The rewrite relation of the following TRS is considered.
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
U11(tt,V) | → | U12(isNeList(activate(V))) | (4) |
U12(tt) | → | tt | (5) |
U21(tt,V1,V2) | → | U22(isList(activate(V1)),activate(V2)) | (6) |
U22(tt,V2) | → | U23(isList(activate(V2))) | (7) |
U23(tt) | → | tt | (8) |
U31(tt,V) | → | U32(isQid(activate(V))) | (9) |
U32(tt) | → | tt | (10) |
U41(tt,V1,V2) | → | U42(isList(activate(V1)),activate(V2)) | (11) |
U42(tt,V2) | → | U43(isNeList(activate(V2))) | (12) |
U43(tt) | → | tt | (13) |
U51(tt,V1,V2) | → | U52(isNeList(activate(V1)),activate(V2)) | (14) |
U52(tt,V2) | → | U53(isList(activate(V2))) | (15) |
U53(tt) | → | tt | (16) |
U61(tt,V) | → | U62(isQid(activate(V))) | (17) |
U62(tt) | → | tt | (18) |
U71(tt,V) | → | U72(isNePal(activate(V))) | (19) |
U72(tt) | → | tt | (20) |
and(tt,X) | → | activate(X) | (21) |
isList(V) | → | U11(isPalListKind(activate(V)),activate(V)) | (22) |
isList(n__nil) | → | tt | (23) |
isList(n____(V1,V2)) | → | U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (24) |
isNeList(V) | → | U31(isPalListKind(activate(V)),activate(V)) | (25) |
isNeList(n____(V1,V2)) | → | U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (26) |
isNeList(n____(V1,V2)) | → | U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (27) |
isNePal(V) | → | U61(isPalListKind(activate(V)),activate(V)) | (28) |
isNePal(n____(I,__(P,I))) | → | and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)),n__isPalListKind(activate(P)))) | (29) |
isPal(V) | → | U71(isPalListKind(activate(V)),activate(V)) | (30) |
isPal(n__nil) | → | tt | (31) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isQid(n__a) | → | tt | (39) |
isQid(n__e) | → | tt | (40) |
isQid(n__i) | → | tt | (41) |
isQid(n__o) | → | tt | (42) |
isQid(n__u) | → | tt | (43) |
nil | → | n__nil | (44) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
__#(__(X,Y),Z) | → | __#(Y,Z) | (63) |
__#(__(X,Y),Z) | → | __#(X,__(Y,Z)) | (64) |
U11#(tt,V) | → | activate#(V) | (65) |
U11#(tt,V) | → | isNeList#(activate(V)) | (66) |
U11#(tt,V) | → | U12#(isNeList(activate(V))) | (67) |
U21#(tt,V1,V2) | → | activate#(V2) | (68) |
U21#(tt,V1,V2) | → | activate#(V1) | (69) |
U21#(tt,V1,V2) | → | isList#(activate(V1)) | (70) |
U21#(tt,V1,V2) | → | U22#(isList(activate(V1)),activate(V2)) | (71) |
U22#(tt,V2) | → | activate#(V2) | (72) |
U22#(tt,V2) | → | isList#(activate(V2)) | (73) |
U22#(tt,V2) | → | U23#(isList(activate(V2))) | (74) |
U31#(tt,V) | → | activate#(V) | (75) |
U31#(tt,V) | → | isQid#(activate(V)) | (76) |
U31#(tt,V) | → | U32#(isQid(activate(V))) | (77) |
U41#(tt,V1,V2) | → | activate#(V2) | (78) |
U41#(tt,V1,V2) | → | activate#(V1) | (79) |
U41#(tt,V1,V2) | → | isList#(activate(V1)) | (80) |
U41#(tt,V1,V2) | → | U42#(isList(activate(V1)),activate(V2)) | (81) |
U42#(tt,V2) | → | activate#(V2) | (82) |
U42#(tt,V2) | → | isNeList#(activate(V2)) | (83) |
U42#(tt,V2) | → | U43#(isNeList(activate(V2))) | (84) |
U51#(tt,V1,V2) | → | activate#(V2) | (85) |
U51#(tt,V1,V2) | → | activate#(V1) | (86) |
U51#(tt,V1,V2) | → | isNeList#(activate(V1)) | (87) |
U51#(tt,V1,V2) | → | U52#(isNeList(activate(V1)),activate(V2)) | (88) |
