The rewrite relation of the following TRS is considered.
There are 232 ruless (increase limit for explicit display).
There are 362 ruless (increase limit for explicit display).
The dependency pairs are split into 46
components.
-
The
1st
component contains the
pair
top#(ok(X)) |
→ |
top#(active(X)) |
(463) |
top#(mark(X)) |
→ |
top#(proper(X)) |
(411) |
1.1.1 Reduction Pair Processor with Usable Rules
Using the argument filter
π(U83#) |
= |
1 |
π(U24#) |
= |
2 |
π(isNeList#) |
= |
1 |
π(top#) |
= |
1 |
π(U52#) |
= |
3 |
π(isQid) |
= |
1 |
π(U42#) |
= |
3 |
π(proper) |
= |
1 |
π(ok) |
= |
1 |
π(U73#) |
= |
2 |
π(proper#) |
= |
1 |
π(active) |
= |
1 |
π(isPalListKind) |
= |
1 |
π(U91#) |
= |
2 |
π(U55#) |
= |
2 |
π(U61#) |
= |
1 |
in combination with the following Weighted Path Order with the following precedence and status
prec(a) |
= |
17 |
|
status(a) |
= |
[] |
|
list-extension(a) |
= |
Lex |
prec(U72#) |
= |
0 |
|
status(U72#) |
= |
[1, 2] |
|
list-extension(U72#) |
= |
Lex |
prec(U32#) |
= |
0 |
|
status(U32#) |
= |
[1, 2] |
|
list-extension(U32#) |
= |
Lex |
prec(U21) |
= |
14 |
|
status(U21) |
= |
[1, 2, 3] |
|
list-extension(U21) |
= |
Lex |
prec(isPalListKind#) |
= |
0 |
|
status(isPalListKind#) |
= |
[] |
|
list-extension(isPalListKind#) |
= |
Lex |
prec(U11) |
= |
8 |
|
status(U11) |
= |
[1, 2] |
|
list-extension(U11) |
= |
Lex |
prec(U24) |
= |
11 |
|
status(U24) |
= |
[2, 1, 3] |
|
list-extension(U24) |
= |
Lex |
prec(U25) |
= |
10 |
|
status(U25) |
= |
[1, 2] |
|
list-extension(U25) |
= |
Lex |
prec(isNeList) |
= |
6 |
|
status(isNeList) |
= |
[1] |
|
list-extension(isNeList) |
= |
Lex |
prec(U56) |
= |
3 |
|
status(U56) |
= |
[1] |
|
list-extension(U56) |
= |
Lex |
prec(isPal) |
= |
21 |
|
status(isPal) |
= |
[1] |
|
list-extension(isPal) |
= |
Lex |
prec(U42) |
= |
21 |
|
status(U42) |
= |
[3, 1, 2] |
|
list-extension(U42) |
= |
Lex |
prec(U91) |
= |
15 |
|
status(U91) |
= |
[2, 1] |
|
list-extension(U91) |
= |
Lex |
prec(u) |
= |
17 |
|
status(u) |
= |
[] |
|
list-extension(u) |
= |
Lex |
prec(U26) |
= |
9 |
|
status(U26) |
= |
[1] |
|
list-extension(U26) |
= |
Lex |
prec(U82#) |
= |
0 |
|
status(U82#) |
= |
[1, 2] |
|
list-extension(U82#) |
= |
Lex |
prec(U71) |
= |
23 |
|
status(U71) |
= |
[3, 2, 1] |
|
list-extension(U71) |
= |
Lex |
prec(top) |
= |
0 |
|
status(top) |
= |
[] |
|
list-extension(top) |
= |
Lex |
prec(U81#) |
= |
0 |
|
status(U81#) |
= |
[2, 1] |
|
list-extension(U81#) |
= |
Lex |
prec(U92#) |
= |
0 |
|
status(U92#) |
= |
[] |
|
list-extension(U92#) |
= |
Lex |
prec(U43) |
= |
20 |
|
status(U43) |
= |
[3, 1, 2] |
|
list-extension(U43) |
= |
Lex |
prec(U23#) |
= |
0 |
|
status(U23#) |
= |
[3, 1] |
|
list-extension(U23#) |
= |
Lex |
prec(U53#) |
= |
0 |
|
status(U53#) |
= |
[3, 2, 1] |
|
list-extension(U53#) |
= |
Lex |
prec(__#) |
= |
0 |
|
status(__#) |
= |
[2, 1] |
|
list-extension(__#) |
= |
Lex |
prec(U44) |
= |
19 |
|
status(U44) |
= |
[3, 1, 2] |
|
list-extension(U44) |
= |
Lex |
prec(U55) |
= |
17 |
|
status(U55) |
= |
[2, 1] |
|
list-extension(U55) |
= |
Lex |
prec(U43#) |
= |
0 |
|
status(U43#) |
= |
[1, 3] |
|
list-extension(U43#) |
= |
Lex |
prec(U23) |
= |
12 |
|
status(U23) |
= |
[3, 1, 2] |
|
list-extension(U23) |
= |
Lex |
prec(U63) |
= |
16 |
|
status(U63) |
= |
[1] |
|
list-extension(U63) |
= |
Lex |
prec(isNePal) |
= |
19 |
|
status(isNePal) |
= |
[1] |
|
list-extension(isNePal) |
= |
Lex |
prec(U72) |
= |
22 |
|
status(U72) |
= |
[1, 2] |
|
list-extension(U72) |
= |
Lex |
prec(U13#) |
= |
0 |
|
status(U13#) |
= |
[] |
|
list-extension(U13#) |
= |
Lex |
prec(isQid#) |
= |
0 |
|
status(isQid#) |
= |
[] |
|
list-extension(isQid#) |
= |
Lex |
prec(isPal#) |
= |
0 |
|
status(isPal#) |
= |
[] |
|
list-extension(isPal#) |
= |
Lex |
prec(U12) |
= |
7 |
|
status(U12) |
= |
[1, 2] |
|
list-extension(U12) |
= |
Lex |
prec(U33#) |
= |
0 |
|
status(U33#) |
= |
[] |
|
list-extension(U33#) |
= |
Lex |
prec(U26#) |
= |
0 |
|
status(U26#) |
= |
[] |
|
list-extension(U26#) |
= |
Lex |
prec(U54) |
= |
18 |
|
status(U54) |
= |
[2, 1, 3] |
|
list-extension(U54) |
= |
Lex |
prec(o) |
= |
17 |
|
status(o) |
= |
[] |
|
list-extension(o) |
= |
Lex |
prec(U44#) |
= |
0 |
|
status(U44#) |
= |
[3, 1, 2] |
|
list-extension(U44#) |
= |
Lex |
prec(U54#) |
= |
0 |
|
status(U54#) |
= |
[1, 3, 2] |
|
list-extension(U54#) |
= |
Lex |
prec(U12#) |
= |
0 |
|
status(U12#) |
= |
[1, 2] |
|
list-extension(U12#) |
= |
Lex |
prec(U62#) |
= |
0 |
|
status(U62#) |
= |
[] |
|
list-extension(U62#) |
= |
Lex |
prec(U83) |
= |
3 |
|
status(U83) |
= |
[1] |
|
list-extension(U83) |
= |
Lex |
prec(isList) |
= |
9 |
|
status(isList) |
= |
[1] |
|
list-extension(isList) |
= |
Lex |
prec(U73) |
= |
18 |
|
status(U73) |
= |
[2, 1] |
|
list-extension(U73) |
= |
Lex |
prec(U74#) |
= |
0 |
|
status(U74#) |
= |
[] |
|
list-extension(U74#) |
= |
Lex |
prec(isNePal#) |
= |
0 |
|
status(isNePal#) |
= |
[] |
|
list-extension(isNePal#) |
= |
Lex |
prec(nil) |
= |
17 |
|
status(nil) |
= |
[] |
|
list-extension(nil) |
= |
Lex |
prec(U25#) |
= |
0 |
|
status(U25#) |
= |
[2, 1] |
|
list-extension(U25#) |
= |
Lex |
prec(U62) |
= |
17 |
|
status(U62) |
= |
[1, 2] |
|
list-extension(U62) |
= |
Lex |
prec(U63#) |
= |
0 |
|
status(U63#) |
= |
[] |
|
list-extension(U63#) |
= |
Lex |
prec(U45) |
= |
18 |
|
status(U45) |
= |
[1, 2] |
|
list-extension(U45) |
= |
Lex |
prec(mark) |
= |
3 |
|
status(mark) |
= |
[1] |
|
list-extension(mark) |
= |
Lex |
prec(isList#) |
= |
0 |
|
status(isList#) |
= |
[] |
|
list-extension(isList#) |
= |
Lex |
prec(U32) |
= |
4 |
|
status(U32) |
= |
[2, 1] |
|
list-extension(U32) |
= |
Lex |
prec(U33) |
= |
3 |
|
status(U33) |
= |
[1] |
|
list-extension(U33) |
= |
Lex |
prec(U46#) |
= |
0 |
|
status(U46#) |
= |
[] |
|
list-extension(U46#) |
= |
Lex |
prec(U56#) |
= |
0 |
|
status(U56#) |
= |
[] |
|
list-extension(U56#) |
= |
Lex |
prec(U46) |
= |
17 |
|
status(U46) |
= |
[1] |
|
list-extension(U46) |
= |
Lex |
prec(i) |
= |
17 |
|
status(i) |
= |
[] |
|
list-extension(i) |
= |
Lex |
prec(U52) |
= |
20 |
|
status(U52) |
= |
[3, 1, 2] |
|
list-extension(U52) |
= |
Lex |
prec(U61) |
= |
18 |
|
status(U61) |
= |
[2, 1] |
|
list-extension(U61) |
= |
Lex |
prec(U51#) |
= |
0 |
|
status(U51#) |
= |
[2, 3, 1] |
|
list-extension(U51#) |
= |
Lex |
prec(e) |
= |
17 |
|
status(e) |
= |
[] |
|
list-extension(e) |
= |
Lex |
prec(U11#) |
= |
0 |
|
status(U11#) |
= |
[2, 1] |
|
list-extension(U11#) |
= |
Lex |
prec(U31) |
= |
5 |
|
status(U31) |
= |
[1, 2] |
|
list-extension(U31) |
= |
Lex |
prec(U92) |
= |
3 |
|
status(U92) |
= |
[1] |
|
list-extension(U92) |
= |
Lex |
prec(U41#) |
= |
0 |
|
status(U41#) |
= |
[1, 3] |
|
list-extension(U41#) |
= |
Lex |
prec(active#) |
= |
0 |
|
status(active#) |
= |
[] |
|
list-extension(active#) |
= |
Lex |
prec(U21#) |
= |
0 |
|
status(U21#) |
= |
[2, 1] |
|
list-extension(U21#) |
= |
Lex |
prec(U81) |
= |
20 |
|
status(U81) |
= |
[2, 1] |
|
list-extension(U81) |
= |
Lex |
prec(U82) |
= |
19 |
|
status(U82) |
= |
[2, 1] |
|
list-extension(U82) |
= |
Lex |
prec(U22#) |
= |
0 |
|
status(U22#) |
= |
[3, 2, 1] |
|
list-extension(U22#) |
= |
Lex |
prec(tt) |
= |
16 |
|
status(tt) |
= |
[] |
|
list-extension(tt) |
= |
Lex |
prec(U71#) |
= |
0 |
|
status(U71#) |
= |
[3, 1, 2] |
|
list-extension(U71#) |
= |
Lex |
prec(U13) |
= |
6 |
|
status(U13) |
= |
[1] |
|
list-extension(U13) |
= |
Lex |
prec(U22) |
= |
13 |
|
status(U22) |
= |
[3, 2, 1] |
|
list-extension(U22) |
= |
Lex |
prec(U45#) |
= |
0 |
|
status(U45#) |
= |
[2, 1] |
|
list-extension(U45#) |
= |
Lex |
prec(U51) |
= |
21 |
|
status(U51) |
= |
[1, 2, 3] |
|
list-extension(U51) |
= |
Lex |
prec(U74) |
= |
17 |
|
status(U74) |
= |
[1] |
|
list-extension(U74) |
= |
Lex |
prec(U53) |
= |
19 |
|
status(U53) |
= |
[3, 2, 1] |
|
list-extension(U53) |
= |
Lex |
prec(U41) |
= |
22 |
|
status(U41) |
= |
[2, 1, 3] |
|
list-extension(U41) |
= |
Lex |
prec(U31#) |
= |
0 |
|
status(U31#) |
= |
[] |
|
list-extension(U31#) |
= |
Lex |
prec(__) |
= |
24 |
|
status(__) |
= |
[1, 2] |
|
list-extension(__) |
= |
Lex |
and the following
Max-polynomial interpretation
[a] |
=
|
0 |
[U72#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U32#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U21(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U24(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U25(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[isNeList(x1)] |
=
|
x1 + 0 |
[U56(x1)] |
=
|
x1 + 0 |
[isPal(x1)] |
=
|
x1 + 0 |
[U42(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U91(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[u] |
=
|
0 |
[U26(x1)] |
=
|
x1 + 0 |
[U82#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U71(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U92#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U23#(x1, x2, x3)] |
=
|
max(x1 + 0, x3 + 0, 0) |
[U53#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[__#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U44(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U55(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U43#(x1, x2, x3)] |
=
|
max(x1 + 0, x3 + 0, 0) |
[U23(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U63(x1)] |
=
|
x1 + 0 |
[isNePal(x1)] |
=
|
x1 + 0 |
[U72(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U12(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U33#(x1)] |
=
|
0 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U54#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U12#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U62#(x1, x2)] |
=
|
max(0) |
[U83(x1)] |
=
|
x1 + 0 |
[isList(x1)] |
=
|
x1 + 0 |
[U73(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[nil] |
=
|
0 |
[U25#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U62(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[mark(x1)] |
=
|
x1 + 0 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U33(x1)] |
=
|
x1 + 0 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 0 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U61(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U51#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[e] |
=
|
0 |
[U11#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U31(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U92(x1)] |
=
|
x1 + 0 |
[U41#(x1, x2, x3)] |
=
|
max(x1 + 0, x3 + 0, 0) |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U81(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U82(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U22#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[tt] |
=
|
0 |
[U71#(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U13(x1)] |
=
|
x1 + 0 |
[U22(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U45#(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
[U51(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U74(x1)] |
=
|
x1 + 0 |
[U53(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U41(x1, x2, x3)] |
=
|
max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U31#(x1, x2)] |
=
|
max(0) |
[__(x1, x2)] |
=
|
max(x1 + 0, x2 + 0, 0) |
together with the usable
rulesThere are 230 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)) |
(411) |
could be deleted.
