The rewrite relation of the following TRS is considered.
There are 103 ruless (increase limit for explicit display).
There are 131 ruless (increase limit for explicit display).
The dependency pairs are split into 21
components.
-
The
1st
component contains the
pair
top#(ok(X)) |
→ |
top#(active(X)) |
(234) |
top#(mark(X)) |
→ |
top#(proper(X)) |
(232) |
1.1.1 Reduction Pair Processor with Usable Rules
Using the
prec(top#) |
= |
0 |
|
stat(top#) |
= |
lex
|
prec(ok) |
= |
0 |
|
stat(ok) |
= |
lex
|
prec(proper) |
= |
0 |
|
stat(proper) |
= |
lex
|
prec(u) |
= |
1 |
|
stat(u) |
= |
lex
|
prec(o) |
= |
1 |
|
stat(o) |
= |
lex
|
prec(i) |
= |
1 |
|
stat(i) |
= |
lex
|
prec(e) |
= |
1 |
|
stat(e) |
= |
lex
|
prec(a) |
= |
1 |
|
stat(a) |
= |
lex
|
prec(isNePal) |
= |
2 |
|
stat(isNePal) |
= |
lex
|
prec(isQid) |
= |
0 |
|
stat(isQid) |
= |
lex
|
prec(U81) |
= |
1 |
|
stat(U81) |
= |
lex
|
prec(U72) |
= |
2 |
|
stat(U72) |
= |
lex
|
prec(isPal) |
= |
3 |
|
stat(isPal) |
= |
lex
|
prec(U71) |
= |
4 |
|
stat(U71) |
= |
lex
|
prec(U61) |
= |
1 |
|
stat(U61) |
= |
lex
|
prec(U52) |
= |
2 |
|
stat(U52) |
= |
lex
|
prec(U51) |
= |
4 |
|
stat(U51) |
= |
lex
|
prec(U42) |
= |
2 |
|
stat(U42) |
= |
lex
|
prec(isNeList) |
= |
2 |
|
stat(isNeList) |
= |
lex
|
prec(U41) |
= |
3 |
|
stat(U41) |
= |
lex
|
prec(U31) |
= |
1 |
|
stat(U31) |
= |
lex
|
prec(U22) |
= |
1 |
|
stat(U22) |
= |
lex
|
prec(isList) |
= |
3 |
|
stat(isList) |
= |
lex
|
prec(U21) |
= |
16 |
|
stat(U21) |
= |
lex
|
prec(U11) |
= |
1 |
|
stat(U11) |
= |
lex
|
prec(tt) |
= |
0 |
|
stat(tt) |
= |
lex
|
prec(nil) |
= |
1 |
|
stat(nil) |
= |
lex
|
prec(mark) |
= |
0 |
|
stat(mark) |
= |
lex
|
prec(active) |
= |
0 |
|
stat(active) |
= |
lex
|
prec(__) |
= |
23 |
|
stat(__) |
= |
lex
|
π(top#) |
= |
1 |
π(ok) |
= |
1 |
π(proper) |
= |
1 |
π(u) |
= |
[] |
π(o) |
= |
[] |
π(i) |
= |
[] |
π(e) |
= |
[] |
π(a) |
= |
[] |
π(isNePal) |
= |
[1] |
π(isQid) |
= |
1 |
π(U81) |
= |
[1] |
π(U72) |
= |
[1] |
π(isPal) |
= |
[1] |
π(U71) |
= |
[1,2] |
π(U61) |
= |
[1] |
π(U52) |
= |
[1] |
π(U51) |
= |
[1,2] |
π(U42) |
= |
[1] |
π(isNeList) |
= |
[1] |
π(U41) |
= |
[1,2] |
π(U31) |
= |
[1] |
π(U22) |
= |
[1] |
π(isList) |
= |
[1] |
π(U21) |
= |
[1,2] |
π(U11) |
= |
[1] |
π(tt) |
= |
[] |
π(nil) |
= |
[] |
π(mark) |
= |
[1] |
π(active) |
= |
1 |
π(__) |
= |
[1,2] |
together with the usable
rulesThere are 101 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
top#(mark(X)) |
→ |
top#(proper(X)) |
(232) |
could be deleted.