U52#(tt,V2) | → | activate#(V2) | (89) |
U52#(tt,V2) | → | isList#(activate(V2)) | (90) |
U52#(tt,V2) | → | U53#(isList(activate(V2))) | (91) |
U61#(tt,V) | → | activate#(V) | (92) |
U61#(tt,V) | → | isQid#(activate(V)) | (93) |
U61#(tt,V) | → | U62#(isQid(activate(V))) | (94) |
U71#(tt,V) | → | activate#(V) | (95) |
U71#(tt,V) | → | isNePal#(activate(V)) | (96) |
U71#(tt,V) | → | U72#(isNePal(activate(V))) | (97) |
and#(tt,X) | → | activate#(X) | (98) |
isList#(V) | → | activate#(V) | (99) |
isList#(V) | → | isPalListKind#(activate(V)) | (100) |
isList#(V) | → | U11#(isPalListKind(activate(V)),activate(V)) | (101) |
isList#(n____(V1,V2)) | → | activate#(V2) | (102) |
isList#(n____(V1,V2)) | → | activate#(V1) | (103) |
isList#(n____(V1,V2)) | → | isPalListKind#(activate(V1)) | (104) |
isList#(n____(V1,V2)) | → | and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (105) |
isList#(n____(V1,V2)) | → | U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (106) |
isNeList#(V) | → | activate#(V) | (107) |
isNeList#(V) | → | isPalListKind#(activate(V)) | (108) |
isNeList#(V) | → | U31#(isPalListKind(activate(V)),activate(V)) | (109) |
isNeList#(n____(V1,V2)) | → | activate#(V2) | (110) |
isNeList#(n____(V1,V2)) | → | activate#(V1) | (111) |
isNeList#(n____(V1,V2)) | → | isPalListKind#(activate(V1)) | (112) |
isNeList#(n____(V1,V2)) | → | and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (113) |
isNeList#(n____(V1,V2)) | → | U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (114) |
isNeList#(n____(V1,V2)) | → | U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (115) |
isNePal#(V) | → | activate#(V) | (116) |
isNePal#(V) | → | isPalListKind#(activate(V)) | (117) |
isNePal#(V) | → | U61#(isPalListKind(activate(V)),activate(V)) | (118) |
isNePal#(n____(I,__(P,I))) | → | activate#(P) | (119) |
isNePal#(n____(I,__(P,I))) | → | isPal#(activate(P)) | (120) |
isNePal#(n____(I,__(P,I))) | → | activate#(I) | (121) |
isNePal#(n____(I,__(P,I))) | → | isQid#(activate(I)) | (122) |
isNePal#(n____(I,__(P,I))) | → | and#(isQid(activate(I)),n__isPalListKind(activate(I))) | (123) |
isNePal#(n____(I,__(P,I))) | → | and#(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)),n__isPalListKind(activate(P)))) | (124) |
isPal#(V) | → | activate#(V) | (125) |
isPal#(V) | → | isPalListKind#(activate(V)) | (126) |
isPal#(V) | → | U71#(isPalListKind(activate(V)),activate(V)) | (127) |
isPalListKind#(n____(V1,V2)) | → | activate#(V2) | (128) |
isPalListKind#(n____(V1,V2)) | → | activate#(V1) | (129) |
isPalListKind#(n____(V1,V2)) | → | isPalListKind#(activate(V1)) | (130) |
isPalListKind#(n____(V1,V2)) | → | and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (131) |
activate#(n__nil) | → | nil# | (132) |
activate#(n____(X1,X2)) | → | __#(X1,X2) | (133) |
activate#(n__isPalListKind(X)) | → | isPalListKind#(X) | (134) |
activate#(n__and(X1,X2)) | → | and#(X1,X2) | (135) |
activate#(n__a) | → | a# | (136) |
activate#(n__e) | → | e# | (137) |
activate#(n__i) | → | i# | (138) |
activate#(n__o) | → | o# | (139) |
activate#(n__u) | → | u# | (140) |
The dependency pairs are split into 4 components.
