Certification Problem
Input (TPDB SRS_Standard/Zantema_04/z082)
The rewrite relation of the following TRS is considered.
|
a(c(a(x1))) |
→ |
c(a(c(x1))) |
(1) |
|
a(a(b(x1))) |
→ |
a(d(b(x1))) |
(2) |
|
a(b(x1)) |
→ |
b(a(a(x1))) |
(3) |
|
d(d(x1)) |
→ |
a(d(b(x1))) |
(4) |
|
b(b(x1)) |
→ |
b(c(x1)) |
(5) |
|
a(d(c(x1))) |
→ |
c(a(x1)) |
(6) |
|
b(c(x1)) |
→ |
a(a(a(x1))) |
(7) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Closure Under Flat Contexts
Using the flat contexts
{a(☐), c(☐), b(☐), d(☐)}
We obtain the transformed TRS
|
a(a(b(x1))) |
→ |
a(d(b(x1))) |
(2) |
|
b(b(x1)) |
→ |
b(c(x1)) |
(5) |
|
a(a(c(a(x1)))) |
→ |
a(c(a(c(x1)))) |
(8) |
|
c(a(c(a(x1)))) |
→ |
c(c(a(c(x1)))) |
(9) |
|
b(a(c(a(x1)))) |
→ |
b(c(a(c(x1)))) |
(10) |
|
d(a(c(a(x1)))) |
→ |
d(c(a(c(x1)))) |
(11) |
|
a(a(b(x1))) |
→ |
a(b(a(a(x1)))) |
(12) |
|
c(a(b(x1))) |
→ |
c(b(a(a(x1)))) |
(13) |
|
b(a(b(x1))) |
→ |
b(b(a(a(x1)))) |
(14) |
|
d(a(b(x1))) |
→ |
d(b(a(a(x1)))) |
(15) |
|
a(d(d(x1))) |
→ |
a(a(d(b(x1)))) |
(16) |
|
c(d(d(x1))) |
→ |
c(a(d(b(x1)))) |
(17) |
|
b(d(d(x1))) |
→ |
b(a(d(b(x1)))) |
(18) |
|
d(d(d(x1))) |
→ |
d(a(d(b(x1)))) |
(19) |
|
a(a(d(c(x1)))) |
→ |
a(c(a(x1))) |
(20) |
|
c(a(d(c(x1)))) |
→ |
c(c(a(x1))) |
(21) |
|
b(a(d(c(x1)))) |
→ |
b(c(a(x1))) |
(22) |
|
d(a(d(c(x1)))) |
→ |
d(c(a(x1))) |
(23) |
|
a(b(c(x1))) |
→ |
a(a(a(a(x1)))) |
(24) |
|
c(b(c(x1))) |
→ |
c(a(a(a(x1)))) |
(25) |
|
b(b(c(x1))) |
→ |
b(a(a(a(x1)))) |
(26) |
|
d(b(c(x1))) |
→ |
d(a(a(a(x1)))) |
(27) |
1.1 Semantic Labeling
Root-labeling is applied.
We obtain the labeled TRS
|
aa(ab(ba(x1))) |
→ |
ad(db(ba(x1))) |
(28) |
|
aa(ab(bb(x1))) |
→ |
ad(db(bb(x1))) |
(29) |
|
aa(ab(bd(x1))) |
→ |
ad(db(bd(x1))) |
(30) |
|
aa(ab(bc(x1))) |
→ |
ad(db(bc(x1))) |
(31) |
|
bb(ba(x1)) |
→ |
bc(ca(x1)) |
(32) |
|
bb(bb(x1)) |
→ |
bc(cb(x1)) |
(33) |
|
bb(bd(x1)) |
→ |
bc(cd(x1)) |
(34) |
|
bb(bc(x1)) |
→ |
bc(cc(x1)) |
(35) |
|
aa(ac(ca(aa(x1)))) |
→ |
ac(ca(ac(ca(x1)))) |
(36) |
|
aa(ac(ca(ab(x1)))) |
→ |
ac(ca(ac(cb(x1)))) |
(37) |
|
aa(ac(ca(ad(x1)))) |
→ |
ac(ca(ac(cd(x1)))) |
(38) |
|
aa(ac(ca(ac(x1)))) |
→ |
ac(ca(ac(cc(x1)))) |
(39) |
|
ca(ac(ca(aa(x1)))) |
→ |
cc(ca(ac(ca(x1)))) |
(40) |
|
