0.00/0.33 YES 0.00/0.33 0.00/0.33 Problem 1: 0.00/0.33 0.00/0.33 (VAR I P V V1 V2 X Y Z) 0.00/0.33 (STRATEGY CONTEXTSENSITIVE 0.00/0.33 (U11 1) 0.00/0.33 (U12 1) 0.00/0.33 (U21 1) 0.00/0.33 (U22 1) 0.00/0.33 (U23 1) 0.00/0.33 (U31 1) 0.00/0.33 (U32 1) 0.00/0.33 (U41 1) 0.00/0.33 (U42 1) 0.00/0.33 (U43 1) 0.00/0.33 (U51 1) 0.00/0.33 (U52 1) 0.00/0.33 (U53 1) 0.00/0.33 (U61 1) 0.00/0.33 (U62 1) 0.00/0.33 (U71 1) 0.00/0.33 (U72 1) 0.00/0.33 (__ 1 2) 0.00/0.33 (and 1) 0.00/0.33 (isList) 0.00/0.33 (isNeList) 0.00/0.33 (isNePal) 0.00/0.33 (isPal) 0.00/0.33 (isPalListKind) 0.00/0.33 (isQid) 0.00/0.33 (a) 0.00/0.33 (e) 0.00/0.33 (i) 0.00/0.33 (nil) 0.00/0.33 (o) 0.00/0.33 (tt) 0.00/0.33 (u) 0.00/0.33 ) 0.00/0.33 (RULES 0.00/0.33 U11(tt,V) -> U12(isNeList(V)) 0.00/0.33 U12(tt) -> tt 0.00/0.33 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.33 U22(tt,V2) -> U23(isList(V2)) 0.00/0.33 U23(tt) -> tt 0.00/0.33 U31(tt,V) -> U32(isQid(V)) 0.00/0.33 U32(tt) -> tt 0.00/0.33 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.33 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.33 U43(tt) -> tt 0.00/0.33 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.33 U52(tt,V2) -> U53(isList(V2)) 0.00/0.33 U53(tt) -> tt 0.00/0.33 U61(tt,V) -> U62(isQid(V)) 0.00/0.33 U62(tt) -> tt 0.00/0.33 U71(tt,V) -> U72(isNePal(V)) 0.00/0.33 U72(tt) -> tt 0.00/0.33 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.33 __(nil,X) -> X 0.00/0.33 __(X,nil) -> X 0.00/0.33 and(tt,X) -> X 0.00/0.33 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 isList(nil) -> tt 0.00/0.33 isList(V) -> U11(isPalListKind(V),V) 0.00/0.33 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.33 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.33 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.33 isPal(nil) -> tt 0.00/0.33 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.33 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 isPalListKind(a) -> tt 0.00/0.33 isPalListKind(e) -> tt 0.00/0.33 isPalListKind(i) -> tt 0.00/0.33 isPalListKind(nil) -> tt 0.00/0.33 isPalListKind(o) -> tt 0.00/0.33 isPalListKind(u) -> tt 0.00/0.33 isQid(a) -> tt 0.00/0.33 isQid(e) -> tt 0.00/0.33 isQid(i) -> tt 0.00/0.33 isQid(o) -> tt 0.00/0.33 isQid(u) -> tt 0.00/0.33 ) 0.00/0.33 0.00/0.33 Problem 1: 0.00/0.33 0.00/0.33 Dependency Pairs Processor: 0.00/0.33 -> Pairs: 0.00/0.33 U11#(tt,V) -> U12#(isNeList(V)) 0.00/0.33 U11#(tt,V) -> ISNELIST(V) 0.00/0.33 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.33 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.33 U22#(tt,V2) -> U23#(isList(V2)) 0.00/0.33 U22#(tt,V2) -> ISLIST(V2) 0.00/0.33 U31#(tt,V) -> U32#(isQid(V)) 0.00/0.33 U31#(tt,V) -> ISQID(V) 0.00/0.33 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.33 U41#(tt,V1,V2) -> ISLIST(V1) 0.00/0.33 U42#(tt,V2) -> U43#(isNeList(V2)) 0.00/0.33 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.33 U51#(tt,V1,V2) -> U52#(isNeList(V1),V2) 0.00/0.33 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.33 U52#(tt,V2) -> U53#(isList(V2)) 0.00/0.33 U52#(tt,V2) -> ISLIST(V2) 0.00/0.33 U61#(tt,V) -> U62#(isQid(V)) 0.00/0.33 U61#(tt,V) -> ISQID(V) 0.00/0.33 U71#(tt,V) -> U72#(isNePal(V)) 0.00/0.33 U71#(tt,V) -> ISNEPAL(V) 0.00/0.33 __#(__(X,Y),Z) -> __#(X,__(Y,Z)) 0.00/0.33 __#(__(X,Y),Z) -> __#(Y,Z) 0.00/0.33 AND(tt,X) -> X 0.00/0.33 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 ISLIST(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 ISLIST(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.33 ISLIST(V) -> U11#(isPalListKind(V),V) 0.00/0.33 ISLIST(V) -> ISPALLISTKIND(V) 0.00/0.33 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 ISNELIST(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 ISNELIST(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.33 ISNELIST(V) -> U31#(isPalListKind(V),V) 0.00/0.33 ISNELIST(V) -> ISPALLISTKIND(V) 0.00/0.33 ISNEPAL(__(I,__(P,I))) -> AND(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.33 