1.1.1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
2nd
component contains the
pair
proper#(U43(X1,X2,X3)) |
→ |
proper#(X1) |
(591) |
proper#(U72(X1,X2)) |
→ |
proper#(X1) |
(589) |
proper#(U81(X1,X2)) |
→ |
proper#(X2) |
(574) |
proper#(U31(X1,X2)) |
→ |
proper#(X2) |
(565) |
proper#(U31(X1,X2)) |
→ |
proper#(X1) |
(562) |
proper#(U52(X1,X2,X3)) |
→ |
proper#(X1) |
(563) |
proper#(U23(X1,X2,X3)) |
→ |
proper#(X3) |
(561) |
proper#(U91(X1,X2)) |
→ |
proper#(X2) |
(556) |
proper#(U42(X1,X2,X3)) |
→ |
proper#(X1) |
(552) |
proper#(U44(X1,X2,X3)) |
→ |
proper#(X1) |
(550) |
proper#(U51(X1,X2,X3)) |
→ |
proper#(X1) |
(544) |
proper#(isPal(X)) |
→ |
proper#(X) |
(540) |
proper#(U32(X1,X2)) |
→ |
proper#(X1) |
(534) |
proper#(U24(X1,X2,X3)) |
→ |
proper#(X1) |
(532) |
proper#(U63(X)) |
→ |
proper#(X) |
(528) |
proper#(U54(X1,X2,X3)) |
→ |
proper#(X2) |
(522) |
proper#(U43(X1,X2,X3)) |
→ |
proper#(X3) |
(514) |
proper#(U11(X1,X2)) |
→ |
proper#(X1) |
(512) |
proper#(U25(X1,X2)) |
→ |
proper#(X2) |
(500) |
proper#(U61(X1,X2)) |
→ |
proper#(X1) |
(491) |
proper#(U54(X1,X2,X3)) |
→ |
proper#(X3) |
(492) |
proper#(U52(X1,X2,X3)) |
→ |
proper#(X2) |
(490) |
proper#(U12(X1,X2)) |
→ |
proper#(X1) |
(486) |
proper#(U24(X1,X2,X3)) |
→ |
proper#(X2) |
(485) |
proper#(U44(X1,X2,X3)) |
→ |
proper#(X3) |
(480) |
proper#(U43(X1,X2,X3)) |
→ |
proper#(X2) |
(478) |
proper#(U24(X1,X2,X3)) |
→ |
proper#(X3) |
(457) |
proper#(U82(X1,X2)) |
→ |
proper#(X2) |
(456) |
proper#(U52(X1,X2,X3)) |
→ |
proper#(X3) |
(449) |
proper#(U82(X1,X2)) |
→ |
proper#(X1) |
(445) |
proper#(U74(X)) |
→ |
proper#(X) |
(444) |
proper#(U53(X1,X2,X3)) |
→ |
proper#(X1) |
(443) |
proper#(U71(X1,X2,X3)) |
→ |
proper#(X1) |
(439) |
proper#(U23(X1,X2,X3)) |
→ |
proper#(X1) |
(438) |
proper#(U46(X)) |
→ |
proper#(X) |
(434) |
proper#(U55(X1,X2)) |
→ |
proper#(X2) |
(416) |
proper#(U21(X1,X2,X3)) |
→ |
proper#(X2) |
(415) |
proper#(U44(X1,X2,X3)) |
→ |
proper#(X2) |
(406) |
proper#(U54(X1,X2,X3)) |
→ |
proper#(X1) |
(402) |
proper#(U45(X1,X2)) |
→ |
proper#(X2) |
(396) |
proper#(U81(X1,X2)) |
→ |
proper#(X1) |
(398) |
proper#(U71(X1,X2,X3)) |
→ |
proper#(X2) |
(395) |
proper#(U33(X)) |
→ |
proper#(X) |
(392) |
proper#(U42(X1,X2,X3)) |
→ |
proper#(X3) |
(389) |
proper#(U22(X1,X2,X3)) |
→ |
proper#(X2) |
(390) |
proper#(U56(X)) |
→ |
proper#(X) |
(385) |
proper#(U42(X1,X2,X3)) |
→ |
proper#(X2) |
(373) |
proper#(U55(X1,X2)) |
→ |
proper#(X1) |
(369) |
proper#(U62(X1,X2)) |
→ |
proper#(X1) |
(363) |
proper#(U21(X1,X2,X3)) |
→ |
proper#(X3) |
(357) |
proper#(U53(X1,X2,X3)) |
→ |
proper#(X2) |
(358) |
proper#(U61(X1,X2)) |
→ |
proper#(X2) |
(352) |
proper#(U73(X1,X2)) |
→ |
proper#(X2) |
(353) |
proper#(U22(X1,X2,X3)) |
→ |
proper#(X3) |
(351) |
proper#(U41(X1,X2,X3)) |
→ |
proper#(X3) |
(349) |
proper#(U21(X1,X2,X3)) |
→ |
proper#(X1) |
(337) |
proper#(U72(X1,X2)) |
→ |
proper#(X2) |
(338) |
proper#(U91(X1,X2)) |
→ |
proper#(X1) |
(331) |
proper#(U25(X1,X2)) |
→ |
proper#(X1) |
(327) |
proper#(U22(X1,X2,X3)) |
→ |
proper#(X1) |
(323) |
proper#(isNePal(X)) |
→ |
proper#(X) |
(318) |
proper#(U26(X)) |
→ |
proper#(X) |
(319) |
proper#(U83(X)) |
→ |
proper#(X) |
(320) |
proper#(U73(X1,X2)) |
→ |
proper#(X1) |
(314) |
proper#(isNeList(X)) |
→ |
proper#(X) |
(303) |
proper#(U51(X1,X2,X3)) |
→ |
proper#(X3) |
(302) |
proper#(U41(X1,X2,X3)) |
→ |
proper#(X2) |
(297) |
proper#(U71(X1,X2,X3)) |
→ |
proper#(X3) |
(296) |
proper#(U41(X1,X2,X3)) |
→ |
proper#(X1) |
(290) |
proper#(__(X1,X2)) |
→ |
proper#(X2) |
(293) |
proper#(isQid(X)) |
→ |
proper#(X) |
(288) |
proper#(U92(X)) |
→ |
proper#(X) |
(285) |
proper#(U62(X1,X2)) |
→ |
proper#(X2) |
(282) |
proper#(U23(X1,X2,X3)) |
→ |
proper#(X2) |
(281) |
proper#(U13(X)) |
→ |
proper#(X) |
(278) |
proper#(__(X1,X2)) |
→ |
proper#(X1) |
(271) |
proper#(U51(X1,X2,X3)) |
→ |
proper#(X2) |
(263) |
proper#(U45(X1,X2)) |
→ |
proper#(X1) |
(261) |
proper#(U11(X1,X2)) |
→ |
proper#(X2) |
(259) |
proper#(U53(X1,X2,X3)) |
→ |
proper#(X3) |
(256) |
proper#(isPalListKind(X)) |
→ |
proper#(X) |
(248) |
proper#(isList(X)) |
→ |
proper#(X) |
(242) |
proper#(U12(X1,X2)) |
→ |
proper#(X2) |
(239) |
proper#(U32(X1,X2)) |
→ |
proper#(X2) |
(234) |
1.1.2 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + x2 + 1 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + x2 + 1 |
[isNeList(x1)] |
=
|
x1 + 2 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
x1 + 4 |
[U42(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U91(x1, x2)] |
=
|
x1 + x2 + 1 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 3 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
x1 + x2 + 1 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 3 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
x1 + 2 |
[U72(x1, x2)] |
=
|
x1 + x2 + 3 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[o] |
=
|
51221 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
x1 + 1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 2 |
[U73(x1, x2)] |
=
|
x1 + x2 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + x2 + 1 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + x2 + 1 |
[mark(x1)] |
=
|
x1 + 0 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
x1 + 0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
28764 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U61(x1, x2)] |
=
|
x1 + x2 + 1 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 0 |
[U31(x1, x2)] |
=
|
x1 + x2 + 1 |
[U92(x1)] |
=
|
x1 + 1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + x2 + 3 |
[U82(x1, x2)] |
=
|
x1 + x2 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
2 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 3 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 2 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 17220 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rulesThere are 128 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
proper#(U43(X1,X2,X3)) |
→ |
proper#(X1) |
(591) |
proper#(U72(X1,X2)) |
→ |
proper#(X1) |
(589) |
proper#(U81(X1,X2)) |
→ |
proper#(X2) |
(574) |
proper#(U31(X1,X2)) |
→ |
proper#(X2) |
(565) |
proper#(U31(X1,X2)) |
→ |
proper#(X1) |
(562) |
proper#(U52(X1,X2,X3)) |
→ |
proper#(X1) |
(563) |
proper#(U23(X1,X2,X3)) |
→ |
proper#(X3) |
(561) |
proper#(U91(X1,X2)) |
→ |
proper#(X2) |
(556) |
proper#(U42(X1,X2,X3)) |
→ |
proper#(X1) |
(552) |
proper#(U44(X1,X2,X3)) |
→ |
proper#(X1) |
(550) |
proper#(U51(X1,X2,X3)) |
→ |
proper#(X1) |
(544) |
proper#(isPal(X)) |
→ |
proper#(X) |
(540) |
proper#(U32(X1,X2)) |
→ |
proper#(X1) |
(534) |
proper#(U24(X1,X2,X3)) |
→ |
proper#(X1) |
(532) |
proper#(U63(X)) |
→ |
proper#(X) |
(528) |
proper#(U54(X1,X2,X3)) |
→ |
proper#(X2) |
(522) |
proper#(U43(X1,X2,X3)) |
→ |
proper#(X3) |
(514) |
proper#(U11(X1,X2)) |
→ |
proper#(X1) |
(512) |
proper#(U25(X1,X2)) |
→ |
proper#(X2) |
(500) |
proper#(U61(X1,X2)) |
→ |
proper#(X1) |
(491) |
proper#(U54(X1,X2,X3)) |
→ |
proper#(X3) |
(492) |
proper#(U52(X1,X2,X3)) |
→ |
proper#(X2) |
(490) |
proper#(U12(X1,X2)) |
→ |
proper#(X1) |
(486) |
proper#(U24(X1,X2,X3)) |
→ |
proper#(X2) |
(485) |
proper#(U44(X1,X2,X3)) |
→ |
proper#(X3) |
(480) |
proper#(U43(X1,X2,X3)) |
→ |
proper#(X2) |
(478) |
proper#(U24(X1,X2,X3)) |
→ |
proper#(X3) |
(457) |
proper#(U82(X1,X2)) |
→ |
proper#(X2) |
(456) |
proper#(U52(X1,X2,X3)) |
→ |
proper#(X3) |
(449) |
proper#(U82(X1,X2)) |
→ |
proper#(X1) |
(445) |
proper#(U74(X)) |
→ |
proper#(X) |
(444) |
proper#(U53(X1,X2,X3)) |
→ |
proper#(X1) |
(443) |
proper#(U71(X1,X2,X3)) |
→ |
proper#(X1) |
(439) |
proper#(U23(X1,X2,X3)) |
→ |
proper#(X1) |
(438) |
proper#(U46(X)) |
→ |
proper#(X) |
(434) |
proper#(U55(X1,X2)) |
→ |
proper#(X2) |
(416) |
proper#(U21(X1,X2,X3)) |
→ |
proper#(X2) |
(415) |
proper#(U44(X1,X2,X3)) |
→ |
proper#(X2) |
(406) |
proper#(U54(X1,X2,X3)) |
→ |
proper#(X1) |
(402) |
proper#(U45(X1,X2)) |
→ |
proper#(X2) |
(396) |