ca(ac(ca(ab(x1)))) |
→ |
cc(ca(ac(cb(x1)))) |
(41) |
|
ca(ac(ca(ad(x1)))) |
→ |
cc(ca(ac(cd(x1)))) |
(42) |
|
ca(ac(ca(ac(x1)))) |
→ |
cc(ca(ac(cc(x1)))) |
(43) |
|
ba(ac(ca(aa(x1)))) |
→ |
bc(ca(ac(ca(x1)))) |
(44) |
|
ba(ac(ca(ab(x1)))) |
→ |
bc(ca(ac(cb(x1)))) |
(45) |
|
ba(ac(ca(ad(x1)))) |
→ |
bc(ca(ac(cd(x1)))) |
(46) |
|
ba(ac(ca(ac(x1)))) |
→ |
bc(ca(ac(cc(x1)))) |
(47) |
|
da(ac(ca(aa(x1)))) |
→ |
dc(ca(ac(ca(x1)))) |
(48) |
|
da(ac(ca(ab(x1)))) |
→ |
dc(ca(ac(cb(x1)))) |
(49) |
|
da(ac(ca(ad(x1)))) |
→ |
dc(ca(ac(cd(x1)))) |
(50) |
|
da(ac(ca(ac(x1)))) |
→ |
dc(ca(ac(cc(x1)))) |
(51) |
|
aa(ab(ba(x1))) |
→ |
ab(ba(aa(aa(x1)))) |
(52) |
|
aa(ab(bb(x1))) |
→ |
ab(ba(aa(ab(x1)))) |
(53) |
|
aa(ab(bd(x1))) |
→ |
ab(ba(aa(ad(x1)))) |
(54) |
|
aa(ab(bc(x1))) |
→ |
ab(ba(aa(ac(x1)))) |
(55) |
|
ca(ab(ba(x1))) |
→ |
cb(ba(aa(aa(x1)))) |
(56) |
|
ca(ab(bb(x1))) |
→ |
cb(ba(aa(ab(x1)))) |
(57) |
|
ca(ab(bd(x1))) |
→ |
cb(ba(aa(ad(x1)))) |
(58) |
|
ca(ab(bc(x1))) |
→ |
cb(ba(aa(ac(x1)))) |
(59) |
|
ba(ab(ba(x1))) |
→ |
bb(ba(aa(aa(x1)))) |
(60) |
|
ba(ab(bb(x1))) |
→ |
bb(ba(aa(ab(x1)))) |
(61) |
|
ba(ab(bd(x1))) |
→ |
bb(ba(aa(ad(x1)))) |
(62) |
|
ba(ab(bc(x1))) |
→ |
bb(ba(aa(ac(x1)))) |
(63) |
|
da(ab(ba(x1))) |
→ |
db(ba(aa(aa(x1)))) |
(64) |
|
da(ab(bb(x1))) |
→ |
db(ba(aa(ab(x1)))) |
(65) |
|
da(ab(bd(x1))) |
→ |
db(ba(aa(ad(x1)))) |
(66) |
|
da(ab(bc(x1))) |
→ |
db(ba(aa(ac(x1)))) |
(67) |
|
ad(dd(da(x1))) |
→ |
aa(ad(db(ba(x1)))) |
(68) |
|
ad(dd(db(x1))) |
→ |
aa(ad(db(bb(x1)))) |
(69) |
|
ad(dd(dd(x1))) |
→ |
aa(ad(db(bd(x1)))) |
(70) |
|
ad(dd(dc(x1))) |
→ |
aa(ad(db(bc(x1)))) |
(71) |
|
cd(dd(da(x1))) |
→ |
ca(ad(db(ba(x1)))) |
(72) |
|
cd(dd(db(x1))) |
→ |
ca(ad(db(bb(x1)))) |
(73) |
|
cd(dd(dd(x1))) |
→ |
ca(ad(db(bd(x1)))) |
(74) |
|
cd(dd(dc(x1))) |
→ |
ca(ad(db(bc(x1)))) |
(75) |
|
bd(dd(da(x1))) |
→ |
ba(ad(db(ba(x1)))) |
(76) |
|
bd(dd(db(x1))) |
→ |
ba(ad(db(bb(x1)))) |
(77) |
|
bd(dd(dd(x1))) |
→ |
ba(ad(db(bd(x1)))) |
(78) |
|
bd(dd(dc(x1))) |
→ |
ba(ad(db(bc(x1)))) |
(79) |
|
dd(dd(da(x1))) |
→ |
da(ad(db(ba(x1)))) |
(80) |
|
dd(dd(db(x1))) |
→ |
da(ad(db(bb(x1)))) |
(81) |
|
dd(dd(dd(x1))) |
→ |
da(ad(db(bd(x1)))) |
(82) |
|
dd(dd(dc(x1))) |
→ |
da(ad(db(bc(x1)))) |