ISNEPAL(__(I,__(P,I))) -> AND(isQid(I),isPalListKind(I)) 0.00/0.33 ISNEPAL(__(I,__(P,I))) -> ISQID(I) 0.00/0.33 ISNEPAL(V) -> U61#(isPalListKind(V),V) 0.00/0.33 ISNEPAL(V) -> ISPALLISTKIND(V) 0.00/0.33 ISPAL(V) -> U71#(isPalListKind(V),V) 0.00/0.33 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.33 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.33 -> Rules: 0.00/0.33 U11(tt,V) -> U12(isNeList(V)) 0.00/0.33 U12(tt) -> tt 0.00/0.33 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.33 U22(tt,V2) -> U23(isList(V2)) 0.00/0.33 U23(tt) -> tt 0.00/0.33 U31(tt,V) -> U32(isQid(V)) 0.00/0.33 U32(tt) -> tt 0.00/0.33 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.33 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.33 U43(tt) -> tt 0.00/0.33 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.33 U52(tt,V2) -> U53(isList(V2)) 0.00/0.33 U53(tt) -> tt 0.00/0.33 U61(tt,V) -> U62(isQid(V)) 0.00/0.33 U62(tt) -> tt 0.00/0.33 U71(tt,V) -> U72(isNePal(V)) 0.00/0.33 U72(tt) -> tt 0.00/0.33 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.33 __(nil,X) -> X 0.00/0.33 __(X,nil) -> X 0.00/0.33 and(tt,X) -> X 0.00/0.33 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 isList(nil) -> tt 0.00/0.33 isList(V) -> U11(isPalListKind(V),V) 0.00/0.33 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.33 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.33 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.33 isPal(nil) -> tt 0.00/0.33 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.33 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 isPalListKind(a) -> tt 0.00/0.33 isPalListKind(e) -> tt 0.00/0.33 isPalListKind(i) -> tt 0.00/0.33 isPalListKind(nil) -> tt 0.00/0.33 isPalListKind(o) -> tt 0.00/0.33 isPalListKind(u) -> tt 0.00/0.33 isQid(a) -> tt 0.00/0.33 isQid(e) -> tt 0.00/0.33 isQid(i) -> tt 0.00/0.33 isQid(o) -> tt 0.00/0.33 isQid(u) -> tt 0.00/0.33 -> Unhiding Rules: 0.00/0.33 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.33 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.33 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.33 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.33 0.00/0.33 Problem 1: 0.00/0.33 0.00/0.33 SCC Processor: 0.00/0.33 -> Pairs: 0.00/0.33 U11#(tt,V) -> U12#(isNeList(V)) 0.00/0.33 U11#(tt,V) -> ISNELIST(V) 0.00/0.33 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.33 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.33 U22#(tt,V2) -> U23#(isList(V2)) 0.00/0.33 U22#(tt,V2) -> ISLIST(V2) 0.00/0.33 U31#(tt,V) -> U32#(isQid(V)) 0.00/0.33 U31#(tt,V) -> ISQID(V) 0.00/0.33 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.33 U41#(tt,V1,V2) -> ISLIST(V1) 0.00/0.33 U42#(tt,V2) -> U43#(isNeList(V2)) 0.00/0.33 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.33 U51#(tt,V1,V2) -> U52#(isNeList(V1),V2) 0.00/0.33 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.33 U52#(tt,V2) -> U53#(isList(V2)) 0.00/0.33 U52#(tt,V2) -> ISLIST(V2) 0.00/0.33 U61#(tt,V) -> U62#(isQid(V)) 0.00/0.33 U61#(tt,V) -> ISQID(V) 0.00/0.33 U71#(tt,V) -> U72#(isNePal(V)) 0.00/0.33 U71#(tt,V) -> ISNEPAL(V) 0.00/0.33 __#(__(X,Y),Z) -> __#(X,__(Y,Z)) 0.00/0.33 __#(__(X,Y),Z) -> __#(Y,Z) 0.00/0.33 AND(tt,X) -> X 0.00/0.33 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 ISLIST(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 ISLIST(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.33 ISLIST(V) -> U11#(isPalListKind(V),V) 0.00/0.33 ISLIST(V) -> ISPALLISTKIND(V) 0.00/0.33 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.33 ISNELIST(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 ISNELIST(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.33 ISNELIST(V) -> U31#(isPalListKind(V),V) 0.00/0.33 ISNELIST(V) -> ISPALLISTKIND(V) 0.00/0.33 ISNEPAL(__(I,__(P,I))) -> AND(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.33 ISNEPAL(__(I,__(P,I))) -> AND(isQid(I),isPalListKind(I)) 0.00/0.33 