proper#(U81(X1,X2)) |
→ |
proper#(X1) |
(398) |
proper#(U71(X1,X2,X3)) |
→ |
proper#(X2) |
(395) |
proper#(U33(X)) |
→ |
proper#(X) |
(392) |
proper#(U42(X1,X2,X3)) |
→ |
proper#(X3) |
(389) |
proper#(U22(X1,X2,X3)) |
→ |
proper#(X2) |
(390) |
proper#(U56(X)) |
→ |
proper#(X) |
(385) |
proper#(U42(X1,X2,X3)) |
→ |
proper#(X2) |
(373) |
proper#(U55(X1,X2)) |
→ |
proper#(X1) |
(369) |
proper#(U62(X1,X2)) |
→ |
proper#(X1) |
(363) |
proper#(U21(X1,X2,X3)) |
→ |
proper#(X3) |
(357) |
proper#(U53(X1,X2,X3)) |
→ |
proper#(X2) |
(358) |
proper#(U61(X1,X2)) |
→ |
proper#(X2) |
(352) |
proper#(U73(X1,X2)) |
→ |
proper#(X2) |
(353) |
proper#(U22(X1,X2,X3)) |
→ |
proper#(X3) |
(351) |
proper#(U41(X1,X2,X3)) |
→ |
proper#(X3) |
(349) |
proper#(U21(X1,X2,X3)) |
→ |
proper#(X1) |
(337) |
proper#(U72(X1,X2)) |
→ |
proper#(X2) |
(338) |
proper#(U91(X1,X2)) |
→ |
proper#(X1) |
(331) |
proper#(U25(X1,X2)) |
→ |
proper#(X1) |
(327) |
proper#(U22(X1,X2,X3)) |
→ |
proper#(X1) |
(323) |
proper#(isNePal(X)) |
→ |
proper#(X) |
(318) |
proper#(U26(X)) |
→ |
proper#(X) |
(319) |
proper#(U83(X)) |
→ |
proper#(X) |
(320) |
proper#(U73(X1,X2)) |
→ |
proper#(X1) |
(314) |
proper#(isNeList(X)) |
→ |
proper#(X) |
(303) |
proper#(U51(X1,X2,X3)) |
→ |
proper#(X3) |
(302) |
proper#(U41(X1,X2,X3)) |
→ |
proper#(X2) |
(297) |
proper#(U71(X1,X2,X3)) |
→ |
proper#(X3) |
(296) |
proper#(U41(X1,X2,X3)) |
→ |
proper#(X1) |
(290) |
proper#(__(X1,X2)) |
→ |
proper#(X2) |
(293) |
proper#(isQid(X)) |
→ |
proper#(X) |
(288) |
proper#(U92(X)) |
→ |
proper#(X) |
(285) |
proper#(U62(X1,X2)) |
→ |
proper#(X2) |
(282) |
proper#(U23(X1,X2,X3)) |
→ |
proper#(X2) |
(281) |
proper#(U13(X)) |
→ |
proper#(X) |
(278) |
proper#(__(X1,X2)) |
→ |
proper#(X1) |
(271) |
proper#(U51(X1,X2,X3)) |
→ |
proper#(X2) |
(263) |
proper#(U45(X1,X2)) |
→ |
proper#(X1) |
(261) |
proper#(U11(X1,X2)) |
→ |
proper#(X2) |
(259) |
proper#(U53(X1,X2,X3)) |
→ |
proper#(X3) |
(256) |
proper#(isPalListKind(X)) |
→ |
proper#(X) |
(248) |
proper#(isList(X)) |
→ |
proper#(X) |
(242) |
proper#(U12(X1,X2)) |
→ |
proper#(X2) |
(239) |
proper#(U32(X1,X2)) |
→ |
proper#(X2) |
(234) |
could be deleted.
1.1.2.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
3rd
component contains the
pair
active#(U54(X1,X2,X3)) |
→ |
active#(X1) |
(585) |
active#(U91(X1,X2)) |
→ |
active#(X1) |
(570) |
active#(U73(X1,X2)) |
→ |
active#(X1) |
(568) |
active#(U12(X1,X2)) |
→ |
active#(X1) |
(542) |
active#(U32(X1,X2)) |
→ |
active#(X1) |
(541) |
active#(U21(X1,X2,X3)) |
→ |
active#(X1) |
(533) |
active#(U63(X)) |
→ |
active#(X) |
(531) |
active#(U72(X1,X2)) |
→ |
active#(X1) |
(518) |
active#(U46(X)) |
→ |
active#(X) |
(513) |
active#(U51(X1,X2,X3)) |
→ |
active#(X1) |
(507) |
active#(U61(X1,X2)) |
→ |
active#(X1) |
(502) |
active#(U82(X1,X2)) |
→ |
active#(X1) |
(494) |
active#(U56(X)) |
→ |
active#(X) |
(470) |
active#(U62(X1,X2)) |
→ |
active#(X1) |
(468) |
active#(U26(X)) |
→ |
active#(X) |
(461) |
active#(U31(X1,X2)) |
→ |
active#(X1) |
(453) |
active#(U92(X)) |
→ |
active#(X) |
(446) |
active#(U22(X1,X2,X3)) |
→ |
active#(X1) |
(436) |
active#(U52(X1,X2,X3)) |
→ |
active#(X1) |
(435) |
active#(__(X1,X2)) |
→ |
active#(X1) |
(423) |
active#(U41(X1,X2,X3)) |
→ |
active#(X1) |
(424) |
active#(__(X1,X2)) |
→ |
active#(X2) |
(418) |
active#(U45(X1,X2)) |
→ |
active#(X1) |
(413) |
active#(U33(X)) |
→ |
active#(X) |
(403) |
active#(U81(X1,X2)) |
→ |
active#(X1) |
(404) |
active#(U74(X)) |
→ |
active#(X) |
(393) |
active#(U13(X)) |
→ |
active#(X) |
(383) |
active#(U43(X1,X2,X3)) |
→ |
active#(X1) |
(334) |
active#(U53(X1,X2,X3)) |
→ |
active#(X1) |
(333) |
active#(U42(X1,X2,X3)) |
→ |
active#(X1) |
(329) |
active#(U83(X)) |
→ |
active#(X) |
(326) |
active#(U44(X1,X2,X3)) |
→ |
active#(X1) |
(316) |
active#(U23(X1,X2,X3)) |
→ |
active#(X1) |
(306) |
active#(U24(X1,X2,X3)) |
→ |
active#(X1) |
(298) |
active#(U25(X1,X2)) |
→ |
active#(X1) |
(277) |
active#(U11(X1,X2)) |
→ |
active#(X1) |
(274) |
active#(U71(X1,X2,X3)) |
→ |
active#(X1) |
(250) |
active#(U55(X1,X2)) |
→ |
active#(X1) |
(233) |
1.1.3 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
27113 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 74633 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + x2 + 37316 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 74633 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + x2 + 37317 |
[isNeList(x1)] |
=
|
x1 + 7035 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
x1 + 100650 |
[U42(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U91(x1, x2)] |
=
|
x1 + x2 + 5822 |
[u] |
=
|
35910 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 119102 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U55(x1, x2)] |
=
|
x1 + x2 + 37317 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 74633 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
x1 + 44469 |
[U72(x1, x2)] |
=
|
x1 + x2 + 105848 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 13000 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
x1 + 1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 37317 |
[U73(x1, x2)] |
=
|
x1 + x2 + 5199 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + x2 + 21797 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + x2 + 7035 |
[mark(x1)] |
=
|
x1 + 0 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U61(x1, x2)] |
=
|
x1 + x2 + 44468 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 0 |
[U31(x1, x2)] |
=
|
x1 + x2 + 1 |
[U92(x1)] |
=
|
x1 + 1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
x1 + 0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + x2 + 44469 |
[U82(x1, x2)] |
=
|
x1 + x2 + 44469 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 5966 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 74633 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 44351 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 37317 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rulesThere are 128 ruless (increase limit for explicit display).
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
active#(U54(X1,X2,X3)) |
→ |
active#(X1) |
(585) |
active#(U91(X1,X2)) |
→ |
active#(X1) |
(570) |
active#(U73(X1,X2)) |
→ |
active#(X1) |
(568) |
active#(U12(X1,X2)) |
→ |
active#(X1) |
(542) |
active#(U32(X1,X2)) |
→ |
active#(X1) |
(541) |
active#(U21(X1,X2,X3)) |
→ |
active#(X1) |
(533) |
active#(U63(X)) |
→ |
active#(X) |
(531) |
active#(U72(X1,X2)) |
→ |
active#(X1) |
(518) |
active#(U46(X)) |
→ |
active#(X) |
(513) |
active#(U51(X1,X2,X3)) |
→ |
active#(X1) |
(507) |
active#(U61(X1,X2)) |
→ |
active#(X1) |
(502) |
active#(U82(X1,X2)) |
→ |
active#(X1) |
(494) |
active#(U56(X)) |
→ |
active#(X) |
(470) |
active#(U62(X1,X2)) |
→ |
active#(X1) |
(468) |
active#(U26(X)) |
→ |
active#(X) |
(461) |
active#(U31(X1,X2)) |
→ |
active#(X1) |
(453) |
active#(U92(X)) |
→ |
active#(X) |
(446) |
active#(U22(X1,X2,X3)) |
→ |
active#(X1) |
(436) |
active#(U52(X1,X2,X3)) |
→ |
active#(X1) |
(435) |
active#(__(X1,X2)) |
→ |
active#(X1) |
(423) |
active#(U41(X1,X2,X3)) |
→ |
active#(X1) |
(424) |
active#(__(X1,X2)) |
→ |
active#(X2) |
(418) |
active#(U45(X1,X2)) |
→ |
active#(X1) |
(413) |
active#(U33(X)) |
→ |
active#(X) |
(403) |
active#(U81(X1,X2)) |
→ |
active#(X1) |
(404) |
active#(U74(X)) |
→ |
active#(X) |
(393) |
active#(U13(X)) |
→ |
active#(X) |
(383) |
active#(U43(X1,X2,X3)) |
→ |
active#(X1) |
(334) |
active#(U53(X1,X2,X3)) |
→ |
active#(X1) |
(333) |
active#(U42(X1,X2,X3)) |
→ |
active#(X1) |
(329) |
active#(U83(X)) |
→ |
active#(X) |
(326) |
active#(U44(X1,X2,X3)) |
→ |
active#(X1) |
(316) |
active#(U23(X1,X2,X3)) |
→ |
active#(X1) |
(306) |
active#(U24(X1,X2,X3)) |
→ |
active#(X1) |
(298) |
active#(U25(X1,X2)) |
→ |
active#(X1) |
(277) |
active#(U11(X1,X2)) |
→ |
active#(X1) |
(274) |
active#(U71(X1,X2,X3)) |
→ |
active#(X1) |
(250) |
active#(U55(X1,X2)) |
→ |
active#(X1) |
(233) |
could be deleted.