U52#(tt,V2) | → | isList#(activate(V2)) | (90) |
isList#(V) | → | U11#(isPalListKind(activate(V)),activate(V)) | (101) |
U11#(tt,V) | → | isNeList#(activate(V)) | (66) |
isNeList#(n____(V1,V2)) | → | U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (114) |
U41#(tt,V1,V2) | → | isList#(activate(V1)) | (80) |
isList#(n____(V1,V2)) | → | U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (106) |
U21#(tt,V1,V2) | → | isList#(activate(V1)) | (70) |
U21#(tt,V1,V2) | → | U22#(isList(activate(V1)),activate(V2)) | (71) |
U22#(tt,V2) | → | isList#(activate(V2)) | (73) |
U41#(tt,V1,V2) | → | U42#(isList(activate(V1)),activate(V2)) | (81) |
U42#(tt,V2) | → | isNeList#(activate(V2)) | (83) |
isNeList#(n____(V1,V2)) | → | U51#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (115) |
U51#(tt,V1,V2) | → | isNeList#(activate(V1)) | (87) |
U51#(tt,V1,V2) | → | U52#(isNeList(activate(V1)),activate(V2)) | (88) |
[U52(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[activate(x1)] | = | 0 · x1 + -∞ |
[U42(x1, x2)] | = | 2 · x1 + 0 · x2 + 8 |
[isList(x1)] | = | 0 · x1 + 0 |
[U41#(x1, x2, x3)] | = | -∞ · x1 + 4 · x2 + 4 · x3 + -∞ |
[nil] | = | 0 |
[U11(x1, x2)] | = | 2 · x1 + 4 · x2 + 0 |
[U43(x1)] | = | 2 · x1 + 0 |
[n__u] | = | 1 |
[isPalListKind(x1)] | = | 0 · x1 + 2 |
[U53(x1)] | = | 2 · x1 + 0 |
[n__a] | = | 2 |
[U51(x1, x2, x3)] | = | -∞ · x1 + 4 · x2 + 4 · x3 + 0 |
[n__nil] | = | 0 |
[n__i] | = | 0 |
[n____(x1, x2)] | = | 1 · x1 + 0 · x2 + 0 |
[isNeList(x1)] | = | -∞ · x1 + 4 |
[n__e] | = | 0 |
[U23(x1)] | = | 5 · x1 + 0 |
[__(x1, x2)] | = | 1 · x1 + 0 · x2 + 0 |
[i] | = | 0 |
[U21(x1, x2, x3)] | = | 2 · x1 + 3 · x2 + 4 · x3 + 12 |
[and(x1, x2)] | = | -∞ · x1 + 0 · x2 + -∞ |
[U22#(x1, x2)] | = | -∞ · x1 + 4 · x2 + -∞ |
[U41(x1, x2, x3)] | = | 0 · x1 + 3 · x2 + 5 · x3 + 0 |
[n__and(x1, x2)] | = | -∞ · x1 + 0 · x2 + -∞ |
[isQid(x1)] | = | 1 · x1 + 0 |
[isNeList#(x1)] | = | 4 · x1 + -∞ |
[U51#(x1, x2, x3)] | = | 0 · x1 + 5 · x2 + 4 · x3 + 0 |
[U31(x1, x2)] | = | -∞ · x1 + 4 · x2 + 0 |
[U22(x1, x2)] | = | 4 · x1 + -∞ · x2 + 0 |
[U32(x1)] | = | 0 · x1 + 0 |
[o] | = | 1 |
[U42#(x1, x2)] | = | -∞ · x1 + 4 · x2 + -∞ |
[U12(x1)] | = | 0 · x1 + 0 |
[e] | = | 0 |
[U52#(x1, x2)] | = | -∞ · x1 + 4 · x2 + 0 |