ISNEPAL(__(I,__(P,I))) -> ISQID(I) 0.00/0.33 ISNEPAL(V) -> U61#(isPalListKind(V),V) 0.00/0.33 ISNEPAL(V) -> ISPALLISTKIND(V) 0.00/0.33 ISPAL(V) -> U71#(isPalListKind(V),V) 0.00/0.33 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.33 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.33 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.33 -> Rules: 0.00/0.33 U11(tt,V) -> U12(isNeList(V)) 0.00/0.33 U12(tt) -> tt 0.00/0.33 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.33 U22(tt,V2) -> U23(isList(V2)) 0.00/0.33 U23(tt) -> tt 0.00/0.33 U31(tt,V) -> U32(isQid(V)) 0.00/0.33 U32(tt) -> tt 0.00/0.33 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.33 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.33 U43(tt) -> tt 0.00/0.33 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.33 U52(tt,V2) -> U53(isList(V2)) 0.00/0.33 U53(tt) -> tt 0.00/0.33 U61(tt,V) -> U62(isQid(V)) 0.00/0.33 U62(tt) -> tt 0.00/0.33 U71(tt,V) -> U72(isNePal(V)) 0.00/0.33 U72(tt) -> tt 0.00/0.33 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.33 __(nil,X) -> X 0.00/0.33 __(X,nil) -> X 0.00/0.34 and(tt,X) -> X 0.00/0.34 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isList(nil) -> tt 0.00/0.34 isList(V) -> U11(isPalListKind(V),V) 0.00/0.34 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.34 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.34 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.34 isPal(nil) -> tt 0.00/0.34 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.34 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.34 isPalListKind(a) -> tt 0.00/0.34 isPalListKind(e) -> tt 0.00/0.34 isPalListKind(i) -> tt 0.00/0.34 isPalListKind(nil) -> tt 0.00/0.34 isPalListKind(o) -> tt 0.00/0.34 isPalListKind(u) -> tt 0.00/0.34 isQid(a) -> tt 0.00/0.34 isQid(e) -> tt 0.00/0.34 isQid(i) -> tt 0.00/0.34 isQid(o) -> tt 0.00/0.34 isQid(u) -> tt 0.00/0.34 -> Unhiding rules: 0.00/0.34 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.34 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.34 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.34 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.34 ->Strongly Connected Components: 0.00/0.34 ->->Cycle: 0.00/0.34 ->->-> Pairs: 0.00/0.34 __#(__(X,Y),Z) -> __#(X,__(Y,Z)) 0.00/0.34 __#(__(X,Y),Z) -> __#(Y,Z) 0.00/0.34 ->->-> Rules: 0.00/0.34 U11(tt,V) -> U12(isNeList(V)) 0.00/0.34 U12(tt) -> tt 0.00/0.34 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.34 U22(tt,V2) -> U23(isList(V2)) 0.00/0.34 U23(tt) -> tt 0.00/0.34 U31(tt,V) -> U32(isQid(V)) 0.00/0.34 U32(tt) -> tt 0.00/0.34 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.34 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.34 U43(tt) -> tt 0.00/0.34 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.34 U52(tt,V2) -> U53(isList(V2)) 0.00/0.34 U53(tt) -> tt 0.00/0.34 U61(tt,V) -> U62(isQid(V)) 0.00/0.34 U62(tt) -> tt 0.00/0.34 U71(tt,V) -> U72(isNePal(V)) 0.00/0.34 U72(tt) -> tt 0.00/0.34 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.34 __(nil,X) -> X 0.00/0.34 __(X,nil) -> X 0.00/0.34 and(tt,X) -> X 0.00/0.34 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isList(nil) -> tt 0.00/0.34 isList(V) -> U11(isPalListKind(V),V) 0.00/0.34 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.34 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.34 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.34 isPal(nil) -> tt 0.00/0.34 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.34 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.34 isPalListKind(a) -> tt 0.00/0.34 isPalListKind(e) -> tt 0.00/0.34 isPalListKind(i) -> tt 0.00/0.34 isPalListKind(nil) -> tt 0.00/0.34 isPalListKind(o) -> tt 0.00/0.34 isPalListKind(u) -> tt 0.00/0.34 isQid(a) -> tt 0.00/0.34 isQid(e) -> tt 0.00/0.34 isQid(i) -> tt 0.00/0.34 isQid(o) -> tt 0.00/0.34 isQid(u) -> tt 0.00/0.34 ->->-> Unhiding rules: 0.00/0.34 Empty 0.00/0.34 ->->Cycle: 0.00/0.34 ->->-> Pairs: 