Certificate for #25187 ⟨a, b | aa=a, ababa=abb⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [5], [6].

Axiom: ababa=abb.

Referenced by [4].

Axiom: abb=c.

Defines rule #6.

Referenced by [4], [5], [8].

Simplify [2] ababa=abb.

Reduce RHS:

Defines rule #7.

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

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

Critical pair: ac=abb.

Reduce RHS:

Defines rule #2.

Referenced by [9], [10].

Overlap of [4] ababa=c with [1] aa=a:

Critical pair: ababa=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] ababa=c with [4] ababa=c:

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [10].

Overlap of [4] ababa=c with [3] abb=c:

Critical pair: ababc=cbb.

Flip LHS and RHS.

Referenced by [11].

Overlap of [4] ababa=c with [5] ac=c:

Critical pair: ababc=cc.

Defines rule #8.

Referenced by [11].

Overlap of [7] cba=abc with [5] ac=c:

Critical pair: cbc=abcc.

Defines rule #5.

Simplify [8] cbb=ababc.

Reduce RHS:

Defines rule #9.