Certificate for #22855 ⟨a, b | aaa=1, bbabb=abb⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #2.

Referenced by [6], [9].

Axiom: bbabb=abb.

Referenced by [4].

Axiom: abb=c.

Referenced by [4], [5], [6], [7], [8], [11].

Simplify [2] bbabb=abb.

Reduce RHS:

Referenced by [5].

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

Critical pair: bbc=c.

Referenced by [7], [8].

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

Critical pair: aac=bb.

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] abb=c with [5] bbc=c:

Critical pair: ac=cc.

Defines rule #1.

Referenced by [9], [10].

Overlap of [3] abb=c with [5] bbc=c:

Critical pair: abc=cbc.

Defines rule #5.

Referenced by [11].

Overlap of [1] aaa=1 with [7] ac=cc:

Critical pair: aacc=c.

Reduce LHS:

Defines rule #3.

Simplify [6] bb=aac.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] abb=c with [10] bb=ccc:

Critical pair: abccc=cb.

Reduce LHS:

Defines rule #4.

Overlap of [10] bb=ccc with [10] bb=ccc:

Critical pair: bccc=cccb.

Flip LHS and RHS.

Defines rule #6.