

Overlap of [1] ababaab=ba with [2] ababa=c:

Critical pair: cab=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5], [6], [8], [9], [10], [11].

Overlap of [2] ababa=c with [3] ba=cab:

Critical pair: acabba=c.

Reduce LHS:

Referenced by [5], [6], [7], [8], [9].

Overlap of [3] ba=cab with [4] acabcab=c:

Critical pair: bc=cabcabcab.

Flip LHS and RHS.

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

Overlap of [4] acabcab=c with [3] ba=cab:

Critical pair: acabcacab=ca.

Referenced by [11].

Overlap of [4] acabcab=c with [5] cabcabcab=bc:

Critical pair: abc=ccab.

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

Overlap of [4] acabcab=c with [5] cabcabcab=bc:

Critical pair: acabbc=ccabcab.

Reduce RHS:

Referenced by [10].

Overlap of [4] acabcab=c with [7] abc=ccab:

Critical pair: acccabab=c.

Reduce LHS:

Defines rule #4.

Referenced by [10], [11].

Overlap of [5] cabcabcab=bc with [7] abc=ccab:

Critical pair: cccababcab=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] acabcacab=ca with [7] abc=ccab:

Critical pair: acccabacab=ca.

Reduce LHS:

Defines rule #1.