1.1.3.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
4th
component contains the
pair
U31#(ok(X1),ok(X2)) |
→ |
U31#(X1,X2) |
(566) |
U31#(mark(X1),X2) |
→ |
U31#(X1,X2) |
(280) |
1.1.4 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 54543 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
15724 |
[U24(x1, x2, x3)] |
=
|
x3 + 29098 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x2 + 54544 |
[isNeList(x1)] |
=
|
x1 + 20681 |
[U56(x1)] |
=
|
21482 |
[isPal(x1)] |
=
|
x1 + 44467 |
[U42(x1, x2, x3)] |
=
|
27330 |
[U91(x1, x2)] |
=
|
x1 + 59961 |
[u] |
=
|
35910 |
[U26(x1)] |
=
|
4484 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 5721 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
30192 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
19825 |
[U55(x1, x2)] |
=
|
26747 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + 1 |
[U63(x1)] |
=
|
1510 |
[isNePal(x1)] |
=
|
x1 + 44472 |
[U72(x1, x2)] |
=
|
10730 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 14105 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
54543 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 2546 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
54543 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
18925 |
[mark(x1)] |
=
|
54544 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 54543 |
[U33(x1)] |
=
|
x1 + 30037 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
64 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U61(x1, x2)] |
=
|
54543 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
19981 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 29087 |
[U92(x1)] |
=
|
34301 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
31145 |
[U82(x1, x2)] |
=
|
47047 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 25655 |
[U22(x1, x2, x3)] |
=
|
x1 + 26143 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
54543 |
[U74(x1)] |
=
|
54544 |
[isPalListKind(x1)] |
=
|
9983 |
[U53(x1, x2, x3)] |
=
|
25734 |
[U41(x1, x2, x3)] |
=
|
50552 |
[U31#(x1, x2)] |
=
|
x2 + 0 |
[__(x1, x2)] |
=
|
x2 + 46662 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U25(mark(X1),X2) |
→ |
mark(U25(X1,X2)) |
(109) |
U25(ok(X1),ok(X2)) |
→ |
ok(U25(X1,X2)) |
(198) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U31#(ok(X1),ok(X2)) |
→ |
U31#(X1,X2) |
(566) |
could be deleted.
1.1.4.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
5th
component contains the
pair
U71#(mark(X1),X2,X3) |
→ |
U71#(X1,X2,X3) |
(578) |
U71#(ok(X1),ok(X2),ok(X3)) |
→ |
U71#(X1,X2,X3) |
(397) |
1.1.5 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 8772 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
x3 + 2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x2 + 26289 |
[isNeList(x1)] |
=
|
x1 + 25955 |
[U56(x1)] |
=
|
22078 |
[isPal(x1)] |
=
|
x1 + 1 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
x1 + 1 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
8432 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
0 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
2 |
[U55(x1, x2)] |
=
|
21217 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + 14351 |
[U63(x1)] |
=
|
22434 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
13594 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 0 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 25220 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
26038 |
[o] |
=
|
45119 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 18229 |
[isList(x1)] |
=
|
x1 + 32031 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 18327 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 12959 |
[U33(x1)] |
=
|
x1 + 507 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
41210 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 8048 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 2 |
[U92(x1)] |
=
|
7319 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
9507 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
x1 + 1 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
0 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
5754 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 8657 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U71#(mark(X1),X2,X3) |
→ |
U71#(X1,X2,X3) |
(578) |
U71#(ok(X1),ok(X2),ok(X3)) |
→ |
U71#(X1,X2,X3) |
(397) |
could be deleted.
1.1.5.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
6th
component contains the
pair
U81#(ok(X1),ok(X2)) |
→ |
U81#(X1,X2) |
(530) |
U81#(mark(X1),X2) |
→ |
U81#(X1,X2) |
(294) |
1.1.6 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 5153 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
x3 + 31043 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x2 + 26289 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
22404 |
[isPal(x1)] |
=
|
x1 + 52834 |
[U42(x1, x2, x3)] |
=
|
22086 |
[U91(x1, x2)] |
=
|
x1 + 12164 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
31989 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 26055 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
x1 + 0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
0 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
25053 |
[U55(x1, x2)] |
=
|
40231 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + 1 |
[U63(x1)] |
=
|
3115 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
11009 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 0 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 38112 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
17625 |
[o] |
=
|
33685 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 19300 |
[isList(x1)] |
=
|
x1 + 21806 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
23695 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
22481 |
[mark(x1)] |
=
|
x1 + 18327 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 31102 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
7305 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 8048 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
48187 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 2 |
[U92(x1)] |
=
|
11594 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
15910 |
[U82(x1, x2)] |
=
|
1664 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
x1 + 1 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
0 |
[U74(x1)] |
=
|
3376 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
12949 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 8657 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U81#(ok(X1),ok(X2)) |
→ |
U81#(X1,X2) |
(530) |
U81#(mark(X1),X2) |
→ |
U81#(X1,X2) |
(294) |
could be deleted.
1.1.6.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
7th
component contains the
pair
U92#(mark(X)) |
→ |
U92#(X) |
(580) |
U92#(ok(X)) |
→ |
U92#(X) |
(473) |
1.1.7 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 5153 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
x3 + 13915 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x2 + 18137 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
22404 |
[isPal(x1)] |
=
|
x1 + 1 |
[U42(x1, x2, x3)] |
=
|
27910 |
[U91(x1, x2)] |
=
|
x1 + 26477 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
38424 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 2909 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
x1 + 0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
0 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
25053 |
[U55(x1, x2)] |
=
|
40231 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + 1 |
[U63(x1)] |
=
|
6221 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
12473 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 0 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
28014 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 38944 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
23695 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
19388 |
[mark(x1)] |
=
|
x1 + 11171 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 6733 |
[U33(x1)] |
=
|
x1 + 8993 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 19035 |
[U92(x1)] |
=
|
32575 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
3830 |
[U82(x1, x2)] |
=
|
21511 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 19505 |
[U22(x1, x2, x3)] |
=
|
x1 + 30250 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
0 |
[U74(x1)] |
=
|
8829 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
14791 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 8657 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U92#(mark(X)) |
→ |
U92#(X) |
(580) |
U92#(ok(X)) |
→ |
U92#(X) |
(473) |
could be deleted.
1.1.7.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
8th
component contains the
pair
U21#(mark(X1),X2,X3) |
→ |
U21#(X1,X2,X3) |
(520) |
U21#(ok(X1),ok(X2),ok(X3)) |
→ |
U21#(X1,X2,X3) |
(249) |
1.1.8 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 5153 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
x3 + 2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x2 + 2 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
22404 |
[isPal(x1)] |
=
|
x1 + 1 |
[U42(x1, x2, x3)] |
=
|
x2 + 12170 |
[U91(x1, x2)] |
=
|
x1 + 2433 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
13298 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 20228 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
0 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
2 |
[U55(x1, x2)] |
=
|
40231 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + 1 |
[U63(x1)] |
=
|
9306 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
4008 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 0 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 12031 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 22085 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
10873 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 2 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 2 |
[U33(x1)] |
=
|
x1 + 8993 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 20910 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 10997 |
[U92(x1)] |
=
|
32575 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
x2 + 0 |
[U81(x1, x2)] |
=
|
3037 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
x1 + 30250 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
0 |
[U74(x1)] |
=
|
8829 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
22185 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 8657 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
U21#(ok(X1),ok(X2),ok(X3)) |
→ |
U21#(X1,X2,X3) |
(249) |
could be deleted.
1.1.8.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
9th
component contains the
pair
U63#(mark(X)) |
→ |
U63#(X) |
(569) |
U63#(ok(X)) |
→ |
U63#(X) |
(417) |
1.1.9 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 24855 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
32765 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
0 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
x1 + 28837 |
[isPal(x1)] |
=
|
0 |
[U42(x1, x2, x3)] |
=
|
x2 + 14242 |
[U91(x1, x2)] |
=
|
12227 |
[u] |
=
|
63338 |
[U26(x1)] |
=
|
37001 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 0 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
0 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
0 |
[U55(x1, x2)] |
=
|
14128 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
0 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
31542 |
[U72(x1, x2)] |
=
|
23421 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 15482 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
22270 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x3 + 15335 |
[o] |
=
|
11585 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
2 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 3 |
[isList(x1)] |
=
|
27665 |
[U73(x1, x2)] |
=
|
x1 + x2 + 10171 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
28385 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 18942 |
[U63#(x1)] |
=
|
x1 + 0 |
[U45(x1, x2)] |
=
|
x1 + 38919 |
[mark(x1)] |
=
|
x1 + 2 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 16201 |
[U33(x1)] |
=
|
9492 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
29244 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
3359 |
[U61(x1, x2)] |
=
|
31636 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
0 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
24655 |
[U92(x1)] |
=
|
0 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 6525 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
0 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 30808 |
[U22(x1, x2, x3)] |
=
|
30679 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
0 |
[isPalListKind(x1)] |
=
|
31879 |
[U53(x1, x2, x3)] |
=
|
7950 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 49530 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U13(mark(X)) |
→ |
mark(U13(X)) |
(104) |
U13(ok(X)) |
→ |
ok(U13(X)) |
(192) |
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U63#(mark(X)) |
→ |
U63#(X) |
(569) |
U63#(ok(X)) |
→ |
U63#(X) |
(417) |
could be deleted.
1.1.9.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
10th
component contains the
pair
U32#(ok(X1),ok(X2)) |
→ |
U32#(X1,X2) |
(308) |
U32#(mark(X1),X2) |
→ |
U32#(X1,X2) |
(243) |
1.1.10 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
x2 + 0 |
[U21(x1, x2, x3)] |
=
|
x3 + 24855 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
50986 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
0 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
0 |
[U42(x1, x2, x3)] |
=
|
x2 + 14242 |
[U91(x1, x2)] |
=
|
3 |
[u] |
=
|
55636 |
[U26(x1)] |
=
|
46267 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 0 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
0 |
[U55(x1, x2)] |
=
|
18298 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
1 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
14625 |
[U72(x1, x2)] |
=
|
54583 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
568 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[o] |
=
|
41402 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
2 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 3 |
[isList(x1)] |
=
|
3 |
[U73(x1, x2)] |
=
|
x1 + x2 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
28723 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 1 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + 1 |
[mark(x1)] |
=
|
x1 + 7526 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 16201 |
[U33(x1)] |
=
|
40465 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
46726 |
[i] |
=
|
28980 |
[U52(x1, x2, x3)] |
=
|
18003 |
[U61(x1, x2)] |
=
|
47449 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
21498 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
34718 |
[U92(x1)] |
=
|
1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 1 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
0 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
30679 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
0 |
[isPalListKind(x1)] |
=
|
3 |
[U53(x1, x2, x3)] |
=
|
7950 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U13(mark(X)) |
→ |
mark(U13(X)) |
(104) |
U13(ok(X)) |
→ |
ok(U13(X)) |
(192) |
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U32#(ok(X1),ok(X2)) |
→ |
U32#(X1,X2) |
(308) |
could be deleted.
1.1.10.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
11th
component contains the
pair
U24#(mark(X1),X2,X3) |
→ |
U24#(X1,X2,X3) |
(583) |
U24#(ok(X1),ok(X2),ok(X3)) |
→ |
U24#(X1,X2,X3) |
(555) |
1.1.11 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 19782 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
59167 |
[U24#(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U25(x1, x2)] |
=
|
0 |
[isNeList(x1)] |
=
|
x1 + 1696 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
0 |
[U42(x1, x2, x3)] |
=
|
x2 + 2 |
[U91(x1, x2)] |
=
|
19543 |
[u] |
=
|
30922 |
[U26(x1)] |
=
|
3 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 0 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
0 |
[U55(x1, x2)] |
=
|
18467 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
1 |
[U63(x1)] |
=
|
x1 + 22911 |
[isNePal(x1)] |
=
|
6373 |
[U72(x1, x2)] |
=
|
7096 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
3 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
2 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 3 |
[isList(x1)] |
=
|
4405 |
[U73(x1, x2)] |
=
|
x1 + x2 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 1 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + 1 |
[mark(x1)] |
=
|
x1 + 24909 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 44965 |
[U33(x1)] |
=
|
24143 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
3 |
[i] |
=
|
47833 |
[U52(x1, x2, x3)] |
=
|
26503 |
[U61(x1, x2)] |
=
|
110179 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
64935 |
[U92(x1)] |
=
|
1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 1 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
0 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
47764 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
0 |
[isPalListKind(x1)] |
=
|
21816 |
[U53(x1, x2, x3)] |
=
|
60786 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U13(mark(X)) |
→ |
mark(U13(X)) |
(104) |
U13(ok(X)) |
→ |
ok(U13(X)) |
(192) |
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U24#(mark(X1),X2,X3) |
→ |
U24#(X1,X2,X3) |
(583) |
U24#(ok(X1),ok(X2),ok(X3)) |
→ |
U24#(X1,X2,X3) |
(555) |
could be deleted.
