Certificate for #3762 ⟨a, b | ababaabaab=b⟩

Completion settings:

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

Axiom: ababaabaab=b.

Referenced by [3].

Axiom: aba=c.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Overlap of [1] ababaabaab=b with [2] aba=c:

Critical pair: cbaabaab=b.

Reduce LHS:

Defines rule #8.

Referenced by [5], [6], [7], [8], [10].

Overlap of [2] aba=c with [2] aba=c:

Critical pair: abc=cba.

Defines rule #3.

Referenced by [6].

Overlap of [3] cbacab=b with [2] aba=c:

Critical pair: cbacc=ba.

Defines rule #2.

Referenced by [7].

Overlap of [4] abc=cba with [3] cbacab=b:

Critical pair: abb=cbabacab.

Reduce RHS:

Referenced by [11].

Overlap of [5] cbacc=ba with [3] cbacab=b:

Critical pair: cbacb=babacab.

Reduce RHS:

Defines rule #7.

Referenced by [8].

Overlap of [7] cbacb=bccab with [3] cbacab=b:

Critical pair: cbab=bccabacab.

Reduce RHS:

Defines rule #6.

Referenced by [9].

Overlap of [8] cbab=bccccab with [2] aba=c:

Critical pair: cbc=bccccaba.

Reduce RHS:

Defines rule #1.

Referenced by [10], [11].

Overlap of [9] cbc=bccccc with [3] cbacab=b:

Critical pair: cbb=bcccccbacab.

Reduce RHS:

Defines rule #5.

Simplify [6] abb=cbccab.

Reduce RHS:

Defines rule #9.