[isList#(x1)] | = | 4 · x1 + -∞ |
[U21#(x1, x2, x3)] | = | 0 · x1 + 4 · x2 + 4 · x3 + 2 |
[a] | = | 2 |
[u] | = | 1 |
[n__o] | = | 1 |
[n__isPalListKind(x1)] | = | 0 · x1 + 2 |
[U11#(x1, x2)] | = | -∞ · x1 + 4 · x2 + -∞ |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
U51#(tt,V1,V2) | → | isNeList#(activate(V1)) | (87) |
[U52(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[activate(x1)] | = | 1 · x1 + 0 |
[U42(x1, x2)] | = | 0 · x1 + 0 · x2 + 2 |
[isList(x1)] | = | 0 · x1 + 0 |
[U41#(x1, x2, x3)] | = | 0 · x1 + 4 · x2 + 2 · x3 + 1 |
[nil] | = | 2 |
[U11(x1, x2)] | = | 2 · x1 + 2 · x2 + 4 |
[U43(x1)] | = | 0 · x1 + 0 |
[n__u] | = | 0 |
[isPalListKind(x1)] | = | 0 · x1 + 2 |
[U53(x1)] | = | 0 · x1 + 1 |
[n__a] | = | 0 |
[U51(x1, x2, x3)] | = | 0 · x1 + 1 · x2 + 0 · x3 + 4 |
[n__nil] | = | 2 |
[n__i] | = | 0 |
[n____(x1, x2)] | = | 2 · x1 + 1 · x2 + 4 |
[isNeList(x1)] | = | 0 · x1 + 0 |
[n__e] | = | 0 |
[U23(x1)] | = | 0 · x1 + 2 |
[__(x1, x2)] | = | 2 · x1 + 1 · x2 + 4 |
[i] | = | 0 |
[U21(x1, x2, x3)] | = | 1 · x1 + 0 · x2 + 0 · x3 + 0 |
[and(x1, x2)] | = | 0 · x1 + 1 · x2 + 0 |
[U22#(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[U41(x1, x2, x3)] | = | 5 · x1 + 0 · x2 + 0 · x3 + 6 |
[n__and(x1, x2)] | = | 0 · x1 + 1 · x2 + 0 |
[isQid(x1)] | = | 0 · x1 + 0 |
[isNeList#(x1)] | = | 2 · x1 + 0 |
[U51#(x1, x2, x3)] | = | 2 · x1 + 0 · x2 + 2 · x3 + 4 |
[U31(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[U22(x1, x2)] | = | 0 · x1 + 0 · x2 + 1 |
[U32(x1)] | = | 0 · x1 + 0 |
[o] | = | 0 |
[U42#(x1, x2)] | = | 0 · x1 + 2 · x2 + 1 |
[U12(x1)] | = | 0 · x1 + 0 |
[e] | = | 0 |
[U52#(x1, x2)] | = | 0 · x1 + 2 · x2 + 4 |
[isList#(x1)] | = | 2 · x1 + 0 |
[U21#(x1, x2, x3)] | = | 4 · x1 + 2 · x2 + 2 · x3 + 0 |
[a] | = | 0 |
[u] | = | 0 |
[n__o] | = | 0 |
[n__isPalListKind(x1)] | = | 0 · x1 + 2 |
[U11#(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
U52#(tt,V2) | → | isList#(activate(V2)) | (90) |
isNeList#(n____(V1,V2)) | → | U41#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (114) |
U41#(tt,V1,V2) | → | isList#(activate(V1)) | (80) |
U42#(tt,V2) | → | isNeList#(activate(V2)) | (83) |
The dependency pairs are split into 1 component.
