| Back: | ⟨a, b | ababaabab=ba⟩ |
|---|
Completion settings:
Axiom: ababaabab=ba.
Referenced by [4].
Axiom: aabab=c.
Referenced by [6].
Axiom: ba=d.
Defines rule #7.
Referenced by [4], [5], [6], [7], [8], [9], [10], [12].
Simplify [1] ababaabab=ba.
Reduce RHS:
| [3] | (ba) |
| ⇒ d |
Referenced by [5].
Overlap of [4] ababaabab=d with [3] ba=d:
Critical pair: adbaabab=d.
Reduce LHS:
| [3] | ad(ba)abab |
| [3] | ⇒ adda(ba)b |
| ⇒ addadb |
Referenced by [9], [10], [11], [16].
Overlap of [2] aabab=c with [3] ba=d:
Critical pair: aadb=c.
Referenced by [7], [8], [11], [17].
Overlap of [3] ba=d with [6] aadb=c:
Critical pair: bc=dadb.
Overlap of [6] aadb=c with [3] ba=d:
Critical pair: aadd=ca.
Overlap of [3] ba=d with [5] addadb=d:
Critical pair: bd=dddadb.
Referenced by [14].
Overlap of [5] addadb=d with [3] ba=d:
Critical pair: addadd=da.
Referenced by [13].
Overlap of [8] aadd=ca with [5] addadb=d:
Critical pair: ad=caadb.
Reduce RHS:
| [6] | c(aadb) |
| ⇒ cc |
Defines rule #1.
Referenced by [12], [13], [14], [16], [17], [18], [19].
Overlap of [3] ba=d with [11] ad=cc:
Critical pair: bcc=dd.
Reduce LHS:
| [7] | (bc)c |
| [11] | ⇒ d(ad)bc |
| [7] | ⇒ dcc(bc) |
| [11] | ⇒ dccd(ad)b |
| ⇒ dccdccb |
Referenced by [15].
Simplify [10] addadd=da.
Reduce LHS:
| [11] | (ad)dadd |
| [11] | ⇒ ccd(ad)d |
| ⇒ ccdccd |
Defines rule #4.
Referenced by [15].
Simplify [9] bd=dddadb.
Reduce RHS:
| [11] | ddd(ad)b |
| ⇒ dddccb |
Defines rule #9.
Overlap of [13] ccdccd=da with [12] dccdccb=dd:
Critical pair: ccdd=daccb.
Flip LHS and RHS.
Referenced by [20].
Overlap of [5] addadb=d with [11] ad=cc:
Critical pair: ccdadb=d.
Reduce LHS:
| [11] | ccd(ad)b |
| ⇒ ccdccb |
Defines rule #6.
Overlap of [6] aadb=c with [11] ad=cc:
Critical pair: accb=c.
Defines rule #5.
Referenced by [20].
Simplify [7] bc=dadb.
Reduce RHS:
| [11] | d(ad)b |
| ⇒ dccb |
Defines rule #8.
Overlap of [8] aadd=ca with [11] ad=cc:
Critical pair: accd=ca.
Defines rule #2.
Overlap of [15] daccb=ccdd with [17] accb=c:
Critical pair: dc=ccdd.
Flip LHS and RHS.
Defines rule #3.