Certificate for #4128 ⟨a, b | aabababba=ab

Completion settings:

[1] aabababba=ab

Axiom: aabababba=ab.

Referenced by [3].

[2] bababba=c

Axiom: bababba=c.

Referenced by [3], [4].

[3] ab=aac

Overlap of [1] aabababba=ab with [2] bababba=c:

aa bababba bababba

Critical pair: aac=ab.

Flip LHS and RHS.

Defines rule #11.

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

[4] baacaacba=c

Overlap of [2] bababba=c with [3] ab=aac:

b ababba ab

Critical pair: baacabba=c.

Reduce LHS:

[3]baac(ab)ba
baacaacba

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

[5] aacaacaacba=ac

Overlap of [3] ab=aac with [4] baacaacba=c:

a b baacaacba

Critical pair: ac=aacaacaacba.

Flip LHS and RHS.

Referenced by [8].

[6] cb=cac

Overlap of [4] baacaacba=c with [3] ab=aac:

baacaacb a ab

Critical pair: baacaacbaac=cb.

Reduce LHS:

[4](baacaacba)ac
cac

Flip LHS and RHS.

Defines rule #10.

Referenced by [7], [8], [12], [13], [14].

[7] baacaacc=cacaacaca

Overlap of [4] baacaacba=c with [4] baacaacba=c:

baacaac ba baacaacba

Critical pair: baacaacc=cacaacba.

Reduce RHS:

[6]cacaa(cb)a
cacaacaca

Defines rule #7.

Referenced by [12].

[8] aacaacaacaca=ac

Simplify [5] aacaacaacba=ac.

Reduce LHS:

[6]aacaacaa(cb)a
aacaacaacaca

Defines rule #6.

Referenced by [9], [10], [11].

[9] acacaacaacaca=acc

Overlap of [8] aacaacaacaca=ac with [8] aacaacaacaca=ac:

aacaacaacac a aacaacaacaca

Critical pair: aacaacaacacac=acacaacaacaca.

Reduce LHS:

[8](aacaacaacaca)c
acc

Flip LHS and RHS.

Referenced by [10], [11], [15], [16].

[10] aacaacaacc=acacaacaca

Overlap of [8] aacaacaacaca=ac with [9] acacaacaacaca=acc:

aacaaca acaca acacaacaacaca

Critical pair: aacaacaacc=acacaacaca.

Defines rule #2.

[11] aacaacaacacc=accaacaacaca

Overlap of [8] aacaacaacaca=ac with [9] acacaacaacaca=acc:

aacaacaac aca acacaacaacaca

Critical pair: aacaacaacacc=accaacaacaca.

Defines rule #5.

[12] cacaacaacc=ccacaacaca

Overlap of [6] cb=cac with [7] baacaacc=cacaacaca:

c b baacaacc

Critical pair: ccacaacaca=cacaacaacc.

Flip LHS and RHS.

Defines rule #1.

[13] baacaacaca=c

Overlap of [4] baacaacba=c with [6] cb=cac:

baacaa cba cb

Critical pair: baacaacaca=c.

Defines rule #9.

Referenced by [14], [15].

[14] cacaacaacaca=cc

Overlap of [6] cb=cac with [13] baacaacaca=c:

c b baacaacaca

Critical pair: cc=cacaacaacaca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [16].

[15] baacaacacc=ccaacaacaca

Overlap of [13] baacaacaca=c with [9] acacaacaacaca=acc:

baacaac aca acacaacaacaca

Critical pair: baacaacacc=ccaacaacaca.

Defines rule #8.

[16] cacaacaacacc=cccaacaacaca

Overlap of [14] cacaacaacaca=cc with [9] acacaacaacaca=acc:

cacaacaac aca acacaacaacaca

Critical pair: cacaacaacacc=cccaacaacaca.

Defines rule #3.