Certificate for #4846 ⟨a, b | ababbbba=aab⟩

Completion settings:

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

Axiom: ababbbba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #5.

Referenced by [3], [5], [6], [9].

Simplify [1] ababbbba=aab.

Reduce RHS:

Defines rule #14.

Referenced by [4], [5], [6], [7], [8], [10], [15].

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

Critical pair: ababbbbc=cbabbbba.

Referenced by [5], [10], [16].

Overlap of [3] ababbbba=c with [2] aab=c:

Critical pair: ababbbbc=cab.

Reduce LHS:

Defines rule #3.

Referenced by [7], [8], [9], [10], [11], [16].

Overlap of [2] aab=c with [3] ababbbba=c:

Critical pair: ac=cabbbba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [12], [13].

Overlap of [6] cabbbba=ac with [3] ababbbba=c:

Critical pair: cabbbbc=acbabbbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [10], [11], [12], [13], [14].

Overlap of [5] cbabbbba=cab with [3] ababbbba=c:

Critical pair: cbabbbbc=cabbabbbba.

Flip LHS and RHS.

Defines rule #15.

Overlap of [5] cbabbbba=cab with [2] aab=c:

Critical pair: cbabbbbc=cabab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10], [14], [15], [17].

Overlap of [3] ababbbba=c with [7] acab=cabbbbc:

Critical pair: ababbbbcabbbbc=ccab.

Reduce LHS:

Defines rule #1.

Overlap of [5] cbabbbba=cab with [7] acab=cabbbbc:

Critical pair: cbabbbbcabbbbc=cabcab.

Defines rule #13.

Overlap of [6] cabbbba=ac with [7] acab=cabbbbc:

Critical pair: cabbbbcabbbbc=accab.

Defines rule #12.

Overlap of [7] acab=cabbbbc with [6] cabbbba=ac:

Critical pair: aac=cabbbbcbbba.

Defines rule #8.

Overlap of [7] acab=cabbbbc with [9] cabab=cbabbbbc:

Critical pair: acbabbbbc=cabbbbcab.

Defines rule #11.

Overlap of [9] cabab=cbabbbbc with [3] ababbbba=c:

Critical pair: cc=cbabbbbcbbba.

Flip LHS and RHS.

Defines rule #4.

Simplify [4] ababbbbc=cbabbbba.

Reduce RHS:

Defines rule #9.

Referenced by [17].

Overlap of [16] ababbbbc=cab with [9] cabab=cbabbbbc:

Critical pair: ababbbbcbabbbbc=cababab.

Reduce LHS:

Reduce RHS:

Defines rule #10.