0.00/0.34 U71#(tt,V) -> ISNEPAL(V) 0.00/0.34 AND(tt,X) -> X 0.00/0.34 ISNEPAL(__(I,__(P,I))) -> AND(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.34 ISNEPAL(__(I,__(P,I))) -> AND(isQid(I),isPalListKind(I)) 0.00/0.34 ISNEPAL(V) -> ISPALLISTKIND(V) 0.00/0.34 ISPAL(V) -> U71#(isPalListKind(V),V) 0.00/0.34 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.34 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.34 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.34 ->->-> Rules: 0.00/0.34 U11(tt,V) -> U12(isNeList(V)) 0.00/0.34 U12(tt) -> tt 0.00/0.34 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.34 U22(tt,V2) -> U23(isList(V2)) 0.00/0.34 U23(tt) -> tt 0.00/0.34 U31(tt,V) -> U32(isQid(V)) 0.00/0.34 U32(tt) -> tt 0.00/0.34 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.34 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.34 U43(tt) -> tt 0.00/0.34 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.34 U52(tt,V2) -> U53(isList(V2)) 0.00/0.34 U53(tt) -> tt 0.00/0.34 U61(tt,V) -> U62(isQid(V)) 0.00/0.34 U62(tt) -> tt 0.00/0.34 U71(tt,V) -> U72(isNePal(V)) 0.00/0.34 U72(tt) -> tt 0.00/0.34 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.34 __(nil,X) -> X 0.00/0.34 __(X,nil) -> X 0.00/0.34 and(tt,X) -> X 0.00/0.34 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isList(nil) -> tt 0.00/0.34 isList(V) -> U11(isPalListKind(V),V) 0.00/0.34 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.34 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.34 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.34 isPal(nil) -> tt 0.00/0.34 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.34 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.34 isPalListKind(a) -> tt 0.00/0.34 isPalListKind(e) -> tt 0.00/0.34 isPalListKind(i) -> tt 0.00/0.34 isPalListKind(nil) -> tt 0.00/0.34 isPalListKind(o) -> tt 0.00/0.34 isPalListKind(u) -> tt 0.00/0.34 isQid(a) -> tt 0.00/0.34 isQid(e) -> tt 0.00/0.34 isQid(i) -> tt 0.00/0.34 isQid(o) -> tt 0.00/0.34 isQid(u) -> tt 0.00/0.34 ->->-> Unhiding rules: 0.00/0.34 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.34 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.34 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.34 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.34 ->->Cycle: 0.00/0.34 ->->-> Pairs: 0.00/0.34 U11#(tt,V) -> ISNELIST(V) 0.00/0.34 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.34 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.34 U22#(tt,V2) -> ISLIST(V2) 0.00/0.34 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.34 U41#(tt,V1,V2) -> ISLIST(V1) 0.00/0.34 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.34 U51#(tt,V1,V2) -> U52#(isNeList(V1),V2) 0.00/0.34 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.34 U52#(tt,V2) -> ISLIST(V2) 0.00/0.34 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 ISLIST(V) -> U11#(isPalListKind(V),V) 0.00/0.34 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 ->->-> Rules: 0.00/0.34 U11(tt,V) -> U12(isNeList(V)) 0.00/0.34 U12(tt) -> tt 0.00/0.34 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.34 U22(tt,V2) -> U23(isList(V2)) 0.00/0.34 U23(tt) -> tt 0.00/0.34 U31(tt,V) -> U32(isQid(V)) 0.00/0.34 U32(tt) -> tt 0.00/0.34 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.34 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.34 U43(tt) -> tt 0.00/0.34 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.34 U52(tt,V2) -> U53(isList(V2)) 0.00/0.34 U53(tt) -> tt 0.00/0.34 U61(tt,V) -> U62(isQid(V)) 0.00/0.34 U62(tt) -> tt 0.00/0.34 U71(tt,V) -> U72(isNePal(V)) 0.00/0.34 U72(tt) -> tt 0.00/0.34 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.34 __(nil,X) -> X 0.00/0.34 __(X,nil) -> X 0.00/0.34 and(tt,X) -> X 0.00/0.34 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isList(nil) -> tt 0.00/0.34 isList(V) -> U11(isPalListKind(V),V) 0.00/0.34 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.34 