4.95/5.06 YES 4.95/5.06 4.95/5.06 Problem 1: 4.95/5.06 4.95/5.06 (VAR v_NonEmpty:S I:S P:S V:S V1:S V2:S X:S X1:S X2:S Y:S Z:S) 4.95/5.06 (RULES 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ) 4.95/5.06 (STRATEGY INNERMOST) 4.95/5.06 4.95/5.06 Problem 1: 4.95/5.06 4.95/5.06 Dependency Pairs Processor: 4.95/5.06 -> Pairs: 4.95/5.06 U11#(active(X:S)) -> U11#(X:S) 4.95/5.06 U11#(mark(X:S)) -> U11#(X:S) 4.95/5.06 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 4.95/5.06 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 4.95/5.06 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 4.95/5.06 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 4.95/5.06 U22#(active(X:S)) -> U22#(X:S) 4.95/5.06 U22#(mark(X:S)) -> U22#(X:S) 4.95/5.06 U31#(active(X:S)) -> U31#(X:S) 4.95/5.06 U31#(mark(X:S)) -> U31#(X:S) 4.95/5.06 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S) 4.95/5.06 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S) 4.95/5.06 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 4.95/5.06 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 4.95/5.06 U42#(active(X:S)) -> U42#(X:S) 4.95/5.06 U42#(mark(X:S)) -> U42#(X:S) 4.95/5.06 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 4.95/5.06 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 4.95/5.06 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 4.95/5.06 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 4.95/5.06 U52#(active(X:S)) -> U52#(X:S) 4.95/5.06 U52#(mark(X:S)) -> U52#(X:S) 4.95/5.06 U61#(active(X:S)) -> U61#(X:S) 4.95/5.06 U61#(mark(X:S)) -> U61#(X:S) 4.95/5.06 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S) 4.95/5.06 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S) 4.95/5.06 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 4.95/5.06 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 4.95/5.06 U72#(active(X:S)) -> U72#(X:S) 4.95/5.06 U72#(mark(X:S)) -> U72#(X:S) 4.95/5.06 U81#(active(X:S)) -> U81#(X:S) 4.95/5.06 U81#(mark(X:S)) -> U81#(X:S) 4.95/5.06 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 4.95/5.06 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 4.95/5.06 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 4.95/5.06 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 4.95/5.06 ACTIVE(U11(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U21(tt,V2:S)) -> U22#(isList(V2:S)) 4.95/5.06 ACTIVE(U21(tt,V2:S)) -> ISLIST(V2:S) 4.95/5.06 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S))) 4.95/5.06 ACTIVE(U22(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U31(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U41(tt,V2:S)) -> U42#(isNeList(V2:S)) 4.95/5.06 ACTIVE(U41(tt,V2:S)) -> ISNELIST(V2:S) 4.95/5.06 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 4.95/5.06 ACTIVE(U42(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U51(tt,V2:S)) -> U52#(isList(V2:S)) 4.95/5.06 ACTIVE(U51(tt,V2:S)) -> ISLIST(V2:S) 4.95/5.06 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 4.95/5.06 ACTIVE(U52(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U61(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U71(tt,P:S)) -> U72#(isPal(P:S)) 4.95/5.06 ACTIVE(U71(tt,P:S)) -> ISPAL(P:S) 4.95/5.06 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 4.95/5.06 ACTIVE(U72(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U81(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 4.95/5.06 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 4.95/5.06 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 4.95/5.06 ACTIVE(__(nil,X:S)) -> MARK(X:S) 4.95/5.06 ACTIVE(__(X:S,nil)) -> MARK(X:S) 4.95/5.06 ACTIVE(isList(__(V1:S,V2:S))) -> U21#(isList(V1:S),V2:S) 4.95/5.06 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S) 4.95/5.06 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 4.95/5.06 ACTIVE(isList(nil)) -> MARK(tt) 4.95/5.06 ACTIVE(isList(V:S)) -> U11#(isNeList(V:S)) 4.95/5.06 ACTIVE(isList(V:S)) -> ISNELIST(V:S) 4.95/5.06 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> U41#(isList(V1:S),V2:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> U51#(isNeList(V1:S),V2:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 4.95/5.06 ACTIVE(isNeList(V:S)) -> U31#(isQid(V:S)) 4.95/5.06 ACTIVE(isNeList(V:S)) -> ISQID(V:S) 4.95/5.06 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 4.95/5.06 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> U71#(isQid(I:S),P:S) 4.95/5.06 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S) 4.95/5.06 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 4.95/5.06 ACTIVE(isNePal(V:S)) -> U61#(isQid(V:S)) 4.95/5.06 ACTIVE(isNePal(V:S)) -> ISQID(V:S) 4.95/5.06 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 4.95/5.06 ACTIVE(isPal(nil)) -> MARK(tt) 4.95/5.06 ACTIVE(isPal(V:S)) -> U81#(isNePal(V:S)) 4.95/5.06 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S) 4.95/5.06 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 4.95/5.06 ACTIVE(isQid(a)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(e)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(i)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(o)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(u)) -> MARK(tt) 4.95/5.06 ISLIST(active(X:S)) -> ISLIST(X:S) 4.95/5.06 ISLIST(mark(X:S)) -> ISLIST(X:S) 4.95/5.06 ISNELIST(active(X:S)) -> ISNELIST(X:S) 4.95/5.06 ISNELIST(mark(X:S)) -> ISNELIST(X:S) 4.95/5.06 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 4.95/5.06 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 4.95/5.06 ISPAL(active(X:S)) -> ISPAL(X:S) 4.95/5.06 ISPAL(mark(X:S)) -> ISPAL(X:S) 4.95/5.06 ISQID(active(X:S)) -> ISQID(X:S) 4.95/5.06 ISQID(mark(X:S)) -> ISQID(X:S) 4.95/5.06 MARK(U11(X:S)) -> U11#(mark(X:S)) 4.95/5.06 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 4.95/5.06 MARK(U11(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U21(X1:S,X2:S)) -> U21#(mark(X1:S),X2:S) 4.95/5.06 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 4.95/5.06 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U22(X:S)) -> U22#(mark(X:S)) 4.95/5.06 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 4.95/5.06 MARK(U22(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U31(X:S)) -> U31#(mark(X:S)) 4.95/5.06 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 4.95/5.06 MARK(U31(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U41(X1:S,X2:S)) -> U41#(mark(X1:S),X2:S) 4.95/5.06 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 4.95/5.06 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U42(X:S)) -> U42#(mark(X:S)) 4.95/5.06 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 4.95/5.06 MARK(U42(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U51(X1:S,X2:S)) -> U51#(mark(X1:S),X2:S) 4.95/5.06 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 4.95/5.06 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U52(X:S)) -> U52#(mark(X:S)) 4.95/5.06 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 4.95/5.06 MARK(U52(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U61(X:S)) -> U61#(mark(X:S)) 4.95/5.06 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 4.95/5.06 MARK(U61(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U71(X1:S,X2:S)) -> U71#(mark(X1:S),X2:S) 4.95/5.06 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 4.95/5.06 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U72(X:S)) -> U72#(mark(X:S)) 4.95/5.06 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 4.95/5.06 MARK(U72(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U81(X:S)) -> U81#(mark(X:S)) 4.95/5.06 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 4.95/5.06 MARK(U81(X:S)) -> MARK(X:S) 4.95/5.06 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S)) 4.95/5.06 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 4.95/5.06 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 