1.1.1.1 Reduction Pair Processor with Usable Rules
Using the
prec(top#) |
= |
0 |
|
stat(top#) |
= |
lex
|
prec(ok) |
= |
0 |
|
stat(ok) |
= |
lex
|
prec(u) |
= |
0 |
|
stat(u) |
= |
lex
|
prec(o) |
= |
0 |
|
stat(o) |
= |
lex
|
prec(i) |
= |
0 |
|
stat(i) |
= |
lex
|
prec(e) |
= |
0 |
|
stat(e) |
= |
lex
|
prec(a) |
= |
0 |
|
stat(a) |
= |
lex
|
prec(isNePal) |
= |
16 |
|
stat(isNePal) |
= |
lex
|
prec(isQid) |
= |
1 |
|
stat(isQid) |
= |
lex
|
prec(U81) |
= |
0 |
|
stat(U81) |
= |
lex
|
prec(U72) |
= |
1 |
|
stat(U72) |
= |
lex
|
prec(isPal) |
= |
1 |
|
stat(isPal) |
= |
lex
|
prec(U71) |
= |
3 |
|
stat(U71) |
= |
lex
|
prec(U61) |
= |
1 |
|
stat(U61) |
= |
lex
|
prec(U52) |
= |
1 |
|
stat(U52) |
= |
lex
|
prec(U51) |
= |
1 |
|
stat(U51) |
= |
lex
|
prec(U42) |
= |
1 |
|
stat(U42) |
= |
lex
|
prec(isNeList) |
= |
1 |
|
stat(isNeList) |
= |
lex
|
prec(U41) |
= |
1 |
|
stat(U41) |
= |
lex
|
prec(U31) |
= |
5 |
|
stat(U31) |
= |
lex
|
prec(U22) |
= |
3 |
|
stat(U22) |
= |
lex
|
prec(isList) |
= |
1 |
|
stat(isList) |
= |
lex
|
prec(U21) |
= |
1 |
|
stat(U21) |
= |
lex
|
prec(U11) |
= |
5 |
|
stat(U11) |
= |
lex
|
prec(tt) |
= |
1 |
|
stat(tt) |
= |
lex
|
prec(nil) |
= |
0 |
|
stat(nil) |
= |
lex
|
prec(mark) |
= |
0 |
|
stat(mark) |
= |
lex
|
prec(active) |
= |
0 |
|
stat(active) |
= |
lex
|
prec(__) |
= |
17 |
|
stat(__) |
= |
lex
|
π(top#) |
= |
1 |
π(ok) |
= |
[1] |
π(u) |
= |
[] |
π(o) |
= |
[] |
π(i) |
= |
[] |
π(e) |
= |
[] |
π(a) |
= |
[] |
π(isNePal) |
= |
[] |
π(isQid) |
= |
[] |
π(U81) |
= |
1 |
π(U72) |
= |
[1] |
π(isPal) |
= |
[] |
π(U71) |
= |
[1] |
π(U61) |
= |
[1] |
π(U52) |
= |
[1] |
π(U51) |
= |
[1] |
π(U42) |
= |
[1] |
π(isNeList) |
= |
[] |
π(U41) |
= |
[1] |
π(U31) |
= |
[1] |
π(U22) |
= |
[1] |
π(isList) |
= |
[] |
π(U21) |
= |
[1] |
π(U11) |
= |
[1] |
π(tt) |
= |
[] |
π(nil) |
= |
[] |
π(mark) |
= |
[] |
π(active) |
= |
1 |
π(__) |
= |
[1] |
together with the usable
rules
active(__(__(X,Y),Z)) |
→ |
mark(__(X,__(Y,Z))) |
(1) |
active(__(X,nil)) |
→ |
mark(X) |
(2) |
active(__(nil,X)) |
→ |
mark(X) |
(3) |
active(U11(tt)) |
→ |
mark(tt) |
(4) |
active(U21(tt,V2)) |
→ |
mark(U22(isList(V2))) |
(5) |
active(U22(tt)) |
→ |
mark(tt) |
(6) |
active(U31(tt)) |
→ |
mark(tt) |
(7) |
active(U41(tt,V2)) |
→ |
mark(U42(isNeList(V2))) |
(8) |
active(U42(tt)) |
→ |
mark(tt) |
(9) |
active(U51(tt,V2)) |
→ |
mark(U52(isList(V2))) |
(10) |
active(U52(tt)) |
→ |
mark(tt) |
(11) |
active(U61(tt)) |
→ |
mark(tt) |
(12) |
active(U71(tt,P)) |
→ |
mark(U72(isPal(P))) |
(13) |
active(U72(tt)) |
→ |
mark(tt) |
(14) |
active(U81(tt)) |
→ |
mark(tt) |
(15) |
active(isList(V)) |
→ |
mark(U11(isNeList(V))) |
(16) |