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.34 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.34 isPal(nil) -> tt 0.00/0.34 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.34 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.34 isPalListKind(a) -> tt 0.00/0.34 isPalListKind(e) -> tt 0.00/0.34 isPalListKind(i) -> tt 0.00/0.34 isPalListKind(nil) -> tt 0.00/0.34 isPalListKind(o) -> tt 0.00/0.34 isPalListKind(u) -> tt 0.00/0.34 isQid(a) -> tt 0.00/0.34 isQid(e) -> tt 0.00/0.34 isQid(i) -> tt 0.00/0.34 isQid(o) -> tt 0.00/0.34 isQid(u) -> tt 0.00/0.34 ->->-> Unhiding rules: 0.00/0.34 Empty 0.00/0.34 0.00/0.34 0.00/0.34 The problem is decomposed in 3 subproblems. 0.00/0.34 0.00/0.34 Problem 1.1: 0.00/0.34 0.00/0.34 SubNColl Processor: 0.00/0.34 -> Pairs: 0.00/0.34 __#(__(X,Y),Z) -> __#(X,__(Y,Z)) 0.00/0.34 __#(__(X,Y),Z) -> __#(Y,Z) 0.00/0.34 -> Rules: 0.00/0.34 U11(tt,V) -> U12(isNeList(V)) 0.00/0.34 U12(tt) -> tt 0.00/0.34 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.34 U22(tt,V2) -> U23(isList(V2)) 0.00/0.34 U23(tt) -> tt 0.00/0.34 U31(tt,V) -> U32(isQid(V)) 0.00/0.34 U32(tt) -> tt 0.00/0.34 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.34 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.34 U43(tt) -> tt 0.00/0.34 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.34 U52(tt,V2) -> U53(isList(V2)) 0.00/0.34 U53(tt) -> tt 0.00/0.34 U61(tt,V) -> U62(isQid(V)) 0.00/0.34 U62(tt) -> tt 0.00/0.34 U71(tt,V) -> U72(isNePal(V)) 0.00/0.34 U72(tt) -> tt 0.00/0.34 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.34 __(nil,X) -> X 0.00/0.34 __(X,nil) -> X 0.00/0.34 and(tt,X) -> X 0.00/0.34 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isList(nil) -> tt 0.00/0.34 isList(V) -> U11(isPalListKind(V),V) 0.00/0.34 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.34 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.34 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.34 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.34 isPal(nil) -> tt 0.00/0.34 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.34 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.34 isPalListKind(a) -> tt 0.00/0.34 isPalListKind(e) -> tt 0.00/0.34 isPalListKind(i) -> tt 0.00/0.34 isPalListKind(nil) -> tt 0.00/0.34 isPalListKind(o) -> tt 0.00/0.34 isPalListKind(u) -> tt 0.00/0.34 isQid(a) -> tt 0.00/0.34 isQid(e) -> tt 0.00/0.34 isQid(i) -> tt 0.00/0.34 isQid(o) -> tt 0.00/0.34 isQid(u) -> tt 0.00/0.34 -> Unhiding rules: 0.00/0.34 Empty 0.00/0.34 ->Projection: 0.00/0.34 pi(__#) = 1 0.00/0.34 0.00/0.34 Problem 1.1: 0.00/0.34 0.00/0.34 Basic Processor: 0.00/0.34 -> Pairs: 0.00/0.34 Empty 0.00/0.34 -> Rules: 0.00/0.34 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 -> Result: 0.00/0.35 Set P is empty 0.00/0.35 0.00/0.35 The problem is finite. 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 Reduction Pairs Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U71#(tt,V) -> ISNEPAL(V) 0.00/0.35 AND(tt,X) -> X 0.00/0.35 ISNEPAL(__(I,__(P,I))) -> AND(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 ISNEPAL(__(I,__(P,I))) -> AND(isQid(I),isPalListKind(I)) 0.00/0.35 ISNEPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPAL(V) -> U71#(isPalListKind(V),V) 0.00/0.35 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.35 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.35 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.35 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.35 -> Usable rules: 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->Interpretation type: 0.00/0.35 Linear 0.00/0.35 ->Coefficients: 0.00/0.35 Natural Numbers 0.00/0.35 ->Dimension: 0.00/0.35 1 0.00/0.35 ->Bound: 0.00/0.35 2 0.00/0.35 ->Interpretation: 0.00/0.35 0.00/0.35 [U61](X1,X2) = 2.X2 0.00/0.35 [U62](X) = X 0.00/0.35 [U71](X1,X2) = X1 0.00/0.35 [U72](X) = 2 0.00/0.35 [__](X1,X2) = X1 + X2 + 2 0.00/0.35 [and](X1,X2) = X2 + 2 0.00/0.35 [isNePal](X) = 2.X 0.00/0.35 [isPal](X) = 2.X + 2 0.00/0.35 [isPalListKind](X) = 2.X + 2 0.00/0.35 [isQid](X) = 2.X 0.00/0.35 [a] = 1 0.00/0.35 [e] = 2 0.00/0.35 [i] = 2 0.00/0.35 [nil] = 2 0.00/0.35 [o] = 1 0.00/0.35 [tt] = 2 0.00/0.35 [u] = 2 0.00/0.35 [U71#](X1,X2) = 2.X2 + 2 0.00/0.35 [AND](X1,X2) = X2 + 2 0.00/0.35 [ISNEPAL](X) = 2.X + 1 0.00/0.35 [ISPAL](X) = 2.X + 2 0.00/0.35 [ISPALLISTKIND](X) = 2.X + 1 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 AND(tt,X) -> X 0.00/0.35 ISNEPAL(__(I,__(P,I))) -> AND(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 ISNEPAL(__(I,__(P,I))) -> AND(isQid(I),isPalListKind(I)) 0.00/0.35 ISNEPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPAL(V) -> U71#(isPalListKind(V),V) 0.00/0.35 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.35 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.35 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.35 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 AND(tt,X) -> X 0.00/0.35 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 ->->-> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->->-> Unhiding rules: 0.00/0.35 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.35 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.35 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.35 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 Reduction Pairs Processor: 0.00/0.35 -> Pairs: 0.00/0.35 AND(tt,X) -> X 0.00/0.35 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.35 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.35 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.35 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.35 -> Usable rules: 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->Interpretation type: 0.00/0.35 Linear 0.00/0.35 ->Coefficients: 0.00/0.35 Natural Numbers 0.00/0.35 ->Dimension: 0.00/0.35 1 0.00/0.35 ->Bound: 0.00/0.35 2 0.00/0.35 ->Interpretation: 0.00/0.35 0.00/0.35 [U61](X1,X2) = X1 + 1 0.00/0.35 [U62](X) = 2 0.00/0.35 [U71](X1,X2) = X1 + 2 0.00/0.35 [U72](X) = 2 0.00/0.35 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.35 [and](X1,X2) = X2 + 2 0.00/0.35 [isNePal](X) = 2.X + 2 0.00/0.35 [isPal](X) = 2.X + 2 0.00/0.35 [isPalListKind](X) = 2.X 0.00/0.35 [isQid](X) = 2.X + 2 0.00/0.35 [a] = 2 0.00/0.35 [e] = 2 0.00/0.35 [i] = 2 0.00/0.35 [nil] = 2 0.00/0.35 [o] = 2 0.00/0.35 [tt] = 2 0.00/0.35 [u] = 2 0.00/0.35 [AND](X1,X2) = X2 + 1 0.00/0.35 [ISPAL](X) = 2.X + 2 0.00/0.35 [ISPALLISTKIND](X) = 2.X 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 ISPAL(V) -> ISPALLISTKIND(V) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> AND(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 and(isPal(P),isPalListKind(P)) -> AND(isPal(P),isPalListKind(P)) 0.00/0.35 and(isPal(P),isPalListKind(P)) -> ISPAL(P) 0.00/0.35 isPalListKind(I) -> ISPALLISTKIND(I) 0.00/0.35 isPalListKind(V2) -> ISPALLISTKIND(V2) 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 ->->-> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->->-> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 SubNColl Processor: 0.00/0.35 -> Pairs: 0.00/0.35 ISPALLISTKIND(__(V1,V2)) -> ISPALLISTKIND(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Projection: 0.00/0.35 pi(ISPALLISTKIND) = 1 0.00/0.35 0.00/0.35 Problem 1.2: 0.00/0.35 0.00/0.35 Basic Processor: 0.00/0.35 -> Pairs: 0.00/0.35 Empty 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 -> Result: 0.00/0.35 Set P is empty 0.00/0.35 0.00/0.35 The problem is finite. 