4.95/5.06 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 4.95/5.06 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 4.95/5.06 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 4.95/5.06 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 4.95/5.06 MARK(isQid(X:S)) -> ACTIVE(isQid(X:S)) 4.95/5.06 -> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 4.95/5.06 Problem 1: 4.95/5.06 4.95/5.06 SCC Processor: 4.95/5.06 -> Pairs: 4.95/5.06 U11#(active(X:S)) -> U11#(X:S) 4.95/5.06 U11#(mark(X:S)) -> U11#(X:S) 4.95/5.06 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 4.95/5.06 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 4.95/5.06 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 4.95/5.06 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 4.95/5.06 U22#(active(X:S)) -> U22#(X:S) 4.95/5.06 U22#(mark(X:S)) -> U22#(X:S) 4.95/5.06 U31#(active(X:S)) -> U31#(X:S) 4.95/5.06 U31#(mark(X:S)) -> U31#(X:S) 4.95/5.06 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S) 4.95/5.06 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S) 4.95/5.06 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 4.95/5.06 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 4.95/5.06 U42#(active(X:S)) -> U42#(X:S) 4.95/5.06 U42#(mark(X:S)) -> U42#(X:S) 4.95/5.06 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 4.95/5.06 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 4.95/5.06 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 4.95/5.06 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 4.95/5.06 U52#(active(X:S)) -> U52#(X:S) 4.95/5.06 U52#(mark(X:S)) -> U52#(X:S) 4.95/5.06 U61#(active(X:S)) -> U61#(X:S) 4.95/5.06 U61#(mark(X:S)) -> U61#(X:S) 4.95/5.06 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S) 4.95/5.06 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S) 4.95/5.06 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 4.95/5.06 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 4.95/5.06 U72#(active(X:S)) -> U72#(X:S) 4.95/5.06 U72#(mark(X:S)) -> U72#(X:S) 4.95/5.06 U81#(active(X:S)) -> U81#(X:S) 4.95/5.06 U81#(mark(X:S)) -> U81#(X:S) 4.95/5.06 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 4.95/5.06 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 4.95/5.06 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 4.95/5.06 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 4.95/5.06 ACTIVE(U11(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U21(tt,V2:S)) -> U22#(isList(V2:S)) 4.95/5.06 ACTIVE(U21(tt,V2:S)) -> ISLIST(V2:S) 4.95/5.06 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S))) 4.95/5.06 ACTIVE(U22(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U31(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U41(tt,V2:S)) -> U42#(isNeList(V2:S)) 4.95/5.06 ACTIVE(U41(tt,V2:S)) -> ISNELIST(V2:S) 4.95/5.06 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 4.95/5.06 ACTIVE(U42(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U51(tt,V2:S)) -> U52#(isList(V2:S)) 4.95/5.06 ACTIVE(U51(tt,V2:S)) -> ISLIST(V2:S) 4.95/5.06 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 4.95/5.06 ACTIVE(U52(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U61(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U71(tt,P:S)) -> U72#(isPal(P:S)) 4.95/5.06 ACTIVE(U71(tt,P:S)) -> ISPAL(P:S) 4.95/5.06 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 4.95/5.06 ACTIVE(U72(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(U81(tt)) -> MARK(tt) 4.95/5.06 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S)) 4.95/5.06 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S) 4.95/5.06 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 4.95/5.06 ACTIVE(__(nil,X:S)) -> MARK(X:S) 4.95/5.06 ACTIVE(__(X:S,nil)) -> MARK(X:S) 4.95/5.06 ACTIVE(isList(__(V1:S,V2:S))) -> U21#(isList(V1:S),V2:S) 4.95/5.06 ACTIVE(isList(__(V1:S,V2:S))) -> ISLIST(V1:S) 4.95/5.06 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 4.95/5.06 ACTIVE(isList(nil)) -> MARK(tt) 4.95/5.06 ACTIVE(isList(V:S)) -> U11#(isNeList(V:S)) 4.95/5.06 ACTIVE(isList(V:S)) -> ISNELIST(V:S) 4.95/5.06 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> U41#(isList(V1:S),V2:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> U51#(isNeList(V1:S),V2:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISLIST(V1:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> ISNELIST(V1:S) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 4.95/5.06 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 4.95/5.06 ACTIVE(isNeList(V:S)) -> U31#(isQid(V:S)) 4.95/5.06 ACTIVE(isNeList(V:S)) -> ISQID(V:S) 4.95/5.06 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 4.95/5.06 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> U71#(isQid(I:S),P:S) 4.95/5.06 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> ISQID(I:S) 4.95/5.06 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 4.95/5.06 ACTIVE(isNePal(V:S)) -> U61#(isQid(V:S)) 4.95/5.06 ACTIVE(isNePal(V:S)) -> ISQID(V:S) 4.95/5.06 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 4.95/5.06 ACTIVE(isPal(nil)) -> MARK(tt) 4.95/5.06 ACTIVE(isPal(V:S)) -> U81#(isNePal(V:S)) 4.95/5.06 ACTIVE(isPal(V:S)) -> ISNEPAL(V:S) 4.95/5.06 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 4.95/5.06 ACTIVE(isQid(a)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(e)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(i)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(o)) -> MARK(tt) 4.95/5.06 ACTIVE(isQid(u)) -> MARK(tt) 4.95/5.06 ISLIST(active(X:S)) -> ISLIST(X:S) 4.95/5.06 ISLIST(mark(X:S)) -> ISLIST(X:S) 4.95/5.06 ISNELIST(active(X:S)) -> ISNELIST(X:S) 4.95/5.06 ISNELIST(mark(X:S)) -> ISNELIST(X:S) 4.95/5.06 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 4.95/5.06 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 4.95/5.06 ISPAL(active(X:S)) -> ISPAL(X:S) 4.95/5.06 ISPAL(mark(X:S)) -> ISPAL(X:S) 4.95/5.06 ISQID(active(X:S)) -> ISQID(X:S) 4.95/5.06 ISQID(mark(X:S)) -> ISQID(X:S) 4.95/5.06 MARK(U11(X:S)) -> U11#(mark(X:S)) 4.95/5.06 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 4.95/5.06 MARK(U11(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U21(X1:S,X2:S)) -> U21#(mark(X1:S),X2:S) 4.95/5.06 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 4.95/5.06 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U22(X:S)) -> U22#(mark(X:S)) 4.95/5.06 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 4.95/5.06 MARK(U22(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U31(X:S)) -> U31#(mark(X:S)) 4.95/5.06 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 4.95/5.06 MARK(U31(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U41(X1:S,X2:S)) -> U41#(mark(X1:S),X2:S) 4.95/5.06 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 4.95/5.06 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U42(X:S)) -> U42#(mark(X:S)) 4.95/5.06 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 4.95/5.06 MARK(U42(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U51(X1:S,X2:S)) -> U51#(mark(X1:S),X2:S) 4.95/5.06 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 4.95/5.06 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U52(X:S)) -> U52#(mark(X:S)) 4.95/5.06 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 4.95/5.06 MARK(U52(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U61(X:S)) -> U61#(mark(X:S)) 4.95/5.06 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 4.95/5.06 MARK(U61(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U71(X1:S,X2:S)) -> U71#(mark(X1:S),X2:S) 4.95/5.06 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 4.95/5.06 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(U72(X:S)) -> U72#(mark(X:S)) 4.95/5.06 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 4.95/5.06 MARK(U72(X:S)) -> MARK(X:S) 4.95/5.06 MARK(U81(X:S)) -> U81#(mark(X:S)) 4.95/5.06 