(83) |
|
aa(ad(dc(ca(x1)))) |
→ |
ac(ca(aa(x1))) |
(84) |
|
aa(ad(dc(cb(x1)))) |
→ |
ac(ca(ab(x1))) |
(85) |
|
aa(ad(dc(cd(x1)))) |
→ |
ac(ca(ad(x1))) |
(86) |
|
aa(ad(dc(cc(x1)))) |
→ |
ac(ca(ac(x1))) |
(87) |
|
ca(ad(dc(ca(x1)))) |
→ |
cc(ca(aa(x1))) |
(88) |
|
ca(ad(dc(cb(x1)))) |
→ |
cc(ca(ab(x1))) |
(89) |
|
ca(ad(dc(cd(x1)))) |
→ |
cc(ca(ad(x1))) |
(90) |
|
ca(ad(dc(cc(x1)))) |
→ |
cc(ca(ac(x1))) |
(91) |
|
ba(ad(dc(ca(x1)))) |
→ |
bc(ca(aa(x1))) |
(92) |
|
ba(ad(dc(cb(x1)))) |
→ |
bc(ca(ab(x1))) |
(93) |
|
ba(ad(dc(cd(x1)))) |
→ |
bc(ca(ad(x1))) |
(94) |
|
ba(ad(dc(cc(x1)))) |
→ |
bc(ca(ac(x1))) |
(95) |
|
da(ad(dc(ca(x1)))) |
→ |
dc(ca(aa(x1))) |
(96) |
|
da(ad(dc(cb(x1)))) |
→ |
dc(ca(ab(x1))) |
(97) |
|
da(ad(dc(cd(x1)))) |
→ |
dc(ca(ad(x1))) |
(98) |
|
da(ad(dc(cc(x1)))) |
→ |
dc(ca(ac(x1))) |
(99) |
|
ab(bc(ca(x1))) |
→ |
aa(aa(aa(aa(x1)))) |
(100) |
|
ab(bc(cb(x1))) |
→ |
aa(aa(aa(ab(x1)))) |
(101) |
|
ab(bc(cd(x1))) |
→ |
aa(aa(aa(ad(x1)))) |
(102) |
|
ab(bc(cc(x1))) |
→ |
aa(aa(aa(ac(x1)))) |
(103) |
|
cb(bc(ca(x1))) |
→ |
ca(aa(aa(aa(x1)))) |
(104) |
|
cb(bc(cb(x1))) |
→ |
ca(aa(aa(ab(x1)))) |
(105) |
|
cb(bc(cd(x1))) |
→ |
ca(aa(aa(ad(x1)))) |
(106) |
|
cb(bc(cc(x1))) |
→ |
ca(aa(aa(ac(x1)))) |
(107) |
|
bb(bc(ca(x1))) |
→ |
ba(aa(aa(aa(x1)))) |
(108) |
|
bb(bc(cb(x1))) |
→ |
ba(aa(aa(ab(x1)))) |
(109) |
|
bb(bc(cd(x1))) |
→ |
ba(aa(aa(ad(x1)))) |
(110) |
|
bb(bc(cc(x1))) |
→ |
ba(aa(aa(ac(x1)))) |
(111) |
|
db(bc(ca(x1))) |
→ |
da(aa(aa(aa(x1)))) |
(112) |
|
db(bc(cb(x1))) |
→ |
da(aa(aa(ab(x1)))) |
(113) |
|
db(bc(cd(x1))) |
→ |
da(aa(aa(ad(x1)))) |
(114) |
|
db(bc(cc(x1))) |
→ |
da(aa(aa(ac(x1)))) |
(115) |
1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [aa(x1)] |
= |
1 · x1
|
| [ab(x1)] |
= |
1 · x1 + 3 |
| [ba(x1)] |
= |
1 · x1
|
| [ad(x1)] |
= |
1 · x1
|
| [db(x1)] |
= |
1 · x1 + 3 |
| [bb(x1)] |
= |
1 · x1 + 3 |
| [bd(x1)] |
= |
1 · x1 + 1 |
| [bc(x1)] |
= |
1 · x1
|
| [ca(x1)] |
= |
1 · x1
|
| [cb(x1)] |
= |
1 · x1 + 3 |
| [cd(x1)] |
= |
1 · x1
|
| [cc(x1)] |
= |
1 · x1
|
| [ac(x1)] |
= |
1 · x1
|
| [da(x1)] |
= |
1 · x1 + 2 |
| [dc(x1)] |
= |
1 · x1 + 1 |
| [dd(x1)] |
= |
1 · x1 + 4 |
all of the following rules can be deleted.