1.1.11.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
12th
component contains the
pair
U82#(mark(X1),X2) |
→ |
U82#(X1,X2) |
(432) |
U82#(ok(X1),ok(X2)) |
→ |
U82#(X1,X2) |
(364) |
1.1.12 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 19782 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
3 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
0 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
0 |
[U42(x1, x2, x3)] |
=
|
x2 + 2 |
[U91(x1, x2)] |
=
|
3 |
[u] |
=
|
33381 |
[U26(x1)] |
=
|
x1 + 17236 |
[U82#(x1, x2)] |
=
|
x1 + 0 |
[U71(x1, x2, x3)] |
=
|
x2 + 0 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
0 |
[U55(x1, x2)] |
=
|
3 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
1 |
[U63(x1)] |
=
|
x1 + 23125 |
[isNePal(x1)] |
=
|
3 |
[U72(x1, x2)] |
=
|
17208 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
10463 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[o] |
=
|
46918 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
2 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 3 |
[isList(x1)] |
=
|
3 |
[U73(x1, x2)] |
=
|
x1 + x2 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
19497 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 9080 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + 1 |
[mark(x1)] |
=
|
x1 + 23936 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 44965 |
[U33(x1)] |
=
|
24143 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
3 |
[i] |
=
|
47833 |
[U52(x1, x2, x3)] |
=
|
3 |
[U61(x1, x2)] |
=
|
15964 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
52588 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
3 |
[U92(x1)] |
=
|
1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 1 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
0 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
16407 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
0 |
[isPalListKind(x1)] |
=
|
3 |
[U53(x1, x2, x3)] |
=
|
3 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U13(mark(X)) |
→ |
mark(U13(X)) |
(104) |
U13(ok(X)) |
→ |
ok(U13(X)) |
(192) |
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U82#(mark(X1),X2) |
→ |
U82#(X1,X2) |
(432) |
U82#(ok(X1),ok(X2)) |
→ |
U82#(X1,X2) |
(364) |
could be deleted.
1.1.12.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
13th
component contains the
pair
U91#(ok(X1),ok(X2)) |
→ |
U91#(X1,X2) |
(590) |
U91#(mark(X1),X2) |
→ |
U91#(X1,X2) |
(399) |
1.1.13 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 25409 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
0 |
[U24(x1, x2, x3)] |
=
|
3 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
0 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
0 |
[U42(x1, x2, x3)] |
=
|
x2 + 2 |
[U91(x1, x2)] |
=
|
3 |
[u] |
=
|
33381 |
[U26(x1)] |
=
|
x1 + 16691 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + 0 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
0 |
[U55(x1, x2)] |
=
|
3 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
1 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
3 |
[U72(x1, x2)] |
=
|
17208 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
10463 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[o] |
=
|
29185 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
2 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 3 |
[isList(x1)] |
=
|
3 |
[U73(x1, x2)] |
=
|
x1 + x2 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 1 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + 1 |
[mark(x1)] |
=
|
x1 + 15997 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 44965 |
[U33(x1)] |
=
|
24143 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
3 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
3 |
[U61(x1, x2)] |
=
|
15964 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
52588 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
3 |
[U92(x1)] |
=
|
1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 1 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
0 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
3530 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
0 |
[isPalListKind(x1)] |
=
|
19802 |
[U53(x1, x2, x3)] |
=
|
3 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + 0 |
[U91#(x1, x2)] |
=
|
x1 + 0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U13(mark(X)) |
→ |
mark(U13(X)) |
(104) |
U13(ok(X)) |
→ |
ok(U13(X)) |
(192) |
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U91#(ok(X1),ok(X2)) |
→ |
U91#(X1,X2) |
(590) |
U91#(mark(X1),X2) |
→ |
U91#(X1,X2) |
(399) |
could be deleted.
1.1.13.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
14th
component contains the
pair
U51#(mark(X1),X2,X3) |
→ |
U51#(X1,X2,X3) |
(529) |
U51#(ok(X1),ok(X2),ok(X3)) |
→ |
U51#(X1,X2,X3) |
(481) |
1.1.14 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x2 + x3 + 1216 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x2 + 17342 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
24399 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
55514 |
[U26(x1)] |
=
|
x1 + 12852 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
20185 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 20181 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
2 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
1232 |
[U72(x1, x2)] |
=
|
x2 + 23040 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 27211 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
27199 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
30352 |
[ok(x1)] |
=
|
x1 + 4370 |
[isList(x1)] |
=
|
5976 |
[U73(x1, x2)] |
=
|
x2 + 2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1686 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
26708 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 2 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
21404 |
[U33(x1)] |
=
|
17272 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
30012 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
22681 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
x1 + 0 |
[e] |
=
|
52588 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
3701 |
[U92(x1)] |
=
|
12088 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
x2 + 8024 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
19310 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U74(x1)] |
=
|
14013 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
14154 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 31400 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U51#(mark(X1),X2,X3) |
→ |
U51#(X1,X2,X3) |
(529) |
U51#(ok(X1),ok(X2),ok(X3)) |
→ |
U51#(X1,X2,X3) |
(481) |
could be deleted.
1.1.14.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
15th
component contains the
pair
U33#(ok(X)) |
→ |
U33#(X) |
(305) |
U33#(mark(X)) |
→ |
U33#(X) |
(289) |
1.1.15 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x2 + x3 + 39562 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x2 + 55688 |
[U24(x1, x2, x3)] |
=
|
38348 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
x1 + 8298 |
[U56(x1)] |
=
|
62745 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
53214 |
[U91(x1, x2)] |
=
|
38348 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
58531 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
38348 |
[U55(x1, x2)] |
=
|
38348 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
38348 |
[isNePal(x1)] |
=
|
15539 |
[U72(x1, x2)] |
=
|
x2 + 61386 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
38348 |
[U33#(x1)] |
=
|
x1 + 0 |
[isQid(x1)] |
=
|
x1 + 27211 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
38348 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
68698 |
[ok(x1)] |
=
|
x1 + 2114 |
[isList(x1)] |
=
|
5976 |
[U73(x1, x2)] |
=
|
x2 + 38348 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
65054 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
38348 |
[mark(x1)] |
=
|
x1 + 38348 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
59750 |
[U33(x1)] |
=
|
55618 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
68358 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
61027 |
[U61(x1, x2)] |
=
|
38348 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
38347 |
[U31(x1, x2)] |
=
|
42047 |
[U92(x1)] |
=
|
50434 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
38348 |
[U82(x1, x2)] |
=
|
x2 + 46370 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
57656 |
[U22(x1, x2, x3)] |
=
|
38348 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U74(x1)] |
=
|
52359 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
38348 |
[U41(x1, x2, x3)] |
=
|
52500 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 69746 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U33#(ok(X)) |
→ |
U33#(X) |
(305) |
U33#(mark(X)) |
→ |
U33#(X) |
(289) |
could be deleted.
1.1.15.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
16th
component contains the
pair
isQid#(ok(X)) |
→ |
isQid#(X) |
(469) |
1.1.16 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x2 + x3 + 1717 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x2 + 27204 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
31749 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
28134 |
[U91(x1, x2)] |
=
|
16387 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
20185 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
15070 |
[U55(x1, x2)] |
=
|
32103 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
18542 |
[U72(x1, x2)] |
=
|
x2 + 27557 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
x1 + 0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 139 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
25572 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
5976 |
[U73(x1, x2)] |
=
|
x2 + 15011 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
26708 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 16187 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
21404 |
[U33(x1)] |
=
|
13670 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
11201 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
4903 |
[U92(x1)] |
=
|
12088 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
x2 + 20491 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
19310 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U74(x1)] |
=
|
14013 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
36496 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
isQid#(ok(X)) |
→ |
isQid#(X) |
(469) |
could be deleted.
1.1.16.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
17th
component contains the
pair
U55#(ok(X1),ok(X2)) |
→ |
U55#(X1,X2) |
(593) |
U55#(mark(X1),X2) |
→ |
U55#(X1,X2) |
(496) |
1.1.17 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x2 + x3 + 2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x2 + 31253 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
2043 |
[U91(x1, x2)] |
=
|
16387 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
7640 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
15070 |
[U55(x1, x2)] |
=
|
32103 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
18542 |
[U72(x1, x2)] |
=
|
x2 + 25227 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
5976 |
[U73(x1, x2)] |
=
|
x2 + 2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 29377 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
21404 |
[U33(x1)] |
=
|
13670 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
5021 |
[U92(x1)] |
=
|
12088 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
x2 + 2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
19310 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U74(x1)] |
=
|
14013 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
36496 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
x2 + 0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U55#(ok(X1),ok(X2)) |
→ |
U55#(X1,X2) |
(593) |
could be deleted.
1.1.17.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
18th
component contains the
pair
U46#(ok(X)) |
→ |
U46#(X) |
(382) |
U46#(mark(X)) |
→ |
U46#(X) |
(345) |
1.1.18 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x2 + x3 + 1134 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x2 + 15083 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
x1 + 9763 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
25482 |
[U91(x1, x2)] |
=
|
41644 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
10836 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 9328 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
44461 |
[U55(x1, x2)] |
=
|
10327 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
18542 |
[U72(x1, x2)] |
=
|
x2 + 27871 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
31181 |
[ok(x1)] |
=
|
x1 + 8677 |
[isList(x1)] |
=
|
24999 |
[U73(x1, x2)] |
=
|
x2 + 32507 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
19503 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
22880 |
[mark(x1)] |
=
|
x1 + 29377 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
51466 |
[U33(x1)] |
=
|
11487 |
[U46#(x1)] |
=
|
x1 + 0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
23769 |
[U61(x1, x2)] |
=
|
14968 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
21030 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
19947 |
[U82(x1, x2)] |
=
|
x2 + 21723 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
27629 |
[U22(x1, x2, x3)] |
=
|
18756 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 10381 |
[U74(x1)] |
=
|
7990 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
3212 |
[U41(x1, x2, x3)] |
=
|
29874 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U46#(ok(X)) |
→ |
U46#(X) |
(382) |
U46#(mark(X)) |
→ |
U46#(X) |
(345) |
could be deleted.
1.1.18.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
19th
component contains the
pair
U61#(mark(X1),X2) |
→ |
U61#(X1,X2) |
(482) |
U61#(ok(X1),ok(X2)) |
→ |
U61#(X1,X2) |
(267) |
1.1.19 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x2 + x3 + 2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x2 + 1707 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
x1 + 1 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
41644 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 8795 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
31804 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 13559 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
44461 |
[U55(x1, x2)] |
=
|
4129 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
2 |
[U72(x1, x2)] |
=
|
x2 + 9530 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
3613 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
24999 |
[U73(x1, x2)] |
=
|
x2 + 18204 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
15512 |
[mark(x1)] |
=
|
x1 + 29377 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
51466 |
[U33(x1)] |
=
|
18541 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
14084 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
23769 |
[U61(x1, x2)] |
=
|
14968 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
28719 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
x2 + 2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
27629 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U74(x1)] |
=
|
7990 |
[isPalListKind(x1)] |
=
|
x1 + 17483 |
[U53(x1, x2, x3)] |
=
|
24011 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x2 + 2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
x2 + 0 |
together with the usable
rule
isNeList(ok(X)) |
→ |
ok(isNeList(X)) |
(193) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U61#(ok(X1),ok(X2)) |
→ |
U61#(X1,X2) |
(267) |
could be deleted.
1.1.19.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
20th
component contains the
pair
U25#(mark(X1),X2) |
→ |
U25#(X1,X2) |
(543) |
U25#(ok(X1),ok(X2)) |
→ |
U25#(X1,X2) |
(360) |
1.1.20 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
0 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 1 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + 0 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
4 |
[U56(x1)] |
=
|
x1 + 2 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
4 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
4 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
2 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
x1 + 0 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
2 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
4 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
2 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
x1 + 0 |
[U62(x1, x2)] |
=
|
3 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
0 |
[mark(x1)] |
=
|
x1 + 29689 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
5 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
0 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 29686 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 4 |
[U82(x1, x2)] |
=
|
3 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + 3 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 1 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U25#(mark(X1),X2) |
→ |
U25#(X1,X2) |
(543) |
U25#(ok(X1),ok(X2)) |
→ |
U25#(X1,X2) |
(360) |
could be deleted.
