Certificate for #4203 ⟨a, b | aabbbabba=ab⟩

Completion settings:

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

Axiom: aabbbabba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #4.

Referenced by [3], [4], [7], [9], [11], [17], [22].

Overlap of [1] aabbbabba=ab with [2] abbb=c:

Critical pair: acabba=ab.

Defines rule #1.

Referenced by [4], [5], [6], [7], [16].

Overlap of [3] acabba=ab with [2] abbb=c:

Critical pair: acabbc=abbbb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [8], [10], [12], [14], [16], [18].

Overlap of [3] acabba=ab with [3] acabba=ab:

Critical pair: acabbab=abcabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [13], [19], [23].

Overlap of [3] acabba=ab with [4] acabbc=cb:

Critical pair: acabbcb=abcabbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [8], [19], [20], [21], [23].

Overlap of [3] acabba=ab with [5] abcabba=abb:

Critical pair: acabbabb=abbcabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [14], [15].

Overlap of [5] abcabba=abb with [4] acabbc=cb:

Critical pair: abcabbcb=abbcabbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Referenced by [24].

Overlap of [5] abcabba=abb with [5] abcabba=abb:

Critical pair: abcabbabb=abbbcabba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11], [12], [13], [15], [20].

Overlap of [4] acabbc=cb with [9] ccabba=cb:

Critical pair: acabbcb=cbcabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [21], [24].

Overlap of [9] ccabba=cb with [2] abbb=c:

Critical pair: ccabbc=cbbbb.

Flip LHS and RHS.

Defines rule #13.

Referenced by [24].

Overlap of [9] ccabba=cb with [4] acabbc=cb:

Critical pair: ccabbcb=cbcabbc.

Defines rule #10.

Referenced by [20].

Overlap of [9] ccabba=cb with [5] abcabba=abb:

Critical pair: ccabbabb=cbbcabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.

Overlap of [4] acabbc=cb with [7] abbcabba=c:

Critical pair: acc=cbabba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [16], [17], [18], [19].

Overlap of [9] ccabba=cb with [7] abbcabba=c:

Critical pair: ccabbc=cbbbcabba.

Flip LHS and RHS.

Defines rule #21.

Overlap of [4] acabbc=cb with [14] cbabba=acc:

Critical pair: acabbacc=cbbabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Referenced by [22].

Overlap of [14] cbabba=acc with [2] abbb=c:

Critical pair: cbabbc=accbbb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [23].

Overlap of [14] cbabba=acc with [4] acabbc=cb:

Critical pair: cbabbcb=acccabbc.

Defines rule #17.

Overlap of [6] abcabbc=cbb with [14] cbabba=acc:

Critical pair: abcabbacc=cbbbabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #19.

Overlap of [9] ccabba=cb with [6] abcabbc=cbb:

Critical pair: ccabbcbb=cbbcabbc.

Reduce LHS:

Defines rule #18.

Referenced by [21], [24].

Overlap of [10] cbcabba=cbb with [6] abcabbc=cbb:

Critical pair: cbcabbcbb=cbbbcabbc.

Reduce LHS:

Defines rule #22.

Referenced by [24].

Overlap of [16] cbbabba=abcc with [2] abbb=c:

Critical pair: cbbabbc=abccbbb.

Defines rule #15.

Overlap of [5] abcabba=abb with [17] accbbb=cbabbc:

Critical pair: abcabbcbabbc=abbccbbb.

Reduce LHS:

Defines rule #20.

Overlap of [10] cbcabba=cbb with [8] abbcabbc=cbbb:

Critical pair: cbcabbcbbb=cbbbbcabbc.

Reduce LHS:

Reduce RHS:

Defines rule #23.