Certificate for #6270 ⟨a, b | aaa=a, babab=a⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [4], [8], [13].

Axiom: babab=a.

Defines rule #9.

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

Axiom: abb=c.

Defines rule #7.

Referenced by [4], [6], [7], [9], [10], [12], [15].

Overlap of [1] aaa=a with [3] abb=c:

Critical pair: aac=abb.

Reduce RHS:

Defines rule #5.

Referenced by [14].

Overlap of [2] babab=a with [2] babab=a:

Critical pair: baa=aab.

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [2] babab=a with [3] abb=c:

Critical pair: babc=ab.

Defines rule #11.

Referenced by [15].

Overlap of [3] abb=c with [2] babab=a:

Critical pair: aba=cabab.

Flip LHS and RHS.

Defines rule #12.

Overlap of [1] aaa=a with [5] aab=baa:

Critical pair: abaa=ab.

Defines rule #2.

Referenced by [10].

Overlap of [5] aab=baa with [3] abb=c:

Critical pair: ac=baab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13], [14].

Overlap of [8] abaa=ab with [5] aab=baa:

Critical pair: abbaa=abb.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [11].

Overlap of [10] caa=c with [5] aab=baa:

Critical pair: cbaa=cb.

Referenced by [12].

Overlap of [3] abb=c with [9] bbaa=ac:

Critical pair: abac=cbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [9] bbaa=ac with [1] aaa=a:

Critical pair: bba=aca.

Defines rule #6.

Overlap of [9] bbaa=ac with [4] aac=c:

Critical pair: bbc=acc.

Defines rule #10.

Overlap of [3] abb=c with [6] babc=ab:

Critical pair: abab=cabc.

Flip LHS and RHS.

Defines rule #13.