|
bb(ba(x1)) |
→ |
bc(ca(x1)) |
(32) |
|
bb(bb(x1)) |
→ |
bc(cb(x1)) |
(33) |
|
bb(bd(x1)) |
→ |
bc(cd(x1)) |
(34) |
|
bb(bc(x1)) |
→ |
bc(cc(x1)) |
(35) |
|
da(ac(ca(aa(x1)))) |
→ |
dc(ca(ac(ca(x1)))) |
(48) |
|
da(ac(ca(ab(x1)))) |
→ |
dc(ca(ac(cb(x1)))) |
(49) |
|
da(ac(ca(ad(x1)))) |
→ |
dc(ca(ac(cd(x1)))) |
(50) |
|
da(ac(ca(ac(x1)))) |
→ |
dc(ca(ac(cc(x1)))) |
(51) |
|
aa(ab(bd(x1))) |
→ |
ab(ba(aa(ad(x1)))) |
(54) |
|
ca(ab(bd(x1))) |
→ |
cb(ba(aa(ad(x1)))) |
(58) |
|
ba(ab(bd(x1))) |
→ |
bb(ba(aa(ad(x1)))) |
(62) |
|
da(ab(ba(x1))) |
→ |
db(ba(aa(aa(x1)))) |
(64) |
|
da(ab(bb(x1))) |
→ |
db(ba(aa(ab(x1)))) |
(65) |
|
da(ab(bd(x1))) |
→ |
db(ba(aa(ad(x1)))) |
(66) |
|
da(ab(bc(x1))) |
→ |
db(ba(aa(ac(x1)))) |
(67) |
|
ad(dd(da(x1))) |
→ |
aa(ad(db(ba(x1)))) |
(68) |
|
ad(dd(db(x1))) |
→ |
aa(ad(db(bb(x1)))) |
(69) |
|
ad(dd(dd(x1))) |
→ |
aa(ad(db(bd(x1)))) |
(70) |
|
ad(dd(dc(x1))) |
→ |
aa(ad(db(bc(x1)))) |
(71) |
|
cd(dd(da(x1))) |
→ |
ca(ad(db(ba(x1)))) |
(72) |
|
cd(dd(db(x1))) |
→ |
ca(ad(db(bb(x1)))) |
(73) |
|
cd(dd(dd(x1))) |
→ |
ca(ad(db(bd(x1)))) |
(74) |
|
cd(dd(dc(x1))) |
→ |
ca(ad(db(bc(x1)))) |
(75) |
|
bd(dd(da(x1))) |
→ |
ba(ad(db(ba(x1)))) |
(76) |
|
bd(dd(db(x1))) |
→ |
ba(ad(db(bb(x1)))) |
(77) |
|
bd(dd(dd(x1))) |
→ |
ba(ad(db(bd(x1)))) |
(78) |
|
bd(dd(dc(x1))) |
→ |
ba(ad(db(bc(x1)))) |
(79) |
|
dd(dd(da(x1))) |
→ |
da(ad(db(ba(x1)))) |
(80) |
|
dd(dd(db(x1))) |
→ |
da(ad(db(bb(x1)))) |
(81) |
|
dd(dd(dd(x1))) |
→ |
da(ad(db(bd(x1)))) |
(82) |
|
dd(dd(dc(x1))) |
→ |
da(ad(db(bc(x1)))) |
(83) |
|
aa(ad(dc(ca(x1)))) |
→ |
ac(ca(aa(x1))) |
(84) |
|
aa(ad(dc(cb(x1)))) |
→ |
ac(ca(ab(x1))) |
(85) |
|
aa(ad(dc(cd(x1)))) |
→ |
ac(ca(ad(x1))) |
(86) |
|
aa(ad(dc(cc(x1)))) |
→ |
ac(ca(ac(x1))) |
(87) |
|
ca(ad(dc(ca(x1)))) |
→ |
cc(ca(aa(x1))) |
(88) |
|
ca(ad(dc(cb(x1)))) |
→ |
cc(ca(ab(x1))) |
(89) |
|
ca(ad(dc(cd(x1)))) |
→ |
cc(ca(ad(x1))) |
(90) |
|
ca(ad(dc(cc(x1)))) |
→ |
cc(ca(ac(x1))) |
(91) |
|
ba(ad(dc(ca(x1)))) |
→ |