U22#(tt,V2) | → | isList#(activate(V2)) | (73) |
isList#(n____(V1,V2)) | → | U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (106) |
U21#(tt,V1,V2) | → | isList#(activate(V1)) | (70) |
U21#(tt,V1,V2) | → | U22#(isList(activate(V1)),activate(V2)) | (71) |
[U52(x1, x2)] | = | 2 · x1 + 2 · x2 + 0 |
[activate(x1)] | = | 0 · x1 + 0 |
[U42(x1, x2)] | = | 5 · x1 + 7 · x2 + 0 |
[isList(x1)] | = | 2 · x1 + 0 |
[nil] | = | 3 |
[U11(x1, x2)] | = | -∞ · x1 + 0 · x2 + 1 |
[U43(x1)] | = | 2 · x1 + 8 |
[n__u] | = | 0 |
[isPalListKind(x1)] | = | 0 · x1 + -∞ |
[U53(x1)] | = | -∞ · x1 + 4 |
[n__a] | = | 1 |
[U51(x1, x2, x3)] | = | -∞ · x1 + 4 · x2 + 0 · x3 + 0 |
[n__nil] | = | 3 |
[n__i] | = | 0 |
[n____(x1, x2)] | = | 3 · x1 + 0 · x2 + 3 |
[isNeList(x1)] | = | 4 · x1 + 0 |
[n__e] | = | 0 |
[U23(x1)] | = | -∞ · x1 + 2 |
[__(x1, x2)] | = | 3 · x1 + 0 · x2 + 3 |
[i] | = | 0 |
[U21(x1, x2, x3)] | = | -∞ · x1 + -∞ · x2 + 0 · x3 + 0 |
[and(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[U22#(x1, x2)] | = | -∞ · x1 + 4 · x2 + 4 |
[U41(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 6 · x3 + 0 |
[n__and(x1, x2)] | = | 0 · x1 + 0 · x2 + -∞ |
[isQid(x1)] | = | -∞ · x1 + 1 |
[U31(x1, x2)] | = | -∞ · x1 + 0 · x2 + 0 |
[U22(x1, x2)] | = | 4 · x1 + 6 · x2 + 0 |
[U32(x1)] | = | 6 · x1 + 0 |
[o] | = | 0 |
[U12(x1)] | = | -∞ · x1 + 0 |
[e] | = | 0 |
[isList#(x1)] | = | 4 · x1 + 0 |
[U21#(x1, x2, x3)] | = | -∞ · x1 + 7 · x2 + 4 · x3 + 5 |
[a] | = | 1 |
[u] | = | 0 |
[n__o] | = | 0 |
[n__isPalListKind(x1)] | = | 0 · x1 + -∞ |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
U21#(tt,V1,V2) | → | isList#(activate(V1)) | (70) |
[U52(x1, x2)] | = | 0 · x1 + 2 · x2 + 3 |
[activate(x1)] | = | 1 · x1 + 0 |
[U42(x1, x2)] | = | 0 · x1 + 2 · x2 + 2 |
[isList(x1)] | = | 0 · x1 + 0 |
[nil] | = | 0 |
[U11(x1, x2)] | = | 0 · x1 + 7/2 · x2 + 1 |
[U43(x1)] | = | 2 · x1 + 3 |
[n__u] | = | 0 |
[isPalListKind(x1)] | = | 3/2 · x1 + 0 |
[U53(x1)] | = | 0 · x1 + 0 |
[n__a] | = | 0 |
[U51(x1, x2, x3)] | = | 0 · x1 + 3 · x2 + 0 · x3 + 0 |
[n__nil] | = | 0 |
[n__i] | = | 2 |
[n____(x1, x2)] | = | 1 · x1 + 1 · x2 + 2 |
[isNeList(x1)] | = | 3/2 · x1 + 1/2 |
[n__e] | = | 1 |
[U23(x1)] | = | 0 · x1 + 0 |
[__(x1, x2)] | = | 1 · x1 + 1 · x2 + 2 |
[i] | = | 2 |
[U21(x1, x2, x3)] | = | 0 · x1 + 2 · x2 + 0 · x3 + 2 |
[and(x1, x2)] | = | 1 · x1 + 1 · x2 + 0 |
[U22#(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[U41(x1, x2, x3)] | = | 0 · x1 + 0 · x2 + 0 · x3 + 2 |
[n__and(x1, x2)] | = | 1 · x1 + 1 · x2 + 0 |
[isQid(x1)] | = | 0 · x1 + 1/2 |
[U31(x1, x2)] | = | 0 · x1 + 0 · x2 + 1 |
[U22(x1, x2)] | = | 0 · x1 + 0 · x2 + 1 |
[U32(x1)] | = | 0 · x1 + 1 |
[o] | = | 0 |
[U12(x1)] | = | 3 · x1 + 1/2 |
[e] | = | 1 |
[isList#(x1)] | = | 2 · x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 · x1 + 2 · x2 + 2 · x3 + 0 |
[a] | = | 0 |
[u] | = | 0 |
[n__o] | = | 0 |
[n__isPalListKind(x1)] | = | 3/2 · x1 + 0 |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
isList#(n____(V1,V2)) | → | U21#(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) | (106) |
The dependency pairs are split into 0 components.