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 4.95/5.06 MARK(U81(X:S)) -> MARK(X:S) 4.95/5.06 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S)) 4.95/5.06 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 4.95/5.06 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.06 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 4.95/5.06 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 4.95/5.06 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 4.95/5.06 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 4.95/5.06 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 4.95/5.06 MARK(isQid(X:S)) -> ACTIVE(isQid(X:S)) 4.95/5.06 -> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->Strongly Connected Components: 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 ISQID(active(X:S)) -> ISQID(X:S) 4.95/5.06 ISQID(mark(X:S)) -> ISQID(X:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 ISPAL(active(X:S)) -> ISPAL(X:S) 4.95/5.06 ISPAL(mark(X:S)) -> ISPAL(X:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 4.95/5.06 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 ISNELIST(active(X:S)) -> ISNELIST(X:S) 4.95/5.06 ISNELIST(mark(X:S)) -> ISNELIST(X:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 ISLIST(active(X:S)) -> ISLIST(X:S) 4.95/5.06 ISLIST(mark(X:S)) -> ISLIST(X:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 4.95/5.06 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 4.95/5.06 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 4.95/5.06 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.06 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.06 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.06 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.06 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.06 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.06 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.06 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.06 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.06 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.06 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.06 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.06 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.06 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.06 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.06 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.06 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.06 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.06 mark(a) -> active(a) 4.95/5.06 mark(e) -> active(e) 4.95/5.06 mark(i) -> active(i) 4.95/5.06 mark(nil) -> active(nil) 4.95/5.06 mark(o) -> active(o) 4.95/5.06 mark(tt) -> active(tt) 4.95/5.06 mark(u) -> active(u) 4.95/5.06 ->->Cycle: 4.95/5.06 ->->-> Pairs: 4.95/5.06 U81#(active(X:S)) -> U81#(X:S) 4.95/5.06 U81#(mark(X:S)) -> U81#(X:S) 4.95/5.06 ->->-> Rules: 4.95/5.06 U11(active(X:S)) -> U11(X:S) 4.95/5.06 U11(mark(X:S)) -> U11(X:S) 4.95/5.06 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.06 U22(active(X:S)) -> U22(X:S) 4.95/5.06 U22(mark(X:S)) -> U22(X:S) 4.95/5.06 U31(active(X:S)) -> U31(X:S) 4.95/5.06 U31(mark(X:S)) -> U31(X:S) 4.95/5.06 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.06 U42(active(X:S)) -> U42(X:S) 4.95/5.06 U42(mark(X:S)) -> U42(X:S) 4.95/5.06 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.06 U52(active(X:S)) -> U52(X:S) 4.95/5.06 U52(mark(X:S)) -> U52(X:S) 4.95/5.06 U61(active(X:S)) -> U61(X:S) 4.95/5.06 U61(mark(X:S)) -> U61(X:S) 4.95/5.06 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.06 U72(active(X:S)) -> U72(X:S) 4.95/5.06 U72(mark(X:S)) -> U72(X:S) 4.95/5.06 U81(active(X:S)) -> U81(X:S) 4.95/5.06 U81(mark(X:S)) -> U81(X:S) 4.95/5.06 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.06 active(U11(tt)) -> mark(tt) 4.95/5.06 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.06 active(U22(tt)) -> mark(tt) 4.95/5.06 active(U31(tt)) -> mark(tt) 4.95/5.06 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.06 active(U42(tt)) -> mark(tt) 4.95/5.06 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.06 active(U52(tt)) -> mark(tt) 4.95/5.06 active(U61(tt)) -> mark(tt) 4.95/5.06 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.06 active(U72(tt)) -> mark(tt) 4.95/5.06 active(U81(tt)) -> mark(tt) 4.95/5.06 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.06 active(__(nil,X:S)) -> mark(X:S) 4.95/5.06 active(__(X:S,nil)) -> mark(X:S) 4.95/5.06 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.06 active(isList(nil)) -> mark(tt) 4.95/5.06 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.06 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.06 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.06 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.06 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.06 active(isPal(nil)) -> mark(tt) 4.95/5.06 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.06 active(isQid(a)) -> mark(tt) 4.95/5.06 active(isQid(e)) -> mark(tt) 4.95/5.06 active(isQid(i)) -> mark(tt) 4.95/5.06 active(isQid(o)) -> mark(tt) 4.95/5.06 active(isQid(u)) -> mark(tt) 4.95/5.06 isList(active(X:S)) -> isList(X:S) 4.95/5.06 isList(mark(X:S)) -> isList(X:S) 4.95/5.06 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.06 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.06 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.06 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.06 isPal(active(X:S)) -> isPal(X:S) 4.95/5.06 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.06 isQid(active(X:S)) -> isQid(X:S) 4.95/5.06 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.06 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U72#(active(X:S)) -> U72#(X:S) 4.95/5.07 U72#(mark(X:S)) -> U72#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S) 4.95/5.07 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S) 4.95/5.07 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 4.95/5.07 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U61#(active(X:S)) -> U61#(X:S) 4.95/5.07 U61#(mark(X:S)) -> U61#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U52#(active(X:S)) -> U52#(X:S) 4.95/5.07 U52#(mark(X:S)) -> U52#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 4.95/5.07 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 4.95/5.07 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 4.95/5.07 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U42#(active(X:S)) -> U42#(X:S) 4.95/5.07 U42#(mark(X:S)) -> U42#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S) 4.95/5.07 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S) 4.95/5.07 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 4.95/5.07 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U31#(active(X:S)) -> U31#(X:S) 4.95/5.07 U31#(mark(X:S)) -> U31#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U22#(active(X:S)) -> U22#(X:S) 4.95/5.07 U22#(mark(X:S)) -> U22#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 4.95/5.07 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 4.95/5.07 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 4.95/5.07 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 U11#(active(X:S)) -> U11#(X:S) 4.95/5.07 U11#(mark(X:S)) -> U11#(X:S) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 4.95/5.07 active(isQid(u)) -> mark(tt) 4.95/5.07 isList(active(X:S)) -> isList(X:S) 4.95/5.07 isList(mark(X:S)) -> isList(X:S) 4.95/5.07 isNeList(active(X:S)) -> isNeList(X:S) 4.95/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 4.95/5.07 isNePal(active(X:S)) -> isNePal(X:S) 4.95/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 4.95/5.07 isPal(active(X:S)) -> isPal(X:S) 4.95/5.07 isPal(mark(X:S)) -> isPal(X:S) 4.95/5.07 isQid(active(X:S)) -> isQid(X:S) 4.95/5.07 isQid(mark(X:S)) -> isQid(X:S) 