active(isList(nil)) |
→ |
mark(tt) |
(17) |
active(isList(__(V1,V2))) |
→ |
mark(U21(isList(V1),V2)) |
(18) |
active(isNeList(V)) |
→ |
mark(U31(isQid(V))) |
(19) |
active(isNeList(__(V1,V2))) |
→ |
mark(U41(isList(V1),V2)) |
(20) |
active(isNeList(__(V1,V2))) |
→ |
mark(U51(isNeList(V1),V2)) |
(21) |
active(isNePal(V)) |
→ |
mark(U61(isQid(V))) |
(22) |
active(isNePal(__(I,__(P,I)))) |
→ |
mark(U71(isQid(I),P)) |
(23) |
active(isPal(V)) |
→ |
mark(U81(isNePal(V))) |
(24) |
active(isPal(nil)) |
→ |
mark(tt) |
(25) |
active(isQid(a)) |
→ |
mark(tt) |
(26) |
active(isQid(e)) |
→ |
mark(tt) |
(27) |
active(isQid(i)) |
→ |
mark(tt) |
(28) |
active(isQid(o)) |
→ |
mark(tt) |
(29) |
active(isQid(u)) |
→ |
mark(tt) |
(30) |
active(__(X1,X2)) |
→ |
__(active(X1),X2) |
(31) |
active(__(X1,X2)) |
→ |
__(X1,active(X2)) |
(32) |
active(U11(X)) |
→ |
U11(active(X)) |
(33) |
active(U21(X1,X2)) |
→ |
U21(active(X1),X2) |
(34) |
active(U22(X)) |
→ |
U22(active(X)) |
(35) |
active(U31(X)) |
→ |
U31(active(X)) |
(36) |
active(U41(X1,X2)) |
→ |
U41(active(X1),X2) |
(37) |
active(U42(X)) |
→ |
U42(active(X)) |
(38) |
active(U51(X1,X2)) |
→ |
U51(active(X1),X2) |
(39) |
active(U52(X)) |
→ |
U52(active(X)) |
(40) |
active(U61(X)) |
→ |
U61(active(X)) |
(41) |
active(U71(X1,X2)) |
→ |
U71(active(X1),X2) |
(42) |
active(U72(X)) |
→ |
U72(active(X)) |
(43) |
active(U81(X)) |
→ |
U81(active(X)) |
(44) |
__(mark(X1),X2) |
→ |
mark(__(X1,X2)) |
(45) |
__(X1,mark(X2)) |
→ |
mark(__(X1,X2)) |
(46) |
__(ok(X1),ok(X2)) |
→ |
ok(__(X1,X2)) |
(84) |
U22(mark(X)) |
→ |
mark(U22(X)) |
(49) |
U22(ok(X)) |
→ |
ok(U22(X)) |
(87) |
U42(mark(X)) |
→ |
mark(U42(X)) |
(52) |
U42(ok(X)) |
→ |
ok(U42(X)) |
(91) |
U52(mark(X)) |
→ |
mark(U52(X)) |
(54) |
U52(ok(X)) |
→ |
ok(U52(X)) |
(94) |
U72(mark(X)) |
→ |
mark(U72(X)) |
(57) |
U72(ok(X)) |
→ |
ok(U72(X)) |
(97) |
U11(mark(X)) |
→ |
mark(U11(X)) |
(47) |
U11(ok(X)) |
→ |
ok(U11(X)) |
(85) |
U21(mark(X1),X2) |
→ |
mark(U21(X1,X2)) |
(48) |
U21(ok(X1),ok(X2)) |
→ |
ok(U21(X1,X2)) |
(86) |
U31(mark(X)) |
→ |
mark(U31(X)) |
(50) |
U31(ok(X)) |
→ |
ok(U31(X)) |
(89) |
U41(mark(X1),X2) |
→ |
mark(U41(X1,X2)) |
(51) |
U41(ok(X1),ok(X2)) |
→ |
ok(U41(X1,X2)) |
(90) |
U51(mark(X1),X2) |
→ |
mark(U51(X1,X2)) |
(53) |
U51(ok(X1),ok(X2)) |
→ |
ok(U51(X1,X2)) |
(93) |
U61(mark(X)) |
→ |
mark(U61(X)) |
(55) |
U61(ok(X)) |
→ |
ok(U61(X)) |
(95) |
U71(mark(X1),X2) |
→ |
mark(U71(X1,X2)) |
(56) |
U71(ok(X1),ok(X2)) |
→ |
ok(U71(X1,X2)) |
(96) |
U81(mark(X)) |
→ |
mark(U81(X)) |
(58) |
U81(ok(X)) |
→ |
ok(U81(X)) |
(99) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
top#(ok(X)) |
→ |
top#(active(X)) |
(234) |
could be deleted.