0.00/0.35 0.00/0.35 Problem 1.3: 0.00/0.35 0.00/0.35 Reduction Pairs Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U11#(tt,V) -> ISNELIST(V) 0.00/0.35 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U22#(tt,V2) -> ISLIST(V2) 0.00/0.35 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.35 U41#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.35 U51#(tt,V1,V2) -> U52#(isNeList(V1),V2) 0.00/0.35 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.35 U52#(tt,V2) -> ISLIST(V2) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ISLIST(V) -> U11#(isPalListKind(V),V) 0.00/0.35 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 -> Usable rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->Interpretation type: 0.00/0.35 Linear 0.00/0.35 ->Coefficients: 0.00/0.35 Natural Numbers 0.00/0.35 ->Dimension: 0.00/0.35 1 0.00/0.35 ->Bound: 0.00/0.35 2 0.00/0.35 ->Interpretation: 0.00/0.35 0.00/0.35 [U11](X1,X2) = X1 0.00/0.35 [U12](X) = 2 0.00/0.35 [U21](X1,X2,X3) = X1 + 2.X2 0.00/0.35 [U22](X1,X2) = 2.X1 + 2 0.00/0.35 [U23](X) = 2 0.00/0.35 [U31](X1,X2) = X1 + X2 + 1 0.00/0.35 [U32](X) = X + 1 0.00/0.35 [U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 0.00/0.35 [U42](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.35 [U43](X) = X + 2 0.00/0.35 [U51](X1,X2,X3) = X2 + 2.X3 + 2 0.00/0.35 [U52](X1,X2) = 2.X2 + 2 0.00/0.35 [U53](X) = 2.X + 2 0.00/0.35 [U61](X1,X2) = 2.X1 + 2 0.00/0.35 [U62](X) = 2 0.00/0.35 [U71](X1,X2) = 2.X2 + 2 0.00/0.35 [U72](X) = X 0.00/0.35 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.35 [and](X1,X2) = X2 + 2 0.00/0.35 [isList](X) = X 0.00/0.35 [isNeList](X) = 2.X + 1 0.00/0.35 [isNePal](X) = 2.X + 2 0.00/0.35 [isPal](X) = 2.X + 2 0.00/0.35 [isPalListKind](X) = X 0.00/0.35 [isQid](X) = X + 2 0.00/0.35 [a] = 2 0.00/0.35 [e] = 2 0.00/0.35 [i] = 2 0.00/0.35 [nil] = 2 0.00/0.35 [o] = 2 0.00/0.35 [tt] = 2 0.00/0.35 [u] = 2 0.00/0.35 [U11#](X1,X2) = 2.X2 + 1 0.00/0.35 [U21#](X1,X2,X3) = 2.X2 + 2.X3 + 2 0.00/0.35 [U22#](X1,X2) = 2.X1 + 2.X2 + 1 0.00/0.35 [U41#](X1,X2,X3) = 2.X2 + 2.X3 + 2 0.00/0.35 [U42#](X1,X2) = 2.X2 0.00/0.35 [U51#](X1,X2,X3) = 2.X2 + 2.X3 + 2 0.00/0.35 [U52#](X1,X2) = X1 + 2.X2 + 1 0.00/0.35 [ISLIST](X) = 2.X + 1 0.00/0.35 [ISNELIST](X) = 2.X 0.00/0.35 0.00/0.35 Problem 1.3: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U22#(tt,V2) -> ISLIST(V2) 0.00/0.35 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.35 U41#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.35 U51#(tt,V1,V2) -> U52#(isNeList(V1),V2) 0.00/0.35 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.35 U52#(tt,V2) -> ISLIST(V2) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ISLIST(V) -> U11#(isPalListKind(V),V) 0.00/0.35 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U22#(tt,V2) -> ISLIST(V2) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ->->-> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->->-> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.35 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.35 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.35 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ->->-> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->->-> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 0.00/0.35 0.00/0.35 The problem is decomposed in 2 subproblems. 0.00/0.35 0.00/0.35 Problem 1.3.1: 0.00/0.35 0.00/0.35 Reduction Pairs Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> U22#(isList(V1),V2) 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U22#(tt,V2) -> ISLIST(V2) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 -> Usable rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->Interpretation type: 0.00/0.35 Linear 0.00/0.35 ->Coefficients: 0.00/0.35 Natural Numbers 0.00/0.35 ->Dimension: 0.00/0.35 1 0.00/0.35 ->Bound: 0.00/0.35 2 0.00/0.35 ->Interpretation: 0.00/0.35 0.00/0.35 [U11](X1,X2) = X1 0.00/0.35 [U12](X) = 2 0.00/0.35 [U21](X1,X2,X3) = 2.X2 + X3 + 2 0.00/0.35 [U22](X1,X2) = 2.X1 + X2 0.00/0.35 [U23](X) = X + 2 0.00/0.35 [U31](X1,X2) = 2.X2 + 2 0.00/0.35 [U32](X) = 2.X + 2 0.00/0.35 [U41](X1,X2,X3) = X1 + 2.X2 + X3 + 1 0.00/0.35 [U42](X1,X2) = 2.X1 + X2 + 1 0.00/0.35 [U43](X) = 2 0.00/0.35 [U51](X1,X2,X3) = X1 + 2.X2 + X3 + 2 0.00/0.35 [U52](X1,X2) = X1 + X2 + 1 0.00/0.35 [U53](X) = X + 2 0.00/0.35 [U61](X1,X2) = 2.X1 0.00/0.35 [U62](X) = 2 0.00/0.35 [U71](X1,X2) = X1 0.00/0.35 [U72](X) = 