Certificate for #2002 ⟨a, b | aabbbaab=ba⟩

Completion settings:

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

Axiom: aabbbaab=ba.

Referenced by [3].

Axiom: bbaab=c.

Referenced by [3], [4], [5], [6], [11], [12].

Overlap of [1] aabbbaab=ba with [2] bbaab=c:

Critical pair: aabc=ba.

Referenced by [5], [7].

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

Critical pair: bbaac=cbaab.

Referenced by [8].

Overlap of [2] bbaab=c with [3] aabc=ba:

Critical pair: bbba=cc.

Referenced by [6], [10].

Overlap of [5] bbba=cc with [2] bbaab=c:

Critical pair: bc=ccab.

Defines rule #3.

Referenced by [7], [9], [10], [11], [12].

Overlap of [3] aabc=ba with [6] bc=ccab:

Critical pair: aaccab=ba.

Flip LHS and RHS.

Defines rule #2.

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

Simplify [4] bbaac=cbaab.

Reduce RHS:

Referenced by [9].

Overlap of [8] bbaac=caaccaaaccabb with [7] ba=aaccab:

Critical pair: baaccabac=caaccaaaccabb.

Reduce LHS:

Referenced by [10], [11].

Overlap of [5] bbba=cc with [7] ba=aaccab:

Critical pair: bbaaccab=cc.

Reduce LHS:

Referenced by [11].

Overlap of [2] bbaab=c with [7] ba=aaccab:

Critical pair: bbaaaaccab=ca.

Reduce LHS:

Defines rule #1.

Overlap of [2] bbaab=c with [7] ba=aaccab:

Critical pair: baaccabab=c.

Reduce LHS:

Defines rule #4.