bc(ca(aa(x1))) |
(92) |
|
ba(ad(dc(cb(x1)))) |
→ |
bc(ca(ab(x1))) |
(93) |
|
ba(ad(dc(cd(x1)))) |
→ |
bc(ca(ad(x1))) |
(94) |
|
ba(ad(dc(cc(x1)))) |
→ |
bc(ca(ac(x1))) |
(95) |
|
da(ad(dc(ca(x1)))) |
→ |
dc(ca(aa(x1))) |
(96) |
|
da(ad(dc(cb(x1)))) |
→ |
dc(ca(ab(x1))) |
(97) |
|
da(ad(dc(cd(x1)))) |
→ |
dc(ca(ad(x1))) |
(98) |
|
da(ad(dc(cc(x1)))) |
→ |
dc(ca(ac(x1))) |
(99) |
|
ab(bc(ca(x1))) |
→ |
aa(aa(aa(aa(x1)))) |
(100) |
|
ab(bc(cb(x1))) |
→ |
aa(aa(aa(ab(x1)))) |
(101) |
|
ab(bc(cd(x1))) |
→ |
aa(aa(aa(ad(x1)))) |
(102) |
|
ab(bc(cc(x1))) |
→ |
aa(aa(aa(ac(x1)))) |
(103) |
|
cb(bc(ca(x1))) |
→ |
ca(aa(aa(aa(x1)))) |
(104) |
|
cb(bc(cb(x1))) |
→ |
ca(aa(aa(ab(x1)))) |
(105) |
|
cb(bc(cd(x1))) |
→ |
ca(aa(aa(ad(x1)))) |
(106) |
|
cb(bc(cc(x1))) |
→ |
ca(aa(aa(ac(x1)))) |
(107) |
|
bb(bc(ca(x1))) |
→ |
ba(aa(aa(aa(x1)))) |
(108) |
|
bb(bc(cb(x1))) |
→ |
ba(aa(aa(ab(x1)))) |
(109) |
|
bb(bc(cd(x1))) |
→ |
ba(aa(aa(ad(x1)))) |
(110) |
|
bb(bc(cc(x1))) |
→ |
ba(aa(aa(ac(x1)))) |
(111) |
|
db(bc(ca(x1))) |
→ |
da(aa(aa(aa(x1)))) |
(112) |
|
db(bc(cb(x1))) |
→ |
da(aa(aa(ab(x1)))) |
(113) |
|
db(bc(cd(x1))) |
→ |
da(aa(aa(ad(x1)))) |
(114) |
|
db(bc(cc(x1))) |
→ |
da(aa(aa(ac(x1)))) |
(115) |
1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [aa(x1)] |
= |
1 · x1
|
| [ab(x1)] |
= |
1 · x1 + 1 |
| [ba(x1)] |
= |
1 · x1
|
| [ad(x1)] |
= |
1 · x1 + 1 |
| [db(x1)] |
= |
1 · x1
|
| [bb(x1)] |
= |
1 · x1 + 1 |
| [bd(x1)] |
= |
1 · x1
|
| [bc(x1)] |
= |
1 · x1
|
| [ac(x1)] |
= |
1 · x1
|
| [ca(x1)] |
= |
1 · x1
|
| [cb(x1)] |
= |
1 · x1
|
| [cd(x1)] |
= |
1 · x1
|
| [cc(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
aa(ac(ca(ab(x1)))) |
→ |
ac(ca(ac(cb(x1)))) |
(37) |
|
aa(ac(ca(ad(x1)))) |
→ |
ac(ca(ac(cd(x1)))) |
(38) |
|
ca(ac(ca(ab(x1)))) |
→ |
cc(ca(ac(cb(x1)))) |
(41) |
|
ca(ac(ca(ad(x1)))) |
→ |
cc(ca(ac(cd(x1)))) |
(42) |
|
ba(ac(ca(ab(x1)))) |
→ |
bc(ca(ac(cb(x1)))) |
(45) |
|
ba(ac(ca(ad(x1)))) |
→ |
bc(ca(ac(cd(x1)))) |
(46) |
|