1.1.20.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
21th
component contains the
pair
U72#(mark(X1),X2) |
→ |
U72#(X1,X2) |
(475) |
U72#(ok(X1),ok(X2)) |
→ |
U72#(X1,X2) |
(378) |
1.1.21 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
0 |
[U72#(x1, x2)] |
=
|
x2 + 0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 29651 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + 0 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
4 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
4 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
2 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
x1 + 0 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
2 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 14846 |
[isList(x1)] |
=
|
2 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
38587 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
3 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
0 |
[mark(x1)] |
=
|
x1 + 92537 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
24833 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
0 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 53948 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 1 |
[U82(x1, x2)] |
=
|
6073 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 1 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
U72#(ok(X1),ok(X2)) |
→ |
U72#(X1,X2) |
(378) |
could be deleted.
1.1.21.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
22th
component contains the
pair
U11#(mark(X1),X2) |
→ |
U11#(X1,X2) |
(505) |
U11#(ok(X1),ok(X2)) |
→ |
U11#(X1,X2) |
(421) |
1.1.22 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
0 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x3 + 1 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + 0 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x2 + 0 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
1 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
x1 + 1 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
2 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U63(x1)] |
=
|
x1 + 0 |
[isNePal(x1)] |
=
|
x1 + 1 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
2 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
2 |
[U73(x1, x2)] |
=
|
x1 + 1 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
0 |
[mark(x1)] |
=
|
x1 + 4 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
4 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
0 |
[U11#(x1, x2)] |
=
|
x1 + x2 + 0 |
[active(x1)] |
=
|
x1 + 1 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 1 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U74(x1)] |
=
|
3 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 1 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U11#(mark(X1),X2) |
→ |
U11#(X1,X2) |
(505) |
U11#(ok(X1),ok(X2)) |
→ |
U11#(X1,X2) |
(421) |
could be deleted.
1.1.22.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
23th
component contains the
pair
U74#(ok(X)) |
→ |
U74#(X) |
(428) |
U74#(mark(X)) |
→ |
U74#(X) |
(346) |
1.1.23 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 31551 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
21398 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 15172 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
28026 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
8509 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
22798 |
[U91(x1, x2)] |
=
|
x1 + x2 + 9123 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
24929 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 5017 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
11984 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 11000 |
[U55(x1, x2)] |
=
|
x1 + x2 + 25297 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 13629 |
[U63(x1)] |
=
|
4933 |
[isNePal(x1)] |
=
|
x1 + 28605 |
[U72(x1, x2)] |
=
|
21334 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 26488 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
12418 |
[o] |
=
|
10911 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
16006 |
[ok(x1)] |
=
|
x1 + 550 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x2 + 24081 |
[U74#(x1)] |
=
|
x1 + 0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
18237 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
247 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
28351 |
[mark(x1)] |
=
|
x1 + 9343 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x1 + x2 + 22058 |
[U33(x1)] |
=
|
6095 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
8345 |
[U52(x1, x2, x3)] |
=
|
x1 + x3 + 26630 |
[U61(x1, x2)] |
=
|
x1 + x2 + 19334 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
20807 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + x2 + 12189 |
[U92(x1)] |
=
|
11556 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
29933 |
[U82(x1, x2)] |
=
|
x1 + x2 + 16881 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
32117 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 29739 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x2 + 8562 |
[U74(x1)] |
=
|
x1 + 32206 |
[isPalListKind(x1)] |
=
|
13021 |
[U53(x1, x2, x3)] |
=
|
4401 |
[U41(x1, x2, x3)] |
=
|
10733 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
32768 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U74#(ok(X)) |
→ |
U74#(X) |
(428) |
U74#(mark(X)) |
→ |
U74#(X) |
(346) |
could be deleted.
1.1.23.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
24th
component contains the
pair
U26#(ok(X)) |
→ |
U26#(X) |
(572) |
U26#(mark(X)) |
→ |
U26#(X) |
(268) |
1.1.24 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x3 + 23765 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
30167 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 26581 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
19371 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
16291 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
15234 |
[U91(x1, x2)] |
=
|
x1 + x2 + 56489 |
[u] |
=
|
2618 |
[U26(x1)] |
=
|
7161 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x3 + 31403 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x2 + 14796 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 15153 |
[U55(x1, x2)] |
=
|
x1 + x2 + 18786 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 15251 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
28606 |
[U72(x1, x2)] |
=
|
21224 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 56639 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
x1 + 0 |
[U54(x1, x2, x3)] |
=
|
13993 |
[o] |
=
|
59018 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 1940 |
[isList(x1)] |
=
|
x1 + 19077 |
[U73(x1, x2)] |
=
|
x2 + 35989 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
19171 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
28449 |
[mark(x1)] |
=
|
x1 + 16822 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
53605 |
[U33(x1)] |
=
|
21650 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 17078 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + 1 |
[U61(x1, x2)] |
=
|
x1 + 26535 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
20807 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + x2 + 27420 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
4373 |
[U82(x1, x2)] |
=
|
x1 + x2 + 1328 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
40451 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + 20912 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x2 + 28196 |
[U74(x1)] |
=
|
x1 + 32528 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
8334 |
[U41(x1, x2, x3)] |
=
|
17343 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U26#(ok(X)) |
→ |
U26#(X) |
(572) |
U26#(mark(X)) |
→ |
U26#(X) |
(268) |
could be deleted.
1.1.24.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
25th
component contains the
pair
U13#(mark(X)) |
→ |
U13#(X) |
(367) |
U13#(ok(X)) |
→ |
U13#(X) |
(251) |
1.1.25 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x3 + 32611 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
25254 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
24839 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
27645 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
28588 |
[U91(x1, x2)] |
=
|
x1 + x2 + 1 |
[u] |
=
|
13345 |
[U26(x1)] |
=
|
20181 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x3 + 44022 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x2 + 26091 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1535 |
[U55(x1, x2)] |
=
|
x1 + x2 + 30464 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
28606 |
[U72(x1, x2)] |
=
|
24434 |
[U13#(x1)] |
=
|
x1 + 0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 14615 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
25403 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 17714 |
[isList(x1)] |
=
|
x1 + 15508 |
[U73(x1, x2)] |
=
|
x2 + 53614 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
8162 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
18688 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
60539 |
[mark(x1)] |
=
|
x1 + 16822 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
24201 |
[U33(x1)] |
=
|
45611 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 3444 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + 1 |
[U61(x1, x2)] |
=
|
x1 + 1 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
3609 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + x2 + 55459 |
[U92(x1)] |
=
|
7190 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2088 |
[U82(x1, x2)] |
=
|
x1 + x2 + 870 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
49038 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + 13751 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x2 + 19273 |
[U74(x1)] |
=
|
x1 + 32528 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
31482 |
[U41(x1, x2, x3)] |
=
|
30961 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U13#(mark(X)) |
→ |
U13#(X) |
(367) |
U13#(ok(X)) |
→ |
U13#(X) |
(251) |
could be deleted.
1.1.25.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
26th
component contains the
pair
isNeList#(ok(X)) |
→ |
isNeList#(X) |
(376) |
1.1.26 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x3 + 6620 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
18530 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
17345 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
1050 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
28588 |
[U91(x1, x2)] |
=
|
x1 + x2 + 1 |
[u] |
=
|
13345 |
[U26(x1)] |
=
|
25137 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
x1 + 0 |
[U43(x1, x2, x3)] |
=
|
x2 + 7926 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1594 |
[U55(x1, x2)] |
=
|
x1 + x2 + 20380 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 11796 |
[U63(x1)] |
=
|
x1 + 31296 |
[isNePal(x1)] |
=
|
22709 |
[U72(x1, x2)] |
=
|
18273 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 9332 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
31844 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 10187 |
[ok(x1)] |
=
|
x1 + 18910 |
[isList(x1)] |
=
|
x1 + 34315 |
[U73(x1, x2)] |
=
|
x2 + 17732 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
50401 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
32607 |
[mark(x1)] |
=
|
x1 + 12490 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
29318 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
4461 |
[U52(x1, x2, x3)] |
=
|
x1 + 1 |
[U61(x1, x2)] |
=
|
x1 + 17218 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + x2 + 52046 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
25040 |
[U82(x1, x2)] |
=
|
x1 + x2 + 33470 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
67987 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x2 + 24632 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
30056 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
8620 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
isNeList#(ok(X)) |
→ |
isNeList#(X) |
(376) |
could be deleted.
1.1.26.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
27th
component contains the
pair
U41#(mark(X1),X2,X3) |
→ |
U41#(X1,X2,X3) |
(384) |
U41#(ok(X1),ok(X2),ok(X3)) |
→ |
U41#(X1,X2,X3) |
(361) |
1.1.27 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
12144 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
17345 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
14367 |
[U91(x1, x2)] |
=
|
x1 + x2 + 1 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x2 + 17467 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
x1 + x2 + 1 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U63(x1)] |
=
|
x1 + 31296 |
[isNePal(x1)] |
=
|
22709 |
[U72(x1, x2)] |
=
|
24654 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 4221 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x2 + 16106 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2854 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
8862 |
[mark(x1)] |
=
|
x1 + 8094 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
30358 |
[U33(x1)] |
=
|
32567 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + 1 |
[U61(x1, x2)] |
=
|
x1 + 19502 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + x2 + 1 |
[U92(x1)] |
=
|
28827 |
[U41#(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
10729 |
[U82(x1, x2)] |
=
|
x1 + x2 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
70760 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x2 + 28833 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U41#(mark(X1),X2,X3) |
→ |
U41#(X1,X2,X3) |
(384) |
U41#(ok(X1),ok(X2),ok(X3)) |
→ |
U41#(X1,X2,X3) |
(361) |
could be deleted.
1.1.27.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
28th
component contains the
pair
U62#(mark(X1),X2) |
→ |
U62#(X1,X2) |
(551) |
U62#(ok(X1),ok(X2)) |
→ |
U62#(X1,X2) |
(272) |
1.1.28 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
6085 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 50075 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
8821 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
44806 |
[U91(x1, x2)] |
=
|
x1 + x2 + 1 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
21666 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x2 + 46327 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 28240 |
[U55(x1, x2)] |
=
|
x1 + x2 + 1 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U63(x1)] |
=
|
x1 + 7483 |
[isNePal(x1)] |
=
|
27998 |
[U72(x1, x2)] |
=
|
26532 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 24460 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
28407 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
x1 + 0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x2 + 18461 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
23639 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
23653 |
[mark(x1)] |
=
|
x1 + 19133 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
7951 |
[U33(x1)] |
=
|
32567 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
25652 |
[U52(x1, x2, x3)] |
=
|
x1 + 1 |
[U61(x1, x2)] |
=
|
x1 + 1 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + x2 + 45824 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2697 |
[U82(x1, x2)] |
=
|
x1 + x2 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
100680 |
[U22(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x2 + 25051 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
24838 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U62#(mark(X1),X2) |
→ |
U62#(X1,X2) |
(551) |
U62#(ok(X1),ok(X2)) |
→ |
U62#(X1,X2) |
(272) |
could be deleted.
1.1.28.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
29th
component contains the
pair
U52#(mark(X1),X2,X3) |
→ |
U52#(X1,X2,X3) |
(549) |
U52#(ok(X1),ok(X2),ok(X3)) |
→ |
U52#(X1,X2,X3) |
(262) |
1.1.29 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
2 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
44293 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 2 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
x1 + 6164 |
[isNePal(x1)] |
=
|
27998 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
x3 + 0 |
[U12(x1, x2)] |
=
|
x2 + 2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
14823 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 1208 |
[isList(x1)] |
=
|
5795 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
0 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
3 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
16447 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
35035 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
11012 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
10092 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
17696 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U52#(ok(X1),ok(X2),ok(X3)) |
→ |
U52#(X1,X2,X3) |
(262) |
could be deleted.
1.1.29.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
30th
component contains the
pair
U53#(mark(X1),X2,X3) |
→ |
U53#(X1,X2,X3) |
(535) |
U53#(ok(X1),ok(X2),ok(X3)) |
→ |
U53#(X1,X2,X3) |
(524) |
1.1.30 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
15728 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
6451 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
28161 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
27496 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
x2 + 0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
25989 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
27998 |
[U72(x1, x2)] |
=
|
21148 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
30978 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2629 |
[ok(x1)] |
=
|
x1 + 16646 |
[isList(x1)] |
=
|
13685 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
0 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 5313 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
11983 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
25933 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
21276 |
[U92(x1)] |
=
|
x1 + 27903 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
16373 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
0 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
15888 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
10291 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U53#(ok(X1),ok(X2),ok(X3)) |
→ |
U53#(X1,X2,X3) |
(524) |
could be deleted.
