Certificate for #4042 ⟨a, b | aaabbbaba=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: aaabbbaba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #11.

Referenced by [3], [4], [8], [11], [13], [17], [21].

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

Critical pair: aacaba=ab.

Defines rule #1.

Referenced by [4], [5], [6], [7], [8], [19].

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

Critical pair: aacabc=abbbb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [9], [12], [14], [20], [23].

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

Critical pair: aacabab=abacaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8], [9], [10], [11], [15], [16], [21].

Overlap of [3] aacaba=ab with [4] aacabc=cb:

Critical pair: aacabcb=abacabc.

Reduce LHS:

Defines rule #5.

Referenced by [12], [13], [18].

Overlap of [3] aacaba=ab with [5] abacaba=abb:

Critical pair: aacabb=abcaba.

Defines rule #8.

Referenced by [17], [18].

Overlap of [3] aacaba=ab with [5] abacaba=abb:

Critical pair: aacababb=abbacaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Referenced by [16], [22].

Overlap of [5] abacaba=abb with [4] aacabc=cb:

Critical pair: abacabcb=abbacabc.

Defines rule #15.

Referenced by [13].

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

Critical pair: abacabb=abbcaba.

Defines rule #14.

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

Critical pair: abacababb=abbbacaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [12], [13], [14], [15], [18].

Overlap of [4] aacabc=cb with [11] cacaba=cb:

Critical pair: aacabcb=cbacaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [23].

Overlap of [11] cacaba=cb with [2] abbb=c:

Critical pair: cacabc=cbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #22.

Overlap of [11] cacaba=cb with [4] aacabc=cb:

Critical pair: cacabcb=cbacabc.

Defines rule #10.

Overlap of [11] cacaba=cb with [5] abacaba=abb:

Critical pair: cacabb=cbcaba.

Defines rule #9.

Overlap of [8] abbacaba=c with [5] abacaba=abb:

Critical pair: abbacabb=ccaba.

Defines rule #21.

Overlap of [7] aacabb=abcaba with [2] abbb=c:

Critical pair: aacc=abcabab.

Flip LHS and RHS.

Defines rule #13.

Referenced by [19], [20], [21], [22].

Overlap of [11] cacaba=cb with [7] aacabb=abcaba:

Critical pair: cacababcaba=cbacabb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #18.

Overlap of [3] aacaba=ab with [17] abcabab=aacc:

Critical pair: aacabaacc=abbcabab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #20.

Overlap of [4] aacabc=cb with [17] abcabab=aacc:

Critical pair: aacaacc=cbabab.

Flip LHS and RHS.

Defines rule #16.

Overlap of [5] abacaba=abb with [17] abcabab=aacc:

Critical pair: abacabaacc=abbbcabab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [8] abbacaba=c with [17] abcabab=aacc:

Critical pair: abbacabaacc=cbcabab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #17.

Overlap of [12] cbacaba=abacabc with [4] aacabc=cb:

Critical pair: cbacabcb=abacabcacabc.

Defines rule #19.