4.95/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 4.95/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 4.95/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 4.95/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 4.95/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 4.95/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 4.95/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 4.95/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 4.95/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 4.95/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 4.95/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 4.95/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 4.95/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 4.95/5.07 mark(isList(X:S)) -> active(isList(X:S)) 4.95/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 4.95/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 4.95/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 4.95/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 4.95/5.07 mark(a) -> active(a) 4.95/5.07 mark(e) -> active(e) 4.95/5.07 mark(i) -> active(i) 4.95/5.07 mark(nil) -> active(nil) 4.95/5.07 mark(o) -> active(o) 4.95/5.07 mark(tt) -> active(tt) 4.95/5.07 mark(u) -> active(u) 4.95/5.07 ->->Cycle: 4.95/5.07 ->->-> Pairs: 4.95/5.07 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S))) 4.95/5.07 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 4.95/5.07 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 4.95/5.07 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 4.95/5.07 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 4.95/5.07 ACTIVE(__(nil,X:S)) -> MARK(X:S) 4.95/5.07 ACTIVE(__(X:S,nil)) -> MARK(X:S) 4.95/5.07 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 4.95/5.07 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 4.95/5.07 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 4.95/5.07 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 4.95/5.07 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 4.95/5.07 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 4.95/5.07 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 4.95/5.07 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 4.95/5.07 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 4.95/5.07 MARK(U11(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 4.95/5.07 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.07 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 4.95/5.07 MARK(U22(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 4.95/5.07 MARK(U31(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 4.95/5.07 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.07 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 4.95/5.07 MARK(U42(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 4.95/5.07 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.07 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 4.95/5.07 MARK(U52(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 4.95/5.07 MARK(U61(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 4.95/5.07 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.07 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 4.95/5.07 MARK(U72(X:S)) -> MARK(X:S) 4.95/5.07 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 4.95/5.07 MARK(U81(X:S)) -> MARK(X:S) 4.95/5.07 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 4.95/5.07 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 4.95/5.07 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 4.95/5.07 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 4.95/5.07 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 4.95/5.07 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 4.95/5.07 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 4.95/5.07 ->->-> Rules: 4.95/5.07 U11(active(X:S)) -> U11(X:S) 4.95/5.07 U11(mark(X:S)) -> U11(X:S) 4.95/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 4.95/5.07 U22(active(X:S)) -> U22(X:S) 4.95/5.07 U22(mark(X:S)) -> U22(X:S) 4.95/5.07 U31(active(X:S)) -> U31(X:S) 4.95/5.07 U31(mark(X:S)) -> U31(X:S) 4.95/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 4.95/5.07 U42(active(X:S)) -> U42(X:S) 4.95/5.07 U42(mark(X:S)) -> U42(X:S) 4.95/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 4.95/5.07 U52(active(X:S)) -> U52(X:S) 4.95/5.07 U52(mark(X:S)) -> U52(X:S) 4.95/5.07 U61(active(X:S)) -> U61(X:S) 4.95/5.07 U61(mark(X:S)) -> U61(X:S) 4.95/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 4.95/5.07 U72(active(X:S)) -> U72(X:S) 4.95/5.07 U72(mark(X:S)) -> U72(X:S) 4.95/5.07 U81(active(X:S)) -> U81(X:S) 4.95/5.07 U81(mark(X:S)) -> U81(X:S) 4.95/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 4.95/5.07 active(U11(tt)) -> mark(tt) 4.95/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 4.95/5.07 active(U22(tt)) -> mark(tt) 4.95/5.07 active(U31(tt)) -> mark(tt) 4.95/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 4.95/5.07 active(U42(tt)) -> mark(tt) 4.95/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 4.95/5.07 active(U52(tt)) -> mark(tt) 4.95/5.07 active(U61(tt)) -> mark(tt) 4.95/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 4.95/5.07 active(U72(tt)) -> mark(tt) 4.95/5.07 active(U81(tt)) -> mark(tt) 4.95/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 4.95/5.07 active(__(nil,X:S)) -> mark(X:S) 4.95/5.07 active(__(X:S,nil)) -> mark(X:S) 4.95/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 4.95/5.07 active(isList(nil)) -> mark(tt) 4.95/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 4.95/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 4.95/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 4.95/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 4.95/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 4.95/5.07 active(isPal(nil)) -> mark(tt) 4.95/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 4.95/5.07 active(isQid(a)) -> mark(tt) 4.95/5.07 active(isQid(e)) -> mark(tt) 4.95/5.07 active(isQid(i)) -> mark(tt) 4.95/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.07 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.07 mark(a) -> active(a) 5.04/5.07 mark(e) -> active(e) 5.04/5.07 mark(i) -> active(i) 5.04/5.07 mark(nil) -> active(nil) 5.04/5.07 mark(o) -> active(o) 5.04/5.07 mark(tt) -> active(tt) 5.04/5.07 mark(u) -> active(u) 5.04/5.07 5.04/5.07 5.04/5.07 The problem is decomposed in 19 subproblems. 5.04/5.07 5.04/5.07 Problem 1.1: 5.04/5.07 5.04/5.07 Subterm Processor: 5.04/5.07 -> Pairs: 5.04/5.07 ISQID(active(X:S)) -> ISQID(X:S) 5.04/5.07 ISQID(mark(X:S)) -> ISQID(X:S) 5.04/5.07 -> Rules: 5.04/5.07 U11(active(X:S)) -> U11(X:S) 5.04/5.07 U11(mark(X:S)) -> U11(X:S) 5.04/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U22(active(X:S)) -> U22(X:S) 5.04/5.07 U22(mark(X:S)) -> U22(X:S) 5.04/5.07 U31(active(X:S)) -> U31(X:S) 5.04/5.07 U31(mark(X:S)) -> U31(X:S) 5.04/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U42(active(X:S)) -> U42(X:S) 5.04/5.07 U42(mark(X:S)) -> U42(X:S) 5.04/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U52(active(X:S)) -> U52(X:S) 5.04/5.07 U52(mark(X:S)) -> U52(X:S) 5.04/5.07 U61(active(X:S)) -> U61(X:S) 5.04/5.07 U61(mark(X:S)) -> U61(X:S) 5.04/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U72(active(X:S)) -> U72(X:S) 5.04/5.07 U72(mark(X:S)) -> U72(X:S) 5.04/5.07 U81(active(X:S)) -> U81(X:S) 5.04/5.07 U81(mark(X:S)) -> U81(X:S) 5.04/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 active(U11(tt)) -> mark(tt) 5.04/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.07 active(U22(tt)) -> mark(tt) 5.04/5.07 active(U31(tt)) -> mark(tt) 5.04/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.07 active(U42(tt)) -> mark(tt) 5.04/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.07 active(U52(tt)) -> mark(tt) 