isPal#(V) | → | U71#(isPalListKind(activate(V)),activate(V)) | (127) |
U71#(tt,V) | → | isNePal#(activate(V)) | (96) |
isNePal#(n____(I,__(P,I))) | → | isPal#(activate(P)) | (120) |
[activate(x1)] | = | 0 · x1 + 0 |
[nil] | = | 0 |
[n__u] | = | 0 |
[isPalListKind(x1)] | = | -∞ · x1 + 0 |
[isNePal#(x1)] | = | 6 · x1 + 0 |
[n__a] | = | 0 |
[n__nil] | = | 0 |
[n__i] | = | 0 |
[n____(x1, x2)] | = | 1 · x1 + 0 · x2 + 1 |
[n__e] | = | 1 |
[__(x1, x2)] | = | 1 · x1 + 0 · x2 + 1 |
[i] | = | 0 |
[and(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[U71#(x1, x2)] | = | 0 · x1 + 7 · x2 + 7 |
[n__and(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[o] | = | 0 |
[isPal#(x1)] | = | 7 · x1 + 7 |
[e] | = | 1 |
[a] | = | 0 |
[u] | = | 0 |
[n__o] | = | 0 |
[n__isPalListKind(x1)] | = | -∞ · x1 + 0 |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
U71#(tt,V) | → | isNePal#(activate(V)) | (96) |
The dependency pairs are split into 0 components.
isPalListKind#(n____(V1,V2)) | → | activate#(V2) | (128) |
activate#(n__isPalListKind(X)) | → | isPalListKind#(X) | (134) |
isPalListKind#(n____(V1,V2)) | → | activate#(V1) | (129) |
activate#(n__and(X1,X2)) | → | and#(X1,X2) | (135) |
and#(tt,X) | → | activate#(X) | (98) |
isPalListKind#(n____(V1,V2)) | → | isPalListKind#(activate(V1)) | (130) |
isPalListKind#(n____(V1,V2)) | → | and#(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (131) |
[activate(x1)] | = | 0 · x1 + 0 |
[nil] | = | 2 |
[n__u] | = | 1 |
[isPalListKind(x1)] | = | 0 · x1 + 0 |
[n__a] | = | 4 |
[n__nil] | = | 2 |
[n__i] | = | 2 |
[n____(x1, x2)] | = | 2 · x1 + 0 · x2 + -∞ |
[and#(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[activate#(x1)] | = | 0 · x1 + -∞ |
[n__e] | = | 0 |
[__(x1, x2)] | = | 2 · x1 + 0 · x2 + -∞ |
[i] | = | 2 |
[and(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__and(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[o] | = | 1 |
[e] | = | 0 |
[a] | = | 4 |
[u] | = | 1 |
[isPalListKind#(x1)] | = | 0 · x1 + 0 |
[n__o] | = | 1 |
[n__isPalListKind(x1)] | = | 0 · x1 + 0 |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
isPalListKind#(n____(V1,V2)) | → | activate#(V1) | (129) |
[activate(x1)] | = | 0 · x1 + -∞ |
[nil] | = | 2 |
[n__u] | = | 0 |
[isPalListKind(x1)] | = | 4 · x1 + -∞ |
[n__a] | = | 0 |
[n__nil] | = | 2 |
[n__i] | = | 0 |
[n____(x1, x2)] | = | 2 · x1 + 0 · x2 + -∞ |
[and#(x1, x2)] | = | 0 · x1 + 0 · x2 + -∞ |
[activate#(x1)] | = | 0 · x1 + -∞ |
[n__e] | = | 1 |
[__(x1, x2)] | = | 2 · x1 + 0 · x2 + -∞ |
[i] | = | 0 |
[and(x1, x2)] | = | 2 · x1 + 0 · x2 + -∞ |
[n__and(x1, x2)] | = | 2 · x1 + 0 · x2 + -∞ |
[o] | = | 1 |
[e] | = | 1 |
[a] | = | 0 |
[u] | = | 0 |
[isPalListKind#(x1)] | = | 4 · x1 + -∞ |
[n__o] | = | 1 |
[n__isPalListKind(x1)] | = | 4 · x1 + -∞ |
[tt] | = | 0 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
isPalListKind#(n____(V1,V2)) | → | activate#(V2) | (128) |
