Certificate for #16536 ⟨a, b | aba=ab, baa=aab⟩

Completion settings:

• Auxiliary generators:
  1. c = bab
• Reduction order:
  • Left-to-right shortlex with a < c < b

Axiom: aba=ab.

Defines rule #4.

Referenced by [5], [6], [7], [8], [10], [11].

Axiom: baa=aab.

Defines rule #8.

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

Axiom: bab=c.

Defines rule #10.

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

Overlap of [3] bab=c with [3] bab=c:

Critical pair: bac=cab.

Referenced by [13].

Overlap of [1] aba=ab with [3] bab=c:

Critical pair: ac=abb.

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [3] bab=c with [1] aba=ab:

Critical pair: bab=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [9], [11], [13].

Overlap of [6] ca=c with [1] aba=ab:

Critical pair: cab=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [1] aba=ab with [5] abb=ac:

Critical pair: abac=abbb.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [6] ca=c with [5] abb=ac:

Critical pair: cac=cbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [1] aba=ab with [2] baa=aab:

Critical pair: aaab=aba.

Reduce RHS:

Defines rule #11.

Overlap of [3] bab=c with [2] baa=aab:

Critical pair: baaab=caa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [12].

Overlap of [2] baa=aab with [11] aac=c:

Critical pair: bc=aabc.

Reduce RHS:

Defines rule #2.

Simplify [4] bac=cab.

Reduce RHS:

Defines rule #9.