1.1.30.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
31th
component contains the
pair
U43#(mark(X1),X2,X3) |
→ |
U43#(X1,X2,X3) |
(477) |
U43#(ok(X1),ok(X2),ok(X3)) |
→ |
U43#(X1,X2,X3) |
(343) |
1.1.31 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
31266 |
[U24(x1, x2, x3)] |
=
|
18004 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
2 |
[isNeList(x1)] |
=
|
3453 |
[U56(x1)] |
=
|
28095 |
[isPal(x1)] |
=
|
912 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
16043 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
x3 + 0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
x1 + 29902 |
[isNePal(x1)] |
=
|
27998 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 32513 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
5559 |
[ok(x1)] |
=
|
x1 + 14805 |
[isList(x1)] |
=
|
13685 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
0 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
3916 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 5313 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
1666 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
24014 |
[U92(x1)] |
=
|
x1 + 1 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
0 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
30142 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
13920 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U43#(ok(X1),ok(X2),ok(X3)) |
→ |
U43#(X1,X2,X3) |
(343) |
could be deleted.
1.1.31.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
32th
component contains the
pair
U73#(mark(X1),X2) |
→ |
U73#(X1,X2) |
(336) |
U73#(ok(X1),ok(X2)) |
→ |
U73#(X1,X2) |
(237) |
1.1.32 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + x2 + 21231 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + x2 + 27532 |
[isNeList(x1)] |
=
|
7802 |
[U56(x1)] |
=
|
x1 + 1 |
[isPal(x1)] |
=
|
32090 |
[U42(x1, x2, x3)] |
=
|
14153 |
[U91(x1, x2)] |
=
|
4721 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
15617 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 28658 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
11916 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 7602 |
[U55(x1, x2)] |
=
|
18414 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
4205 |
[U63(x1)] |
=
|
9965 |
[isNePal(x1)] |
=
|
8413 |
[U72(x1, x2)] |
=
|
x1 + 4737 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 11751 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
7852 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + 1 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 8411 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
1970 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
x2 + 0 |
[nil] |
=
|
2363 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 19980 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
7268 |
[mark(x1)] |
=
|
18415 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x2 + 18414 |
[U33(x1)] |
=
|
x1 + 1 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
7195 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
12275 |
[U61(x1, x2)] |
=
|
x2 + 479 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
12183 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
13899 |
[U92(x1)] |
=
|
x1 + 6511 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
9864 |
[U82(x1, x2)] |
=
|
8297 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
6047 |
[U22(x1, x2, x3)] |
=
|
10879 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x3 + 2894 |
[U74(x1)] |
=
|
10816 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
4502 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 52429 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
U73#(ok(X1),ok(X2)) |
→ |
U73#(X1,X2) |
(237) |
could be deleted.
1.1.32.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
33th
component contains the
pair
isPal#(ok(X)) |
→ |
isPal#(X) |
(330) |
1.1.33 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + x2 + 0 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + x2 + 0 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
2 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
7066 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
x1 + x2 + 0 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x3 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
x1 + 0 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
x1 + 0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
2 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 3 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x1 + 0 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 0 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + x2 + 0 |
[mark(x1)] |
=
|
x1 + 15817 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x1 + x2 + 0 |
[U33(x1)] |
=
|
x1 + 0 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 0 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U61(x1, x2)] |
=
|
x2 + 1 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
2 |
[U31(x1, x2)] |
=
|
3 |
[U92(x1)] |
=
|
x1 + 0 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 0 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
x1 + 0 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
isList(ok(X)) |
→ |
ok(isList(X)) |
(199) |
U45(ok(X1),ok(X2)) |
→ |
ok(U45(X1,X2)) |
(209) |
U45(mark(X1),X2) |
→ |
mark(U45(X1,X2)) |
(118) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
isPal#(ok(X)) |
→ |
isPal#(X) |
(330) |
could be deleted.
1.1.33.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
34th
component contains the
pair
U56#(mark(X)) |
→ |
U56#(X) |
(375) |
U56#(ok(X)) |
→ |
U56#(X) |
(304) |
1.1.34 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + x2 + 0 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + x2 + 0 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
8538 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
8840 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x3 + 1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
x1 + x2 + 0 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x3 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
x1 + 0 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
11316 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
29071 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x1 + 0 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 0 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + x2 + 0 |
[mark(x1)] |
=
|
x1 + 3 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
x1 + x2 + 0 |
[U33(x1)] |
=
|
x1 + 0 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
x1 + 0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 0 |
[i] |
=
|
21267 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U61(x1, x2)] |
=
|
x2 + 1 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
13227 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
2 |
[U31(x1, x2)] |
=
|
4610 |
[U92(x1)] |
=
|
x1 + 0 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 0 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
x1 + 0 |
[isPalListKind(x1)] |
=
|
x1 + 57327 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
isList(ok(X)) |
→ |
ok(isList(X)) |
(199) |
U45(ok(X1),ok(X2)) |
→ |
ok(U45(X1,X2)) |
(209) |
U45(mark(X1),X2) |
→ |
mark(U45(X1,X2)) |
(118) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U56#(mark(X)) |
→ |
U56#(X) |
(375) |
U56#(ok(X)) |
→ |
U56#(X) |
(304) |
could be deleted.
1.1.34.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
35th
component contains the
pair
isList#(ok(X)) |
→ |
isList#(X) |
(576) |
1.1.35 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
x1 + x2 + 0 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + x2 + 0 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
8538 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
19179 |
[u] |
=
|
31835 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
x3 + 1 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
x1 + x2 + 0 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
x1 + x3 + 0 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
x1 + 0 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
2 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 10911 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
x1 + 0 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + 0 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
x1 + x2 + 0 |
[mark(x1)] |
=
|
x1 + 3 |
[isList#(x1)] |
=
|
x1 + 0 |
[U32(x1, x2)] |
=
|
x1 + x2 + 0 |
[U33(x1)] |
=
|
x1 + 0 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 0 |
[i] |
=
|
21267 |
[U52(x1, x2, x3)] |
=
|
x1 + x2 + 0 |
[U61(x1, x2)] |
=
|
x2 + 1 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
4966 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
2 |
[U31(x1, x2)] |
=
|
24413 |
[U92(x1)] |
=
|
x1 + 0 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x1 + 0 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
2 |
[U22(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
x1 + 0 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
isList(ok(X)) |
→ |
ok(isList(X)) |
(199) |
U45(ok(X1),ok(X2)) |
→ |
ok(U45(X1,X2)) |
(209) |
U45(mark(X1),X2) |
→ |
mark(U45(X1,X2)) |
(118) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
isList#(ok(X)) |
→ |
isList#(X) |
(576) |
could be deleted.
1.1.35.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
36th
component contains the
pair
U54#(mark(X1),X2,X3) |
→ |
U54#(X1,X2,X3) |
(495) |
U54#(ok(X1),ok(X2),ok(X3)) |
→ |
U54#(X1,X2,X3) |
(442) |
1.1.36 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
7049 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
2 |
[isNeList(x1)] |
=
|
227 |
[U56(x1)] |
=
|
24620 |
[isPal(x1)] |
=
|
8538 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
25120 |
[u] |
=
|
16419 |
[U26(x1)] |
=
|
20867 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 31230 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
1273 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 5745 |
[U55(x1, x2)] |
=
|
470 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
20083 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
13592 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
5745 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
4489 |
[o] |
=
|
16652 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
21614 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
16905 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
15260 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
23771 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
3078 |
[mark(x1)] |
=
|
31230 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
4478 |
[U33(x1)] |
=
|
3807 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
17401 |
[U52(x1, x2, x3)] |
=
|
630 |
[U61(x1, x2)] |
=
|
155 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
4386 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
4826 |
[U92(x1)] |
=
|
26124 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
16443 |
[U82(x1, x2)] |
=
|
26189 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
6810 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
11785 |
[U22(x1, x2, x3)] |
=
|
24813 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
17946 |
[U74(x1)] |
=
|
19992 |
[isPalListKind(x1)] |
=
|
15775 |
[U53(x1, x2, x3)] |
=
|
6228 |
[U41(x1, x2, x3)] |
=
|
9057 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 1 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rules
U71(mark(X1),X2,X3) |
→ |
mark(U71(X1,X2,X3)) |
(129) |
U71(ok(X1),ok(X2),ok(X3)) |
→ |
ok(U71(X1,X2,X3)) |
(220) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U54#(ok(X1),ok(X2),ok(X3)) |
→ |
U54#(X1,X2,X3) |
(442) |
could be deleted.
1.1.36.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
37th
component contains the
pair
U22#(ok(X1),ok(X2),ok(X3)) |
→ |
U22#(X1,X2,X3) |
(422) |
U22#(mark(X1),X2,X3) |
→ |
U22#(X1,X2,X3) |
(244) |
1.1.37 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
3064 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
15030 |
[isPal(x1)] |
=
|
2249 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
0 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
1743 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 14654 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
26458 |
[U63(x1)] |
=
|
22526 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 16026 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
2 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 25665 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
12798 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
0 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
x3 + 0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
278 |
[isPalListKind(x1)] |
=
|
15775 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
13722 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
U22#(ok(X1),ok(X2),ok(X3)) |
→ |
U22#(X1,X2,X3) |
(422) |
could be deleted.
1.1.37.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
38th
component contains the
pair
U83#(mark(X)) |
→ |
U83#(X) |
(499) |
U83#(ok(X)) |
→ |
U83#(X) |
(467) |
1.1.38 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
x1 + 0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
21203 |
[isNeList(x1)] |
=
|
16907 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
2249 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
30741 |
[u] |
=
|
43280 |
[U26(x1)] |
=
|
0 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 30193 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 26817 |
[U55(x1, x2)] |
=
|
49853 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
22858 |
[U63(x1)] |
=
|
42167 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 18033 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
13740 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 3857 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
3040 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
18190 |
[mark(x1)] |
=
|
x1 + 25665 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
52460 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 27078 |
[i] |
=
|
7177 |
[U52(x1, x2, x3)] |
=
|
29365 |
[U61(x1, x2)] |
=
|
28067 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
34400 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x2 + 0 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 13302 |
[U22(x1, x2, x3)] |
=
|
29994 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
27804 |
[isPalListKind(x1)] |
=
|
15775 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U83#(mark(X)) |
→ |
U83#(X) |
(499) |
U83#(ok(X)) |
→ |
U83#(X) |
(467) |
could be deleted.
1.1.38.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
39th
component contains the
pair
isNePal#(ok(X)) |
→ |
isNePal#(X) |
(472) |
1.1.39 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
2 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
2 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
24631 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
26272 |
[u] |
=
|
43280 |
[U26(x1)] |
=
|
0 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x2 + x3 + 2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x2 + x3 + 2 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
42167 |
[isNePal(x1)] |
=
|
28642 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x2 + 18033 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
13740 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2 |
[o] |
=
|
50775 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 14421 |
[isList(x1)] |
=
|
x1 + 1 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
x1 + 0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
18190 |
[mark(x1)] |
=
|
x1 + 25665 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
52460 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
x1 + 1 |
[i] |
=
|
33881 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
35102 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
x2 + 0 |
[U82(x1, x2)] |
=
|
2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
29994 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
2 |
[U74(x1)] |
=
|
27804 |
[isPalListKind(x1)] |
=
|
15775 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
x1 + x2 + 0 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
isNePal#(ok(X)) |
→ |
isNePal#(X) |
(472) |
could be deleted.
1.1.39.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
40th
component contains the
pair
U42#(mark(X1),X2,X3) |
→ |
U42#(X1,X2,X3) |
(545) |
U42#(ok(X1),ok(X2),ok(X3)) |
→ |
U42#(X1,X2,X3) |
(523) |
1.1.40 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
170 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
1658 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
3 |
[U24(x1, x2, x3)] |
=
|
x1 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + 1 |
[isNeList(x1)] |
=
|
2453 |
[U56(x1)] |
=
|
3 |
[isPal(x1)] |
=
|
2 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
2134 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 514 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U55(x1, x2)] |
=
|
3 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
0 |
[U72(x1, x2)] |
=
|
3 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 4 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x3 + 3 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
x1 + x3 + 0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 10081 |
[isList(x1)] |
=
|
2 |
[U73(x1, x2)] |
=
|
4 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
23065 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 3569 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
3 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
3 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
819 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 1 |
[U31(x1, x2)] |
=
|
4 |
[U92(x1)] |
=
|
3 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
1 |
[U82(x1, x2)] |
=
|
x1 + 2 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
4 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + 3 |
[U74(x1)] |
=
|
x1 + 2770 |
[isPalListKind(x1)] |
=
|
3 |
[U53(x1, x2, x3)] |
=
|
3 |
[U41(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
3567 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
U42#(mark(X1),X2,X3) |
→ |
U42#(X1,X2,X3) |
(545) |
U42#(ok(X1),ok(X2),ok(X3)) |
→ |
U42#(X1,X2,X3) |
(523) |
could be deleted.