isPalListKind#(n____(V1,V2)) | → | isPalListKind#(activate(V1)) | (130) |
[activate(x1)] | = | -∞ · x1 + 0 |
[nil] | = | 6 |
[n__u] | = | 1 |
[isPalListKind(x1)] | = | 1 · x1 + 0 |
[n__a] | = | 3 |
[n__nil] | = | 5 |
[n__i] | = | 0 |
[n____(x1, x2)] | = | 3 · x1 + 0 · x2 + 0 |
[and#(x1, x2)] | = | -∞ · x1 + 0 · x2 + 0 |
[activate#(x1)] | = | 0 · x1 + -∞ |
[n__e] | = | 2 |
[__(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[i] | = | 0 |
[and(x1, x2)] | = | 2 · x1 + 0 · x2 + 0 |
[n__and(x1, x2)] | = | 0 · x1 + 4 · x2 + 1 |
[o] | = | 0 |
[e] | = | 0 |
[a] | = | 0 |
[u] | = | 0 |
[isPalListKind#(x1)] | = | -∞ · x1 + 0 |
[n__o] | = | 0 |
[n__isPalListKind(x1)] | = | -∞ · x1 + 0 |
[tt] | = | 2 |
activate#(n__and(X1,X2)) | → | and#(X1,X2) | (135) |
[activate(x1)] | = | 1 · x1 + 0 |
[nil] | = | 3 |
[n__u] | = | 3 |
[isPalListKind(x1)] | = | 1 · x1 + 0 |
[n__a] | = | 4 |
[n__nil] | = | 3 |
[n__i] | = | 3 |
[n____(x1, x2)] | = | 2 · x1 + 1 · x2 + 0 |
[and#(x1, x2)] | = | 3 · x1 + 4 · x2 + 0 |
[activate#(x1)] | = | 4 · x1 + 0 |
[n__e] | = | 3 |
[__(x1, x2)] | = | 2 · x1 + 1 · x2 + 0 |
[i] | = | 3 |
[and(x1, x2)] | = | 2 · x1 + 1 · x2 + 0 |
[n__and(x1, x2)] | = | 2 · x1 + 1 · x2 + 0 |
[o] | = | 3 |
[e] | = | 3 |
[a] | = | 4 |
[u] | = | 3 |
[isPalListKind#(x1)] | = | 4 · x1 + 0 |
[n__o] | = | 3 |
[n__isPalListKind(x1)] | = | 1 · x1 + 0 |
[tt] | = | 3 |
activate(n__nil) | → | nil | (53) |
activate(n____(X1,X2)) | → | __(X1,X2) | (54) |
activate(n__isPalListKind(X)) | → | isPalListKind(X) | (55) |
activate(n__and(X1,X2)) | → | and(X1,X2) | (56) |
activate(n__a) | → | a | (57) |
activate(n__e) | → | e | (58) |
activate(n__i) | → | i | (59) |
activate(n__o) | → | o | (60) |
activate(n__u) | → | u | (61) |
activate(X) | → | X | (62) |
nil | → | n__nil | (44) |
__(__(X,Y),Z) | → | __(X,__(Y,Z)) | (1) |
__(X,nil) | → | X | (2) |
__(nil,X) | → | X | (3) |
__(X1,X2) | → | n____(X1,X2) | (45) |
isPalListKind(n__a) | → | tt | (32) |
isPalListKind(n__e) | → | tt | (33) |
isPalListKind(n__i) | → | tt | (34) |
isPalListKind(n__nil) | → | tt | (35) |
isPalListKind(n__o) | → | tt | (36) |
isPalListKind(n__u) | → | tt | (37) |
isPalListKind(n____(V1,V2)) | → | and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) | (38) |
isPalListKind(X) | → | n__isPalListKind(X) | (46) |
and(tt,X) | → | activate(X) | (21) |
and(X1,X2) | → | n__and(X1,X2) | (47) |
a | → | n__a | (48) |
e | → | n__e | (49) |
i | → | n__i | (50) |
o | → | n__o | (51) |
u | → | n__u | (52) |
and#(tt,X) | → | activate#(X) | (98) |
The dependency pairs are split into 0 components.
__#(__(X,Y),Z) | → | __#(Y,Z) | (63) |
__#(__(X,Y),Z) | → | __#(X,__(Y,Z)) | (64) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
__#(__(X,Y),Z) | → | __#(Y,Z) | (63) |
2 | ≥ | 2 | |
1 | > | 1 | |
__#(__(X,Y),Z) | → | __#(X,__(Y,Z)) | (64) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.