Certificate for #25251 ⟨a, b | aa=a, bbabb=abb⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #11.

Referenced by [6], [12].

Axiom: bbabb=abb.

Referenced by [4].

Axiom: bab=c.

Defines rule #9.

Referenced by [4], [5], [7], [8], [10].

Overlap of [2] bbabb=abb with [3] bab=c:

Critical pair: bcb=abb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6], [7], [8], [9], [11].

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

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #10.

Overlap of [1] aa=a with [4] abb=bcb:

Critical pair: abcb=abb.

Reduce RHS:

Referenced by [14].

Overlap of [3] bab=c with [4] abb=bcb:

Critical pair: bbcb=cb.

Defines rule #3.

Referenced by [9], [10], [15].

Overlap of [4] abb=bcb with [3] bab=c:

Critical pair: abc=bcbab.

Reduce RHS:

Defines rule #6.

Referenced by [12], [14].

Overlap of [4] abb=bcb with [7] bbcb=cb:

Critical pair: acb=bcbcb.

Defines rule #7.

Overlap of [7] bbcb=cb with [3] bab=c:

Critical pair: bbcc=cbab.

Reduce RHS:

Defines rule #4.

Referenced by [11], [13], [15].

Overlap of [4] abb=bcb with [10] bbcc=cc:

Critical pair: acc=bcbcc.

Defines rule #8.

Overlap of [1] aa=a with [8] abc=bcc:

Critical pair: abcc=abc.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [10] bbcc=cc with [12] bccc=bcc:

Critical pair: bbcc=ccc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Simplify [6] abcb=bcb.

Reduce LHS:

Referenced by [15].

Overlap of [10] bbcc=cc with [14] bccb=bcb:

Critical pair: bbcb=ccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.