2 0.00/0.35 [__](X1,X2) = 2.X1 + X2 + 2 0.00/0.35 [and](X1,X2) = 2.X1 + X2 + 1 0.00/0.35 [isList](X) = X + 1 0.00/0.35 [isNeList](X) = 2.X + 2 0.00/0.35 [isNePal](X) = 2.X 0.00/0.35 [isPal](X) = X 0.00/0.35 [isPalListKind](X) = X 0.00/0.35 [isQid](X) = X 0.00/0.35 [a] = 2 0.00/0.35 [e] = 2 0.00/0.35 [i] = 2 0.00/0.35 [nil] = 2 0.00/0.35 [o] = 2 0.00/0.35 [tt] = 2 0.00/0.35 [u] = 2 0.00/0.35 [U21#](X1,X2,X3) = 2.X2 + 2.X3 + 2 0.00/0.35 [U22#](X1,X2) = X1 + 2.X2 0.00/0.35 [ISLIST](X) = 2.X + 1 0.00/0.35 0.00/0.35 Problem 1.3.1: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 U22#(tt,V2) -> ISLIST(V2) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 ->->Cycle: 0.00/0.35 ->->-> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ->->-> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 ->->-> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 0.00/0.35 Problem 1.3.1: 0.00/0.35 0.00/0.35 SubNColl Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 ISLIST(__(V1,V2)) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Projection: 0.00/0.35 pi(U21#) = 2 0.00/0.35 pi(ISLIST) = 1 0.00/0.35 0.00/0.35 Problem 1.3.1: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U21#(tt,V1,V2) -> ISLIST(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 There is no strongly connected component 0.00/0.35 0.00/0.35 The problem is finite. 0.00/0.35 0.00/0.35 Problem 1.3.2: 0.00/0.35 0.00/0.35 SubNColl Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.35 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.35 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.35 ISNELIST(__(V1,V2)) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 ISNELIST(__(V1,V2)) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Projection: 0.00/0.35 pi(U41#) = 3 0.00/0.35 pi(U42#) = 2 0.00/0.35 pi(U51#) = 2 0.00/0.35 pi(ISNELIST) = 1 0.00/0.35 0.00/0.35 Problem 1.3.2: 0.00/0.35 0.00/0.35 SCC Processor: 0.00/0.35 -> Pairs: 0.00/0.35 U41#(tt,V1,V2) -> U42#(isList(V1),V2) 0.00/0.35 U42#(tt,V2) -> ISNELIST(V2) 0.00/0.35 U51#(tt,V1,V2) -> ISNELIST(V1) 0.00/0.35 -> Rules: 0.00/0.35 U11(tt,V) -> U12(isNeList(V)) 0.00/0.35 U12(tt) -> tt 0.00/0.35 U21(tt,V1,V2) -> U22(isList(V1),V2) 0.00/0.35 U22(tt,V2) -> U23(isList(V2)) 0.00/0.35 U23(tt) -> tt 0.00/0.35 U31(tt,V) -> U32(isQid(V)) 0.00/0.35 U32(tt) -> tt 0.00/0.35 U41(tt,V1,V2) -> U42(isList(V1),V2) 0.00/0.35 U42(tt,V2) -> U43(isNeList(V2)) 0.00/0.35 U43(tt) -> tt 0.00/0.35 U51(tt,V1,V2) -> U52(isNeList(V1),V2) 0.00/0.35 U52(tt,V2) -> U53(isList(V2)) 0.00/0.35 U53(tt) -> tt 0.00/0.35 U61(tt,V) -> U62(isQid(V)) 0.00/0.35 U62(tt) -> tt 0.00/0.35 U71(tt,V) -> U72(isNePal(V)) 0.00/0.35 U72(tt) -> tt 0.00/0.35 __(__(X,Y),Z) -> __(X,__(Y,Z)) 0.00/0.35 __(nil,X) -> X 0.00/0.35 __(X,nil) -> X 0.00/0.35 and(tt,X) -> X 0.00/0.35 isList(__(V1,V2)) -> U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isList(nil) -> tt 0.00/0.35 isList(V) -> U11(isPalListKind(V),V) 0.00/0.35 isNeList(__(V1,V2)) -> U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(__(V1,V2)) -> U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2) 0.00/0.35 isNeList(V) -> U31(isPalListKind(V),V) 0.00/0.35 isNePal(__(I,__(P,I))) -> and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))) 0.00/0.35 isNePal(V) -> U61(isPalListKind(V),V) 0.00/0.35 isPal(nil) -> tt 0.00/0.35 isPal(V) -> U71(isPalListKind(V),V) 0.00/0.35 isPalListKind(__(V1,V2)) -> and(isPalListKind(V1),isPalListKind(V2)) 0.00/0.35 isPalListKind(a) -> tt 0.00/0.35 isPalListKind(e) -> tt 0.00/0.35 isPalListKind(i) -> tt 0.00/0.35 isPalListKind(nil) -> tt 0.00/0.35 isPalListKind(o) -> tt 0.00/0.35 isPalListKind(u) -> tt 0.00/0.35 isQid(a) -> tt 0.00/0.35 isQid(e) -> tt 0.00/0.35 isQid(i) -> tt 0.00/0.35 isQid(o) -> tt 0.00/0.35 isQid(u) -> tt 0.00/0.35 -> Unhiding rules: 0.00/0.35 Empty 0.00/0.35 ->Strongly Connected Components: 0.00/0.35 There is no strongly connected component 0.00/0.35 0.00/0.35 The problem is finite. 0.00/0.35 EOF