1.1.1.1.1 P is empty
There are no pairs anymore.
-
The
2nd
component contains the
pair
proper#(isNePal(X)) |
→ |
proper#(X) |
(211) |
proper#(isQid(X)) |
→ |
proper#(X) |
(209) |
proper#(U81(X)) |
→ |
proper#(X) |
(207) |
proper#(isPal(X)) |
→ |
proper#(X) |
(205) |
proper#(U72(X)) |
→ |
proper#(X) |
(203) |
proper#(U71(X1,X2)) |
→ |
proper#(X1) |
(201) |
proper#(U71(X1,X2)) |
→ |
proper#(X2) |
(200) |
proper#(U61(X)) |
→ |
proper#(X) |
(198) |
proper#(U52(X)) |
→ |
proper#(X) |
(196) |
proper#(U51(X1,X2)) |
→ |
proper#(X1) |
(194) |
proper#(U51(X1,X2)) |
→ |
proper#(X2) |
(193) |
proper#(isNeList(X)) |
→ |
proper#(X) |
(191) |
proper#(U42(X)) |
→ |
proper#(X) |
(189) |
proper#(U41(X1,X2)) |
→ |
proper#(X1) |
(187) |
proper#(U41(X1,X2)) |
→ |
proper#(X2) |
(186) |
proper#(U31(X)) |
→ |
proper#(X) |
(184) |
proper#(isList(X)) |
→ |
proper#(X) |
(182) |
proper#(U22(X)) |
→ |
proper#(X) |
(180) |
proper#(U21(X1,X2)) |
→ |
proper#(X1) |
(178) |
proper#(U21(X1,X2)) |
→ |
proper#(X2) |
(177) |
proper#(U11(X)) |
→ |
proper#(X) |
(175) |
proper#(__(X1,X2)) |
→ |
proper#(X1) |
(173) |
proper#(__(X1,X2)) |
→ |
proper#(X2) |
(172) |
1.1.2 Subterm Criterion Processor
We use the projection
and remove the pairs:
proper#(isNePal(X)) |
→ |
proper#(X) |
(211) |
proper#(isQid(X)) |
→ |
proper#(X) |
(209) |
proper#(U81(X)) |
→ |
proper#(X) |
(207) |
proper#(isPal(X)) |
→ |
proper#(X) |
(205) |
proper#(U72(X)) |
→ |
proper#(X) |
(203) |
proper#(U71(X1,X2)) |
→ |
proper#(X1) |
(201) |
proper#(U71(X1,X2)) |
→ |
proper#(X2) |
(200) |
proper#(U61(X)) |
→ |
proper#(X) |
(198) |
proper#(U52(X)) |
→ |
proper#(X) |
(196) |
proper#(U51(X1,X2)) |
→ |
proper#(X1) |
(194) |
proper#(U51(X1,X2)) |
→ |
proper#(X2) |
(193) |
proper#(isNeList(X)) |
→ |
proper#(X) |
(191) |
proper#(U42(X)) |
→ |
proper#(X) |
(189) |
proper#(U41(X1,X2)) |
→ |
proper#(X1) |
(187) |
proper#(U41(X1,X2)) |
→ |
proper#(X2) |
(186) |
proper#(U31(X)) |
→ |
proper#(X) |
(184) |
proper#(isList(X)) |
→ |
proper#(X) |
(182) |
proper#(U22(X)) |
→ |
proper#(X) |
(180) |
proper#(U21(X1,X2)) |
→ |
proper#(X1) |
(178) |
proper#(U21(X1,X2)) |
→ |
proper#(X2) |
(177) |
proper#(U11(X)) |
→ |
proper#(X) |
(175) |
proper#(__(X1,X2)) |
→ |
proper#(X1) |
(173) |
proper#(__(X1,X2)) |
→ |
proper#(X2) |
(172) |
1.1.2.1 P is empty
There are no pairs anymore.