5.04/5.07 active(U61(tt)) -> mark(tt) 5.04/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.07 active(U72(tt)) -> mark(tt) 5.04/5.07 active(U81(tt)) -> mark(tt) 5.04/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.07 active(__(nil,X:S)) -> mark(X:S) 5.04/5.07 active(__(X:S,nil)) -> mark(X:S) 5.04/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.07 active(isList(nil)) -> mark(tt) 5.04/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.07 active(isPal(nil)) -> mark(tt) 5.04/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.07 active(isQid(a)) -> mark(tt) 5.04/5.07 active(isQid(e)) -> mark(tt) 5.04/5.07 active(isQid(i)) -> mark(tt) 5.04/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.07 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.07 mark(a) -> active(a) 5.04/5.07 mark(e) -> active(e) 5.04/5.07 mark(i) -> active(i) 5.04/5.07 mark(nil) -> active(nil) 5.04/5.07 mark(o) -> active(o) 5.04/5.07 mark(tt) -> active(tt) 5.04/5.07 mark(u) -> active(u) 5.04/5.07 ->Projection: 5.04/5.07 pi(ISQID) = 1 5.04/5.07 5.04/5.07 Problem 1.1: 5.04/5.07 5.04/5.07 SCC Processor: 5.04/5.07 -> Pairs: 5.04/5.07 Empty 5.04/5.07 -> Rules: 5.04/5.07 U11(active(X:S)) -> U11(X:S) 5.04/5.07 U11(mark(X:S)) -> U11(X:S) 5.04/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U22(active(X:S)) -> U22(X:S) 5.04/5.07 U22(mark(X:S)) -> U22(X:S) 5.04/5.07 U31(active(X:S)) -> U31(X:S) 5.04/5.07 U31(mark(X:S)) -> U31(X:S) 5.04/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U42(active(X:S)) -> U42(X:S) 5.04/5.07 U42(mark(X:S)) -> U42(X:S) 5.04/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U52(active(X:S)) -> U52(X:S) 5.04/5.07 U52(mark(X:S)) -> U52(X:S) 5.04/5.07 U61(active(X:S)) -> U61(X:S) 5.04/5.07 U61(mark(X:S)) -> U61(X:S) 5.04/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U72(active(X:S)) -> U72(X:S) 5.04/5.07 U72(mark(X:S)) -> U72(X:S) 5.04/5.07 U81(active(X:S)) -> U81(X:S) 5.04/5.07 U81(mark(X:S)) -> U81(X:S) 5.04/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 active(U11(tt)) -> mark(tt) 5.04/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.07 active(U22(tt)) -> mark(tt) 5.04/5.07 active(U31(tt)) -> mark(tt) 5.04/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.07 active(U42(tt)) -> mark(tt) 5.04/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.07 active(U52(tt)) -> mark(tt) 5.04/5.07 active(U61(tt)) -> mark(tt) 5.04/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.07 active(U72(tt)) -> mark(tt) 5.04/5.07 active(U81(tt)) -> mark(tt) 5.04/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.07 active(__(nil,X:S)) -> mark(X:S) 5.04/5.07 active(__(X:S,nil)) -> mark(X:S) 5.04/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.07 active(isList(nil)) -> mark(tt) 5.04/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.07 active(isPal(nil)) -> mark(tt) 5.04/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.07 active(isQid(a)) -> mark(tt) 5.04/5.07 active(isQid(e)) -> mark(tt) 5.04/5.07 active(isQid(i)) -> mark(tt) 5.04/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.07 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.07 mark(a) -> active(a) 5.04/5.07 mark(e) -> active(e) 5.04/5.07 mark(i) -> active(i) 5.04/5.07 mark(nil) -> active(nil) 5.04/5.07 mark(o) -> active(o) 5.04/5.07 mark(tt) -> active(tt) 5.04/5.07 mark(u) -> active(u) 5.04/5.07 ->Strongly Connected Components: 5.04/5.07 There is no strongly connected component 5.04/5.07 5.04/5.07 The problem is finite. 5.04/5.07 5.04/5.07 Problem 1.2: 5.04/5.07 5.04/5.07 Subterm Processor: 5.04/5.07 -> Pairs: 5.04/5.07 ISPAL(active(X:S)) -> ISPAL(X:S) 5.04/5.07 ISPAL(mark(X:S)) -> ISPAL(X:S) 5.04/5.07 -> Rules: 5.04/5.07 U11(active(X:S)) -> U11(X:S) 5.04/5.07 U11(mark(X:S)) -> U11(X:S) 5.04/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U22(active(X:S)) -> U22(X:S) 5.04/5.07 U22(mark(X:S)) -> U22(X:S) 5.04/5.07 U31(active(X:S)) -> U31(X:S) 5.04/5.07 U31(mark(X:S)) -> U31(X:S) 5.04/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U42(active(X:S)) -> U42(X:S) 5.04/5.07 U42(mark(X:S)) -> U42(X:S) 5.04/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U52(active(X:S)) -> U52(X:S) 5.04/5.07 U52(mark(X:S)) -> U52(X:S) 5.04/5.07 U61(active(X:S)) -> U61(X:S) 5.04/5.07 U61(mark(X:S)) -> U61(X:S) 5.04/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U72(active(X:S)) -> U72(X:S) 5.04/5.07 U72(mark(X:S)) -> U72(X:S) 5.04/5.07 U81(active(X:S)) -> U81(X:S) 5.04/5.07 U81(mark(X:S)) -> U81(X:S) 5.04/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 active(U11(tt)) -> mark(tt) 5.04/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.07 active(U22(tt)) -> mark(tt) 5.04/5.07 active(U31(tt)) -> mark(tt) 5.04/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.07 active(U42(tt)) -> mark(tt) 5.04/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.07 active(U52(tt)) -> mark(tt) 5.04/5.07 active(U61(tt)) -> mark(tt) 5.04/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.07 active(U72(tt)) -> mark(tt) 5.04/5.07 active(U81(tt)) -> mark(tt) 5.04/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.07 active(__(nil,X:S)) -> mark(X:S) 5.04/5.07 active(__(X:S,nil)) -> mark(X:S) 5.04/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.07 active(isList(nil)) -> mark(tt) 5.04/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.07 active(isPal(nil)) -> mark(tt) 5.04/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.07 active(isQid(a)) -> mark(tt) 5.04/5.07 active(isQid(e)) -> mark(tt) 5.04/5.07 active(isQid(i)) -> mark(tt) 5.04/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.07 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.07 mark(a) -> active(a) 5.04/5.07 mark(e) -> active(e) 5.04/5.07 mark(i) -> active(i) 5.04/5.07 mark(nil) -> active(nil) 5.04/5.07 mark(o) -> active(o) 5.04/5.07 mark(tt) -> active(tt) 5.04/5.07 mark(u) -> active(u) 5.04/5.07 ->Projection: 5.04/5.07 pi(ISPAL) = 1 5.04/5.07 5.04/5.07 Problem 1.2: 5.04/5.07 5.04/5.07 SCC Processor: 5.04/5.07 -> Pairs: 5.04/5.07 Empty 5.04/5.07 -> Rules: 5.04/5.07 U11(active(X:S)) -> U11(X:S) 5.04/5.07 U11(mark(X:S)) -> U11(X:S) 5.04/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U22(active(X:S)) -> U22(X:S) 5.04/5.07 U22(mark(X:S)) -> U22(X:S) 5.04/5.07 U31(active(X:S)) -> U31(X:S) 5.04/5.07 U31(mark(X:S)) -> U31(X:S) 5.04/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U42(active(X:S)) -> U42(X:S) 5.04/5.07 U42(mark(X:S)) -> U42(X:S) 5.04/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U52(active(X:S)) -> U52(X:S) 5.04/5.07 U52(mark(X:S)) -> U52(X:S) 5.04/5.07 U61(active(X:S)) -> U61(X:S) 5.04/5.07 U61(mark(X:S)) -> U61(X:S) 5.04/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U72(active(X:S)) -> U72(X:S) 5.04/5.07 U72(mark(X:S)) -> U72(X:S) 5.04/5.07 U81(active(X:S)) -> U81(X:S) 5.04/5.07 U81(mark(X:S)) -> U81(X:S) 5.04/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 active(U11(tt)) -> mark(tt) 5.04/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.07 active(U22(tt)) -> mark(tt) 5.04/5.07 active(U31(tt)) -> mark(tt) 5.04/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.07 active(U42(tt)) -> mark(tt) 5.04/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.07 active(U52(tt)) -> mark(tt) 5.04/5.07 active(U61(tt)) -> mark(tt) 5.04/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.07 active(U72(tt)) -> mark(tt) 5.04/5.07 active(U81(tt)) -> mark(tt) 5.04/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.07 active(__(nil,X:S)) -> mark(X:S) 5.04/5.07 active(__(X:S,nil)) -> mark(X:S) 5.04/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.07 active(isList(nil)) -> mark(tt) 5.04/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.07 active(isPal(nil)) -> mark(tt) 5.04/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.07 active(isQid(a)) -> mark(tt) 5.04/5.07 active(isQid(e)) -> mark(tt) 5.04/5.07 active(isQid(i)) -> mark(tt) 5.04/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.07 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.07 mark(a) -> active(a) 5.04/5.07 mark(e) -> active(e) 5.04/5.07 mark(i) -> active(i) 5.04/5.07 mark(nil) -> active(nil) 5.04/5.07 mark(o) -> active(o) 5.04/5.07 mark(tt) -> active(tt) 5.04/5.07 mark(u) -> active(u) 5.04/5.07 ->Strongly Connected Components: 5.04/5.07 There is no strongly connected component 5.04/5.07 5.04/5.07 The problem is finite. 