Certificate for #4348 ⟨a, b | abbabbbba=ab⟩

Completion settings:

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

Axiom: abbabbbba=ab.

Referenced by [3].

Axiom: abbbb=c.

Referenced by [3], [4], [6], [7], [9].

Overlap of [1] abbabbbba=ab with [2] abbbb=c:

Critical pair: abbca=ab.

Referenced by [4], [5], [6], [8], [10], [15], [16].

Overlap of [3] abbca=ab with [2] abbbb=c:

Critical pair: abbcc=abbbbb.

Reduce RHS:

Referenced by [10], [14].

Overlap of [3] abbca=ab with [3] abbca=ab:

Critical pair: abbcab=abbbca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7], [8], [11], [12].

Overlap of [3] abbca=ab with [5] abbbca=abb:

Critical pair: abbcabb=abbbbca.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8], [9], [10], [11], [12].

Overlap of [5] abbbca=abb with [2] abbbb=c:

Critical pair: abbbcc=abbbbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [14].

Overlap of [5] abbbca=abb with [3] abbca=ab:

Critical pair: abbbcab=abbbbca.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [2] abbbb=c with [6] abbb=cca:

Critical pair: ccab=c.

Referenced by [10], [12], [15].

Overlap of [3] abbca=ab with [6] abbb=cca:

Critical pair: abbccca=abbbb.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [5] abbbca=abb with [6] abbb=cca:

Critical pair: ccaca=abb.

Flip LHS and RHS.

Referenced by [12], [14], [16].

Overlap of [5] abbbca=abb with [6] abbb=cca:

Critical pair: abbbccca=abbbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [13], [14], [15], [17].

Simplify [10] cbca=c.

Reduce LHS:

Referenced by [14].

Overlap of [4] abbcc=cb with [13] ccacccaca=c:

Critical pair: abbcc=cbcacccaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [15], [17].

Overlap of [9] ccab=c with [3] abbca=ab:

Critical pair: ccab=cbca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] abbca=ab with [11] abb=ccaca:

Critical pair: ccacaca=ab.

Flip LHS and RHS.

Defines rule #4.

Simplify [12] cb=ccaccca.

Reduce RHS:

Defines rule #5.