-
The
3rd
component contains the
pair
active#(U81(X)) |
→ |
active#(X) |
(156) |
active#(U72(X)) |
→ |
active#(X) |
(154) |
active#(U71(X1,X2)) |
→ |
active#(X1) |
(152) |
active#(U61(X)) |
→ |
active#(X) |
(150) |
active#(U52(X)) |
→ |
active#(X) |
(148) |
active#(U51(X1,X2)) |
→ |
active#(X1) |
(146) |
active#(U42(X)) |
→ |
active#(X) |
(144) |
active#(U41(X1,X2)) |
→ |
active#(X1) |
(142) |
active#(U31(X)) |
→ |
active#(X) |
(140) |
active#(U22(X)) |
→ |
active#(X) |
(138) |
active#(U21(X1,X2)) |
→ |
active#(X1) |
(136) |
active#(U11(X)) |
→ |
active#(X) |
(134) |
active#(__(X1,X2)) |
→ |
active#(X2) |
(132) |
active#(__(X1,X2)) |
→ |
active#(X1) |
(130) |
1.1.3 Subterm Criterion Processor
We use the projection
and remove the pairs:
active#(U81(X)) |
→ |
active#(X) |
(156) |
active#(U72(X)) |
→ |
active#(X) |
(154) |
active#(U71(X1,X2)) |
→ |
active#(X1) |
(152) |
active#(U61(X)) |
→ |
active#(X) |
(150) |
active#(U52(X)) |
→ |
active#(X) |
(148) |
active#(U51(X1,X2)) |
→ |
active#(X1) |
(146) |
active#(U42(X)) |
→ |
active#(X) |
(144) |
active#(U41(X1,X2)) |
→ |
active#(X1) |
(142) |
active#(U31(X)) |
→ |
active#(X) |
(140) |
active#(U22(X)) |
→ |
active#(X) |
(138) |
active#(U21(X1,X2)) |
→ |
active#(X1) |
(136) |
active#(U11(X)) |
→ |
active#(X) |
(134) |
active#(__(X1,X2)) |
→ |
active#(X2) |
(132) |
active#(__(X1,X2)) |
→ |
active#(X1) |
(130) |
1.1.3.1 P is empty
There are no pairs anymore.
-
The
4th
component contains the
pair
isPal#(ok(X)) |
→ |
isPal#(X) |
(227) |
1.1.4 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
isPal#(ok(X)) |
→ |
isPal#(X) |
(227) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
5th
component contains the
pair
isList#(ok(X)) |
→ |
isList#(X) |
(217) |
1.1.5 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
isList#(ok(X)) |
→ |
isList#(X) |
(217) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
6th
component contains the
pair
isNeList#(ok(X)) |
→ |
isNeList#(X) |
(221) |
1.1.6 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
isNeList#(ok(X)) |
→ |
isNeList#(X) |
(221) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
7th
component contains the
pair
isQid#(ok(X)) |
→ |
isQid#(X) |
(229) |
1.1.7 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
isQid#(ok(X)) |
→ |
isQid#(X) |
(229) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
8th
component contains the
pair
isNePal#(ok(X)) |
→ |
isNePal#(X) |
(230) |
1.1.8 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
isNePal#(ok(X)) |
→ |
isNePal#(X) |
(230) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
9th
component contains the
pair
__#(ok(X1),ok(X2)) |
→ |
__#(X1,X2) |
(213) |
__#(X1,mark(X2)) |
→ |
__#(X1,X2) |
(159) |
__#(mark(X1),X2) |
→ |
__#(X1,X2) |
(158) |
1.1.9 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
__#(ok(X1),ok(X2)) |
→ |
__#(X1,X2) |
(213) |
|
2 |
> |
2 |
1 |
> |
1 |
__#(X1,mark(X2)) |
→ |
__#(X1,X2) |
(159) |
|
2 |
> |
2 |
1 |
≥ |
1 |
__#(mark(X1),X2) |
→ |
__#(X1,X2) |
(158) |
|
2 |
≥ |
2 |
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
10th
component contains the
pair
U11#(ok(X)) |
→ |
U11#(X) |
(214) |
U11#(mark(X)) |
→ |
U11#(X) |
(160) |
1.1.10 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U11#(ok(X)) |
→ |
U11#(X) |
(214) |
|
1 |
> |
1 |
U11#(mark(X)) |
→ |
U11#(X) |
(160) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
11th
component contains the
pair
U21#(ok(X1),ok(X2)) |
→ |
U21#(X1,X2) |
(215) |
U21#(mark(X1),X2) |
→ |
U21#(X1,X2) |
(161) |
1.1.11 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U21#(ok(X1),ok(X2)) |
→ |
U21#(X1,X2) |