5.04/5.07 5.04/5.07 Problem 1.3: 5.04/5.07 5.04/5.07 Subterm Processor: 5.04/5.07 -> Pairs: 5.04/5.07 ISNEPAL(active(X:S)) -> ISNEPAL(X:S) 5.04/5.07 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S) 5.04/5.07 -> Rules: 5.04/5.07 U11(active(X:S)) -> U11(X:S) 5.04/5.07 U11(mark(X:S)) -> U11(X:S) 5.04/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U22(active(X:S)) -> U22(X:S) 5.04/5.07 U22(mark(X:S)) -> U22(X:S) 5.04/5.07 U31(active(X:S)) -> U31(X:S) 5.04/5.07 U31(mark(X:S)) -> U31(X:S) 5.04/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U42(active(X:S)) -> U42(X:S) 5.04/5.07 U42(mark(X:S)) -> U42(X:S) 5.04/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U52(active(X:S)) -> U52(X:S) 5.04/5.07 U52(mark(X:S)) -> U52(X:S) 5.04/5.07 U61(active(X:S)) -> U61(X:S) 5.04/5.07 U61(mark(X:S)) -> U61(X:S) 5.04/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U72(active(X:S)) -> U72(X:S) 5.04/5.07 U72(mark(X:S)) -> U72(X:S) 5.04/5.07 U81(active(X:S)) -> U81(X:S) 5.04/5.07 U81(mark(X:S)) -> U81(X:S) 5.04/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 active(U11(tt)) -> mark(tt) 5.04/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.07 active(U22(tt)) -> mark(tt) 5.04/5.07 active(U31(tt)) -> mark(tt) 5.04/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.07 active(U42(tt)) -> mark(tt) 5.04/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.07 active(U52(tt)) -> mark(tt) 5.04/5.07 active(U61(tt)) -> mark(tt) 5.04/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.07 active(U72(tt)) -> mark(tt) 5.04/5.07 active(U81(tt)) -> mark(tt) 5.04/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.07 active(__(nil,X:S)) -> mark(X:S) 5.04/5.07 active(__(X:S,nil)) -> mark(X:S) 5.04/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.07 active(isList(nil)) -> mark(tt) 5.04/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.07 active(isPal(nil)) -> mark(tt) 5.04/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.07 active(isQid(a)) -> mark(tt) 5.04/5.07 active(isQid(e)) -> mark(tt) 5.04/5.07 active(isQid(i)) -> mark(tt) 5.04/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.07 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.07 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.07 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.07 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.07 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.07 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.07 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.07 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.07 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.07 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.07 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.07 mark(a) -> active(a) 5.04/5.07 mark(e) -> active(e) 5.04/5.07 mark(i) -> active(i) 5.04/5.07 mark(nil) -> active(nil) 5.04/5.07 mark(o) -> active(o) 5.04/5.07 mark(tt) -> active(tt) 5.04/5.07 mark(u) -> active(u) 5.04/5.07 ->Projection: 5.04/5.07 pi(ISNEPAL) = 1 5.04/5.07 5.04/5.07 Problem 1.3: 5.04/5.07 5.04/5.07 SCC Processor: 5.04/5.07 -> Pairs: 5.04/5.07 Empty 5.04/5.07 -> Rules: 5.04/5.07 U11(active(X:S)) -> U11(X:S) 5.04/5.07 U11(mark(X:S)) -> U11(X:S) 5.04/5.07 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.07 U22(active(X:S)) -> U22(X:S) 5.04/5.07 U22(mark(X:S)) -> U22(X:S) 5.04/5.07 U31(active(X:S)) -> U31(X:S) 5.04/5.07 U31(mark(X:S)) -> U31(X:S) 5.04/5.07 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.07 U42(active(X:S)) -> U42(X:S) 5.04/5.07 U42(mark(X:S)) -> U42(X:S) 5.04/5.07 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.07 U52(active(X:S)) -> U52(X:S) 5.04/5.07 U52(mark(X:S)) -> U52(X:S) 5.04/5.07 U61(active(X:S)) -> U61(X:S) 5.04/5.07 U61(mark(X:S)) -> U61(X:S) 5.04/5.07 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.07 U72(active(X:S)) -> U72(X:S) 5.04/5.07 U72(mark(X:S)) -> U72(X:S) 5.04/5.07 U81(active(X:S)) -> U81(X:S) 5.04/5.07 U81(mark(X:S)) -> U81(X:S) 5.04/5.07 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.07 active(U11(tt)) -> mark(tt) 5.04/5.07 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.07 active(U22(tt)) -> mark(tt) 5.04/5.07 active(U31(tt)) -> mark(tt) 5.04/5.07 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.07 active(U42(tt)) -> mark(tt) 5.04/5.07 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.07 active(U52(tt)) -> mark(tt) 5.04/5.07 active(U61(tt)) -> mark(tt) 5.04/5.07 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.07 active(U72(tt)) -> mark(tt) 5.04/5.07 active(U81(tt)) -> mark(tt) 5.04/5.07 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.07 active(__(nil,X:S)) -> mark(X:S) 5.04/5.07 active(__(X:S,nil)) -> mark(X:S) 5.04/5.07 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.07 active(isList(nil)) -> mark(tt) 5.04/5.07 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.07 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.07 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.07 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.07 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.07 active(isPal(nil)) -> mark(tt) 5.04/5.07 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.07 active(isQid(a)) -> mark(tt) 5.04/5.07 active(isQid(e)) -> mark(tt) 5.04/5.07 active(isQid(i)) -> mark(tt) 5.04/5.07 active(isQid(o)) -> mark(tt) 5.04/5.07 active(isQid(u)) -> mark(tt) 5.04/5.07 isList(active(X:S)) -> isList(X:S) 5.04/5.07 isList(mark(X:S)) -> isList(X:S) 5.04/5.07 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.07 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.07 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.07 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.07 isPal(active(X:S)) -> isPal(X:S) 5.04/5.07 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.07 isQid(active(X:S)) -> isQid(X:S) 5.04/5.07 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.07 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.07 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.07 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.07 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.07 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.07 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.07 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.4: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 ISNELIST(active(X:S)) -> ISNELIST(X:S) 5.04/5.08 ISNELIST(mark(X:S)) -> ISNELIST(X:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(ISNELIST) = 1 5.04/5.08 5.04/5.08 Problem 1.4: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 Empty 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.5: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 ISLIST(active(X:S)) -> ISLIST(X:S) 5.04/5.08 ISLIST(mark(X:S)) -> ISLIST(X:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(ISLIST) = 1 5.04/5.08 5.04/5.08 Problem 1.5: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 Empty 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.6: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S) 5.04/5.08 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S) 5.04/5.08 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(__#) = 1 5.04/5.08 5.04/5.08 Problem 1.6: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 ->->Cycle: 5.04/5.08 ->->-> Pairs: 5.04/5.08 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 ->->-> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 5.04/5.08 Problem 1.6: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(__#) = 2 5.04/5.08 5.04/5.08 Problem 1.6: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 Empty 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.7: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 U81#(active(X:S)) -> U81#(X:S) 5.04/5.08 U81#(mark(X:S)) -> U81#(X:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(U81#) = 1 5.04/5.08 5.04/5.08 Problem 1.7: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 Empty 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.8: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 U72#(active(X:S)) -> U72#(X:S) 5.04/5.08 U72#(mark(X:S)) -> U72#(X:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(U72#) = 1 5.04/5.08 5.04/5.08 Problem 1.8: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 Empty 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.9: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 U71#(active(X1:S),X2:S) -> U71#(X1:S,X2:S) 5.04/5.08 U71#(mark(X1:S),X2:S) -> U71#(X1:S,X2:S) 5.04/5.08 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(U71#) = 1 5.04/5.08 5.04/5.08 Problem 1.9: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 ->->Cycle: 5.04/5.08 ->->-> Pairs: 5.04/5.08 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 ->->-> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 5.04/5.08 Problem 1.9: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 U71#(X1:S,active(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 U71#(X1:S,mark(X2:S)) -> U71#(X1:S,X2:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Projection: 5.04/5.08 pi(U71#) = 2 5.04/5.08 5.04/5.08 Problem 1.9: 5.04/5.08 5.04/5.08 SCC Processor: 5.04/5.08 -> Pairs: 5.04/5.08 Empty 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.08 active(isList(nil)) -> mark(tt) 5.04/5.08 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.08 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.08 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.08 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.08 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.08 active(isPal(nil)) -> mark(tt) 5.04/5.08 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.08 active(isQid(a)) -> mark(tt) 5.04/5.08 active(isQid(e)) -> mark(tt) 5.04/5.08 active(isQid(i)) -> mark(tt) 5.04/5.08 active(isQid(o)) -> mark(tt) 5.04/5.08 active(isQid(u)) -> mark(tt) 5.04/5.08 isList(active(X:S)) -> isList(X:S) 5.04/5.08 isList(mark(X:S)) -> isList(X:S) 5.04/5.08 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.08 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.08 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.08 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.08 isPal(active(X:S)) -> isPal(X:S) 5.04/5.08 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.08 isQid(active(X:S)) -> isQid(X:S) 5.04/5.08 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.08 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.08 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.08 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.08 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.08 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.08 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.08 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.08 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.08 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.08 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.08 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.08 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.08 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.08 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.08 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.08 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.08 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.08 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.08 mark(a) -> active(a) 5.04/5.08 mark(e) -> active(e) 5.04/5.08 mark(i) -> active(i) 5.04/5.08 mark(nil) -> active(nil) 5.04/5.08 mark(o) -> active(o) 5.04/5.08 mark(tt) -> active(tt) 5.04/5.08 mark(u) -> active(u) 5.04/5.08 ->Strongly Connected Components: 5.04/5.08 There is no strongly connected component 5.04/5.08 5.04/5.08 The problem is finite. 5.04/5.08 5.04/5.08 Problem 1.10: 5.04/5.08 5.04/5.08 Subterm Processor: 5.04/5.08 -> Pairs: 5.04/5.08 U61#(active(X:S)) -> U61#(X:S) 5.04/5.08 U61#(mark(X:S)) -> U61#(X:S) 5.04/5.08 -> Rules: 5.04/5.08 U11(active(X:S)) -> U11(X:S) 5.04/5.08 U11(mark(X:S)) -> U11(X:S) 5.04/5.08 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.08 U22(active(X:S)) -> U22(X:S) 5.04/5.08 U22(mark(X:S)) -> U22(X:S) 5.04/5.08 U31(active(X:S)) -> U31(X:S) 5.04/5.08 U31(mark(X:S)) -> U31(X:S) 5.04/5.08 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.08 U42(active(X:S)) -> U42(X:S) 5.04/5.08 U42(mark(X:S)) -> U42(X:S) 5.04/5.08 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.08 U52(active(X:S)) -> U52(X:S) 5.04/5.08 U52(mark(X:S)) -> U52(X:S) 5.04/5.08 U61(active(X:S)) -> U61(X:S) 5.04/5.08 U61(mark(X:S)) -> U61(X:S) 5.04/5.08 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.08 U72(active(X:S)) -> U72(X:S) 5.04/5.08 U72(mark(X:S)) -> U72(X:S) 5.04/5.08 U81(active(X:S)) -> U81(X:S) 5.04/5.08 U81(mark(X:S)) -> U81(X:S) 5.04/5.08 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.08 active(U11(tt)) -> mark(tt) 5.04/5.08 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.08 active(U22(tt)) -> mark(tt) 5.04/5.08 active(U31(tt)) -> mark(tt) 5.04/5.08 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.08 active(U42(tt)) -> mark(tt) 5.04/5.08 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.08 active(U52(tt)) -> mark(tt) 5.04/5.08 active(U61(tt)) -> mark(tt) 5.04/5.08 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.08 active(U72(tt)) -> mark(tt) 5.04/5.08 active(U81(tt)) -> mark(tt) 5.04/5.08 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.08 active(__(nil,X:S)) -> mark(X:S) 5.04/5.08 active(__(X:S,nil)) -> mark(X:S) 5.04/5.08 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U61#) = 1 5.04/5.09 5.04/5.09 Problem 1.10: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 There is no strongly connected component 5.04/5.09 5.04/5.09 The problem is finite. 5.04/5.09 5.04/5.09 Problem 1.11: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U52#(active(X:S)) -> U52#(X:S) 5.04/5.09 U52#(mark(X:S)) -> U52#(X:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U52#) = 1 5.04/5.09 5.04/5.09 Problem 1.11: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 There is no strongly connected component 5.04/5.09 5.04/5.09 The problem is finite. 5.04/5.09 5.04/5.09 Problem 1.12: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 5.04/5.09 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 5.04/5.09 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U51#) = 1 5.04/5.09 5.04/5.09 Problem 1.12: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 ->->Cycle: 5.04/5.09 ->->-> Pairs: 5.04/5.09 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 ->->-> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 5.04/5.09 Problem 1.12: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U51#) = 2 5.04/5.09 5.04/5.09 Problem 1.12: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 There is no strongly connected component 5.04/5.09 5.04/5.09 The problem is finite. 5.04/5.09 5.04/5.09 Problem 1.13: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U42#(active(X:S)) -> U42#(X:S) 5.04/5.09 U42#(mark(X:S)) -> U42#(X:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U42#) = 1 5.04/5.09 5.04/5.09 Problem 1.13: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 There is no strongly connected component 5.04/5.09 5.04/5.09 The problem is finite. 