Certificate for #964 ⟨a, b | aabbbba=ab⟩

Completion settings:

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

Axiom: aabbbba=ab.

Referenced by [4], [5], [6], [7], [13].

Axiom: babbbba=c.

Referenced by [3], [4], [5], [6], [8], [9], [14].

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

Critical pair: babbbc=cbbbba.

Referenced by [15].

Overlap of [1] aabbbba=ab with [1] aabbbba=ab:

Critical pair: aabbbbab=ababbbba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [5], [6], [7], [8], [13], [14], [16].

Overlap of [1] aabbbba=ab with [2] babbbba=c:

Critical pair: aabbbc=abbbbba.

Reduce LHS:

Reduce RHS:

Referenced by [17].

Overlap of [2] babbbba=c with [1] aabbbba=ab:

Critical pair: babbbbab=cabbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [1] aabbbba=ab with [4] abb=ac:

Critical pair: aabbbbac=abbb.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [9].

Overlap of [2] babbbba=c with [4] abb=ac:

Critical pair: babbbbac=cbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [12], [13], [14], [15], [17], [19], [20].

Overlap of [2] babbbba=c with [7] abc=acb:

Critical pair: babbbbacb=cbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [16], [18].

Simplify [6] cacbba=cb.

Reduce LHS:

Defines rule #10.

Referenced by [11].

Overlap of [10] cacca=cb with [10] cacca=cb:

Critical pair: caccb=cbcca.

Reduce RHS:

Defines rule #6.

Referenced by [12].

Overlap of [11] caccb=cccba with [8] cbb=cc:

Critical pair: caccc=cccbab.

Defines rule #8.

Overlap of [1] aabbbba=ab with [4] abb=ac:

Critical pair: aacbba=ab.

Reduce LHS:

Defines rule #13.

Overlap of [2] babbbba=c with [4] abb=ac:

Critical pair: bacbba=c.

Reduce LHS:

Defines rule #9.

Simplify [3] babbbc=cbbbba.

Reduce RHS:

Referenced by [16].

Overlap of [15] babbbc=ccca with [4] abb=ac:

Critical pair: bacbc=ccca.

Reduce LHS:

Defines rule #5.

Referenced by [19].

Simplify [5] aacbc=acbbba.

Reduce RHS:

Referenced by [18].

Overlap of [17] aacbc=accba with [9] cbc=ccb:

Critical pair: aaccb=accba.

Defines rule #11.

Referenced by [20].

Overlap of [16] baccb=ccca with [8] cbb=cc:

Critical pair: baccc=cccab.

Defines rule #7.

Overlap of [18] aaccb=accba with [8] cbb=cc:

Critical pair: aaccc=accbab.

Defines rule #12.