(215) |
|
2 |
> |
2 |
1 |
> |
1 |
U21#(mark(X1),X2) |
→ |
U21#(X1,X2) |
(161) |
|
2 |
≥ |
2 |
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
12th
component contains the
pair
U22#(ok(X)) |
→ |
U22#(X) |
(216) |
U22#(mark(X)) |
→ |
U22#(X) |
(162) |
1.1.12 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U22#(ok(X)) |
→ |
U22#(X) |
(216) |
|
1 |
> |
1 |
U22#(mark(X)) |
→ |
U22#(X) |
(162) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
13th
component contains the
pair
U31#(ok(X)) |
→ |
U31#(X) |
(218) |
U31#(mark(X)) |
→ |
U31#(X) |
(163) |
1.1.13 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U31#(ok(X)) |
→ |
U31#(X) |
(218) |
|
1 |
> |
1 |
U31#(mark(X)) |
→ |
U31#(X) |
(163) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
14th
component contains the
pair
U41#(ok(X1),ok(X2)) |
→ |
U41#(X1,X2) |
(219) |
U41#(mark(X1),X2) |
→ |
U41#(X1,X2) |
(164) |
1.1.14 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U41#(ok(X1),ok(X2)) |
→ |
U41#(X1,X2) |
(219) |
|
2 |
> |
2 |
1 |
> |
1 |
U41#(mark(X1),X2) |
→ |
U41#(X1,X2) |
(164) |
|
2 |
≥ |
2 |
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
15th
component contains the
pair
U42#(ok(X)) |
→ |
U42#(X) |
(220) |
U42#(mark(X)) |
→ |
U42#(X) |
(165) |
1.1.15 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U42#(ok(X)) |
→ |
U42#(X) |
(220) |
|
1 |
> |
1 |
U42#(mark(X)) |
→ |
U42#(X) |
(165) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
16th
component contains the
pair
U51#(ok(X1),ok(X2)) |
→ |
U51#(X1,X2) |
(222) |
U51#(mark(X1),X2) |
→ |
U51#(X1,X2) |
(166) |
1.1.16 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U51#(ok(X1),ok(X2)) |
→ |
U51#(X1,X2) |
(222) |
|
2 |
> |
2 |
1 |
> |
1 |
U51#(mark(X1),X2) |
→ |
U51#(X1,X2) |
(166) |
|
2 |
≥ |
2 |
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
17th
component contains the
pair
U52#(ok(X)) |
→ |
U52#(X) |
(223) |
U52#(mark(X)) |
→ |
U52#(X) |
(167) |
1.1.17 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U52#(ok(X)) |
→ |
U52#(X) |
(223) |
|
1 |
> |
1 |
U52#(mark(X)) |
→ |
U52#(X) |
(167) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
18th
component contains the
pair
U61#(ok(X)) |
→ |
U61#(X) |
(224) |
U61#(mark(X)) |
→ |
U61#(X) |
(168) |
1.1.18 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U61#(ok(X)) |
→ |
U61#(X) |
(224) |
|
1 |
> |
1 |
U61#(mark(X)) |
→ |
U61#(X) |
(168) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
19th
component contains the
pair
U71#(ok(X1),ok(X2)) |
→ |
U71#(X1,X2) |
(225) |
U71#(mark(X1),X2) |
→ |
U71#(X1,X2) |
(169) |
1.1.19 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U71#(ok(X1),ok(X2)) |
→ |
U71#(X1,X2) |
(225) |
|
2 |
> |
2 |
1 |
> |
1 |
U71#(mark(X1),X2) |
→ |
U71#(X1,X2) |
(169) |
|
2 |
≥ |
2 |
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
20th
component contains the
pair
U72#(ok(X)) |
→ |
U72#(X) |
(226) |
U72#(mark(X)) |
→ |
U72#(X) |
(170) |
1.1.20 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U72#(ok(X)) |
→ |
U72#(X) |
(226) |
|
1 |
> |
1 |
U72#(mark(X)) |
→ |
U72#(X) |
(170) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.
-
The
21th
component contains the
pair
U81#(ok(X)) |
→ |
U81#(X) |
(228) |
U81#(mark(X)) |
→ |
U81#(X) |
(171) |
1.1.21 Size-Change Termination
Using size-change termination in combination with
the subterm criterion
one obtains the following initial size-change graphs.
U81#(ok(X)) |
→ |
U81#(X) |
(228) |
|
1 |
> |
1 |
U81#(mark(X)) |
→ |
U81#(X) |
(171) |
|
1 |
> |
1 |
As there is no critical graph in the transitive closure, there are no infinite chains.