ca(ab(ba(x1))) |
→ |
cb(ba(aa(aa(x1)))) |
(56) |
|
ca(ab(bb(x1))) |
→ |
cb(ba(aa(ab(x1)))) |
(57) |
|
ca(ab(bc(x1))) |
→ |
cb(ba(aa(ac(x1)))) |
(59) |
1.1.1.1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [aa(x1)] |
= |
1 · x1
|
| [ab(x1)] |
= |
1 · x1 + 1 |
| [ba(x1)] |
= |
1 · x1
|
| [ad(x1)] |
= |
1 · x1
|
| [db(x1)] |
= |
1 · x1
|
| [bb(x1)] |
= |
1 · x1 + 1 |
| [bd(x1)] |
= |
1 · x1
|
| [bc(x1)] |
= |
1 · x1
|
| [ac(x1)] |
= |
1 · x1
|
| [ca(x1)] |
= |
1 · x1
|
| [cc(x1)] |
= |
1 · x1
|
all of the following rules can be deleted.
|
aa(ab(ba(x1))) |
→ |
ad(db(ba(x1))) |
(28) |
|
aa(ab(bb(x1))) |
→ |
ad(db(bb(x1))) |
(29) |
|
aa(ab(bd(x1))) |
→ |
ad(db(bd(x1))) |
(30) |
|
aa(ab(bc(x1))) |
→ |
ad(db(bc(x1))) |
(31) |
1.1.1.1.1.1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
aa#(ac(ca(aa(x1)))) |
→ |
ca#(ac(ca(x1))) |
(116) |
|
aa#(ac(ca(aa(x1)))) |
→ |
ca#(x1) |
(117) |
|
aa#(ac(ca(ac(x1)))) |
→ |
ca#(ac(cc(x1))) |
(118) |
|
ca#(ac(ca(aa(x1)))) |
→ |
ca#(ac(ca(x1))) |
(119) |
|
ca#(ac(ca(aa(x1)))) |
→ |
ca#(x1) |
(120) |
|
ca#(ac(ca(ac(x1)))) |
→ |
ca#(ac(cc(x1))) |
(121) |
|
ba#(ac(ca(aa(x1)))) |
→ |
ca#(ac(ca(x1))) |
(122) |
|
ba#(ac(ca(aa(x1)))) |
→ |
ca#(x1) |
(123) |
|
ba#(ac(ca(ac(x1)))) |
→ |
ca#(ac(cc(x1))) |
(124) |
|
aa#(ab(ba(x1))) |
→ |
ba#(aa(aa(x1))) |
(125) |
|
aa#(ab(ba(x1))) |
→ |
aa#(aa(x1)) |
(126) |
|
aa#(ab(ba(x1))) |
→ |
aa#(x1) |
(127) |
|
aa#(ab(bb(x1))) |
→ |
ba#(aa(ab(x1))) |
(128) |
|
aa#(ab(bb(x1))) |
→ |
aa#(ab(x1)) |
(129) |
|
aa#(ab(bc(x1))) |
→ |
ba#(aa(ac(x1))) |
(130) |
|
aa#(ab(bc(x1))) |
→ |
aa#(ac(x1)) |
(131) |
|
ba#(ab(ba(x1))) |
→ |
ba#(aa(aa(x1))) |
(132) |
|
ba#(ab(ba(x1))) |
→ |
aa#(aa(x1)) |
(133) |
|
ba#(ab(ba(x1))) |
→ |
aa#(x1) |
(134) |
|
ba#(ab(bb(x1))) |
→ |
ba#(aa(ab(x1))) |
(135) |
|
ba#(ab(bb(x1))) |
→ |
aa#(ab(x1)) |
(136) |
|
ba#(ab(bc(x1))) |
→ |
ba#(aa(ac(x1))) |
(137) |
|
ba#(ab(bc(x1))) |
→ |
aa#(ac(x1)) |
(138) |
1.1.1.1.1.1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.