1.1.40.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
41th
component contains the
pair
__#(ok(X1),ok(X2)) |
→ |
__#(X1,X2) |
(458) |
__#(X1,mark(X2)) |
→ |
__#(X1,X2) |
(350) |
__#(mark(X1),X2) |
→ |
__#(X1,X2) |
(307) |
1.1.41 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
x1 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + 1 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
2 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
x2 + 0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
0 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x3 + 1 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
2 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
23065 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 4 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 1 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
1 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + 1 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
__#(ok(X1),ok(X2)) |
→ |
__#(X1,X2) |
(458) |
__#(X1,mark(X2)) |
→ |
__#(X1,X2) |
(350) |
could be deleted.
1.1.41.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
42th
component contains the
pair
U23#(mark(X1),X2,X3) |
→ |
U23#(X1,X2,X3) |
(321) |
U23#(ok(X1),ok(X2),ok(X3)) |
→ |
U23#(X1,X2,X3) |
(270) |
1.1.42 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
4 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
x1 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
x1 + 1 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
2 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
3 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
3 |
[U23#(x1, x2, x3)] |
=
|
x2 + 0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 0 |
[U55(x1, x2)] |
=
|
3 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
2 |
[isNePal(x1)] |
=
|
0 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
x1 + 1 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x3 + 1 |
[o] |
=
|
0 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
x1 + 1 |
[ok(x1)] |
=
|
x1 + 2 |
[isList(x1)] |
=
|
2 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
2 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 4 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
0 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
x1 + 1 |
[U31(x1, x2)] |
=
|
2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
1 |
[U82(x1, x2)] |
=
|
x1 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + 1 |
[U74(x1)] |
=
|
x1 + 1 |
[isPalListKind(x1)] |
=
|
2 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
x2 + x3 + 0 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
together with the usable
rule
isQid(ok(X)) |
→ |
ok(isQid(X)) |
(204) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pair
U23#(ok(X1),ok(X2),ok(X3)) |
→ |
U23#(X1,X2,X3) |
(270) |
could be deleted.
1.1.42.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
43th
component contains the
pair
U12#(ok(X1),ok(X2)) |
→ |
U12#(X1,X2) |
(412) |
U12#(mark(X1),X2) |
→ |
U12#(X1,X2) |
(359) |
1.1.43 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
165 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 26974 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
10513 |
[isNeList(x1)] |
=
|
1739 |
[U56(x1)] |
=
|
14301 |
[isPal(x1)] |
=
|
9179 |
[U42(x1, x2, x3)] |
=
|
2164 |
[U91(x1, x2)] |
=
|
11867 |
[u] |
=
|
6463 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
31670 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
25 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 28686 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
26491 |
[U63(x1)] |
=
|
x1 + 12086 |
[isNePal(x1)] |
=
|
567 |
[U72(x1, x2)] |
=
|
11792 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 4519 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 28775 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
x2 + 0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
40884 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
15043 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + x2 + 24143 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 2170 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
13687 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
11841 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
32275 |
[U82(x1, x2)] |
=
|
x1 + x2 + 29626 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
53696 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
26716 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + 15066 |
[U74(x1)] |
=
|
24237 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
23545 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
14780 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
U12#(ok(X1),ok(X2)) |
→ |
U12#(X1,X2) |
(412) |
could be deleted.
1.1.43.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
44th
component contains the
pair
U45#(mark(X1),X2) |
→ |
U45#(X1,X2) |
(488) |
U45#(ok(X1),ok(X2)) |
→ |
U45#(X1,X2) |
(310) |
1.1.44 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
2 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
2 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
x2 + 2 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
2 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
567 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 1 |
[isList(x1)] |
=
|
14772 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + x2 + 1 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 2170 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
12928 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
2 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
1077 |
[U82(x1, x2)] |
=
|
x1 + x2 + 1 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
x1 + 0 |
[U51(x1, x2, x3)] |
=
|
x1 + 1 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pairs
U45#(mark(X1),X2) |
→ |
U45#(X1,X2) |
(488) |
U45#(ok(X1),ok(X2)) |
→ |
U45#(X1,X2) |
(310) |
could be deleted.
1.1.44.1 Dependency Graph Processor
The dependency pairs are split into 0
components.
-
The
45th
component contains the
pair
U44#(mark(X1),X2,X3) |
→ |
U44#(X1,X2,X3) |
(516) |
U44#(ok(X1),ok(X2),ok(X3)) |
→ |
U44#(X1,X2,X3) |
(387) |
1.1.45 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
0 |
[U11(x1, x2)] |
=
|
2 |
[U24(x1, x2, x3)] |
=
|
x1 + x2 + 1 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
2 |
[isNeList(x1)] |
=
|
2 |
[U56(x1)] |
=
|
2 |
[isPal(x1)] |
=
|
21268 |
[U42(x1, x2, x3)] |
=
|
2 |
[U91(x1, x2)] |
=
|
x2 + 1905 |
[u] |
=
|
1 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
15775 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
2 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
2 |
[U63(x1)] |
=
|
x1 + 1 |
[isNePal(x1)] |
=
|
567 |
[U72(x1, x2)] |
=
|
2 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
x1 + 1 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 1 |
[o] |
=
|
1 |
[U44#(x1, x2, x3)] |
=
|
x3 + 0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
2 |
[ok(x1)] |
=
|
x1 + 28720 |
[isList(x1)] |
=
|
14772 |
[U73(x1, x2)] |
=
|
2 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x1 + x2 + 1 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2 |
[mark(x1)] |
=
|
x1 + 2170 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
2 |
[U33(x1)] |
=
|
2 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
2 |
[i] |
=
|
1 |
[U52(x1, x2, x3)] |
=
|
2 |
[U61(x1, x2)] |
=
|
x2 + 11353 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x2 + 2 |
[U92(x1)] |
=
|
2 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2 |
[U82(x1, x2)] |
=
|
x1 + x2 + 20105 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
1 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
x1 + 1 |
[U22(x1, x2, x3)] |
=
|
2 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
x1 + 1 |
[U74(x1)] |
=
|
2 |
[isPalListKind(x1)] |
=
|
x1 + 1 |
[U53(x1, x2, x3)] |
=
|
2 |
[U41(x1, x2, x3)] |
=
|
2 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
2 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
U44#(ok(X1),ok(X2),ok(X3)) |
→ |
U44#(X1,X2,X3) |
(387) |
could be deleted.
1.1.45.1 Dependency Graph Processor
The dependency pairs are split into 1
component.
-
The
46th
component contains the
pair
isPalListKind#(ok(X)) |
→ |
isPalListKind#(X) |
(286) |
1.1.46 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation
[a] |
=
|
1 |
[U72#(x1, x2)] |
=
|
0 |
[U32#(x1, x2)] |
=
|
0 |
[U21(x1, x2, x3)] |
=
|
2 |
[U83#(x1)] |
=
|
0 |
[isPalListKind#(x1)] |
=
|
x1 + 0 |
[U11(x1, x2)] |
=
|
1163 |
[U24(x1, x2, x3)] |
=
|
2223 |
[U24#(x1, x2, x3)] |
=
|
0 |
[U25(x1, x2)] |
=
|
1011 |
[isNeList(x1)] |
=
|
28231 |
[U56(x1)] |
=
|
3696 |
[isPal(x1)] |
=
|
27938 |
[U42(x1, x2, x3)] |
=
|
2698 |
[U91(x1, x2)] |
=
|
x2 + 3201 |
[u] |
=
|
16612 |
[U26(x1)] |
=
|
2 |
[U82#(x1, x2)] |
=
|
0 |
[U71(x1, x2, x3)] |
=
|
3696 |
[top(x1)] |
=
|
0 |
[U81#(x1, x2)] |
=
|
0 |
[U92#(x1)] |
=
|
0 |
[isNeList#(x1)] |
=
|
0 |
[U43(x1, x2, x3)] |
=
|
3696 |
[U23#(x1, x2, x3)] |
=
|
0 |
[U53#(x1, x2, x3)] |
=
|
0 |
[top#(x1)] |
=
|
0 |
[__#(x1, x2)] |
=
|
0 |
[U44(x1, x2, x3)] |
=
|
x1 + x2 + x3 + 22967 |
[U55(x1, x2)] |
=
|
2 |
[U43#(x1, x2, x3)] |
=
|
0 |
[U23(x1, x2, x3)] |
=
|
365 |
[U63(x1)] |
=
|
346 |
[isNePal(x1)] |
=
|
567 |
[U72(x1, x2)] |
=
|
x1 + x2 + 11901 |
[U13#(x1)] |
=
|
0 |
[isQid#(x1)] |
=
|
0 |
[isPal#(x1)] |
=
|
0 |
[U52#(x1, x2, x3)] |
=
|
0 |
[U12(x1, x2)] |
=
|
2231 |
[U33#(x1)] |
=
|
0 |
[isQid(x1)] |
=
|
28198 |
[U26#(x1)] |
=
|
0 |
[U54(x1, x2, x3)] |
=
|
2593 |
[o] |
=
|
4 |
[U44#(x1, x2, x3)] |
=
|
0 |
[U54#(x1, x2, x3)] |
=
|
0 |
[U42#(x1, x2, x3)] |
=
|
0 |
[U12#(x1, x2)] |
=
|
0 |
[proper(x1)] |
=
|
1 |
[U62#(x1, x2)] |
=
|
0 |
[U83(x1)] |
=
|
1081 |
[ok(x1)] |
=
|
x1 + 17392 |
[isList(x1)] |
=
|
6190 |
[U73(x1, x2)] |
=
|
1257 |
[U74#(x1)] |
=
|
0 |
[isNePal#(x1)] |
=
|
0 |
[U73#(x1, x2)] |
=
|
0 |
[nil] |
=
|
1 |
[U25#(x1, x2)] |
=
|
0 |
[U62(x1, x2)] |
=
|
x2 + 3263 |
[U63#(x1)] |
=
|
0 |
[U45(x1, x2)] |
=
|
2835 |
[mark(x1)] |
=
|
3697 |
[isList#(x1)] |
=
|
0 |
[U32(x1, x2)] |
=
|
373 |
[U33(x1)] |
=
|
951 |
[U46#(x1)] |
=
|
0 |
[U56#(x1)] |
=
|
0 |
[proper#(x1)] |
=
|
0 |
[U46(x1)] |
=
|
362 |
[i] |
=
|
27498 |
[U52(x1, x2, x3)] |
=
|
3148 |
[U61(x1, x2)] |
=
|
x2 + 1411 |
[U51#(x1, x2, x3)] |
=
|
0 |
[e] |
=
|
1 |
[U11#(x1, x2)] |
=
|
0 |
[active(x1)] |
=
|
1 |
[U31(x1, x2)] |
=
|
x1 + 17078 |
[U92(x1)] |
=
|
x1 + 6022 |
[U41#(x1, x2, x3)] |
=
|
0 |
[active#(x1)] |
=
|
0 |
[U21#(x1, x2, x3)] |
=
|
0 |
[U81(x1, x2)] |
=
|
2711 |
[U82(x1, x2)] |
=
|
x2 + 3692 |
[U22#(x1, x2, x3)] |
=
|
0 |
[tt] |
=
|
8714 |
[U71#(x1, x2, x3)] |
=
|
0 |
[U13(x1)] |
=
|
3299 |
[U22(x1, x2, x3)] |
=
|
1472 |
[U45#(x1, x2)] |
=
|
0 |
[U51(x1, x2, x3)] |
=
|
1253 |
[U74(x1)] |
=
|
152 |
[isPalListKind(x1)] |
=
|
11664 |
[U53(x1, x2, x3)] |
=
|
2360 |
[U41(x1, x2, x3)] |
=
|
575 |
[U31#(x1, x2)] |
=
|
0 |
[__(x1, x2)] |
=
|
1507 |
[U91#(x1, x2)] |
=
|
0 |
[U55#(x1, x2)] |
=
|
0 |
[U61#(x1, x2)] |
=
|
0 |
having no usable rules (w.r.t. the implicit argument filter of the
reduction pair),
the
pair
isPalListKind#(ok(X)) |
→ |
isPalListKind#(X) |
(286) |
could be deleted.
1.1.46.1 Dependency Graph Processor
The dependency pairs are split into 0
components.