5.04/5.09 5.04/5.09 Problem 1.14: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U41#(active(X1:S),X2:S) -> U41#(X1:S,X2:S) 5.04/5.09 U41#(mark(X1:S),X2:S) -> U41#(X1:S,X2:S) 5.04/5.09 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U41#) = 1 5.04/5.09 5.04/5.09 Problem 1.14: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 ->->Cycle: 5.04/5.09 ->->-> Pairs: 5.04/5.09 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 ->->-> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 5.04/5.09 Problem 1.14: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U41#(X1:S,active(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 U41#(X1:S,mark(X2:S)) -> U41#(X1:S,X2:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U41#) = 2 5.04/5.09 5.04/5.09 Problem 1.14: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 There is no strongly connected component 5.04/5.09 5.04/5.09 The problem is finite. 5.04/5.09 5.04/5.09 Problem 1.15: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U31#(active(X:S)) -> U31#(X:S) 5.04/5.09 U31#(mark(X:S)) -> U31#(X:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U31#) = 1 5.04/5.09 5.04/5.09 Problem 1.15: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Strongly Connected Components: 5.04/5.09 There is no strongly connected component 5.04/5.09 5.04/5.09 The problem is finite. 5.04/5.09 5.04/5.09 Problem 1.16: 5.04/5.09 5.04/5.09 Subterm Processor: 5.04/5.09 -> Pairs: 5.04/5.09 U22#(active(X:S)) -> U22#(X:S) 5.04/5.09 U22#(mark(X:S)) -> U22#(X:S) 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.09 U52(mark(X:S)) -> U52(X:S) 5.04/5.09 U61(active(X:S)) -> U61(X:S) 5.04/5.09 U61(mark(X:S)) -> U61(X:S) 5.04/5.09 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.09 U72(active(X:S)) -> U72(X:S) 5.04/5.09 U72(mark(X:S)) -> U72(X:S) 5.04/5.09 U81(active(X:S)) -> U81(X:S) 5.04/5.09 U81(mark(X:S)) -> U81(X:S) 5.04/5.09 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.09 active(U11(tt)) -> mark(tt) 5.04/5.09 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.09 active(U22(tt)) -> mark(tt) 5.04/5.09 active(U31(tt)) -> mark(tt) 5.04/5.09 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.09 active(U42(tt)) -> mark(tt) 5.04/5.09 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.09 active(U52(tt)) -> mark(tt) 5.04/5.09 active(U61(tt)) -> mark(tt) 5.04/5.09 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.09 active(U72(tt)) -> mark(tt) 5.04/5.09 active(U81(tt)) -> mark(tt) 5.04/5.09 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.09 active(__(nil,X:S)) -> mark(X:S) 5.04/5.09 active(__(X:S,nil)) -> mark(X:S) 5.04/5.09 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.09 active(isList(nil)) -> mark(tt) 5.04/5.09 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.09 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.09 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.09 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.09 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.09 active(isPal(nil)) -> mark(tt) 5.04/5.09 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.09 active(isQid(a)) -> mark(tt) 5.04/5.09 active(isQid(e)) -> mark(tt) 5.04/5.09 active(isQid(i)) -> mark(tt) 5.04/5.09 active(isQid(o)) -> mark(tt) 5.04/5.09 active(isQid(u)) -> mark(tt) 5.04/5.09 isList(active(X:S)) -> isList(X:S) 5.04/5.09 isList(mark(X:S)) -> isList(X:S) 5.04/5.09 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.09 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.09 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.09 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.09 isPal(active(X:S)) -> isPal(X:S) 5.04/5.09 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.09 isQid(active(X:S)) -> isQid(X:S) 5.04/5.09 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.09 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.09 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.09 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.09 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.09 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.09 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.09 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.09 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.09 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.09 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.09 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.09 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.09 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.09 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.09 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.09 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.09 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.09 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.09 mark(a) -> active(a) 5.04/5.09 mark(e) -> active(e) 5.04/5.09 mark(i) -> active(i) 5.04/5.09 mark(nil) -> active(nil) 5.04/5.09 mark(o) -> active(o) 5.04/5.09 mark(tt) -> active(tt) 5.04/5.09 mark(u) -> active(u) 5.04/5.09 ->Projection: 5.04/5.09 pi(U22#) = 1 5.04/5.09 5.04/5.09 Problem 1.16: 5.04/5.09 5.04/5.09 SCC Processor: 5.04/5.09 -> Pairs: 5.04/5.09 Empty 5.04/5.09 -> Rules: 5.04/5.09 U11(active(X:S)) -> U11(X:S) 5.04/5.09 U11(mark(X:S)) -> U11(X:S) 5.04/5.09 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.09 U22(active(X:S)) -> U22(X:S) 5.04/5.09 U22(mark(X:S)) -> U22(X:S) 5.04/5.09 U31(active(X:S)) -> U31(X:S) 5.04/5.09 U31(mark(X:S)) -> U31(X:S) 5.04/5.09 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.09 U42(active(X:S)) -> U42(X:S) 5.04/5.09 U42(mark(X:S)) -> U42(X:S) 5.04/5.09 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.09 U52(active(X:S)) -> U52(X:S) 5.04/5.10 U52(mark(X:S)) -> U52(X:S) 5.04/5.10 U61(active(X:S)) -> U61(X:S) 5.04/5.10 U61(mark(X:S)) -> U61(X:S) 5.04/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.10 U72(active(X:S)) -> U72(X:S) 5.04/5.10 U72(mark(X:S)) -> U72(X:S) 5.04/5.10 U81(active(X:S)) -> U81(X:S) 5.04/5.10 U81(mark(X:S)) -> U81(X:S) 5.04/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.10 active(U11(tt)) -> mark(tt) 5.04/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.10 active(U22(tt)) -> mark(tt) 5.04/5.10 active(U31(tt)) -> mark(tt) 5.04/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.10 active(U42(tt)) -> mark(tt) 5.04/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.10 active(U52(tt)) -> mark(tt) 5.04/5.10 active(U61(tt)) -> mark(tt) 5.04/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.10 active(U72(tt)) -> mark(tt) 5.04/5.10 active(U81(tt)) -> mark(tt) 5.04/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.10 active(__(nil,X:S)) -> mark(X:S) 5.04/5.10 active(__(X:S,nil)) -> mark(X:S) 5.04/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.10 active(isList(nil)) -> mark(tt) 5.04/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.10 active(isPal(nil)) -> mark(tt) 5.04/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.10 active(isQid(a)) -> mark(tt) 5.04/5.10 active(isQid(e)) -> mark(tt) 5.04/5.10 active(isQid(i)) -> mark(tt) 5.04/5.10 active(isQid(o)) -> mark(tt) 5.04/5.10 active(isQid(u)) -> mark(tt) 5.04/5.10 isList(active(X:S)) -> isList(X:S) 5.04/5.10 isList(mark(X:S)) -> isList(X:S) 5.04/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.10 isPal(active(X:S)) -> isPal(X:S) 5.04/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.10 isQid(active(X:S)) -> isQid(X:S) 5.04/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.10 mark(a) -> active(a) 5.04/5.10 mark(e) -> active(e) 5.04/5.10 mark(i) -> active(i) 5.04/5.10 mark(nil) -> active(nil) 5.04/5.10 mark(o) -> active(o) 5.04/5.10 mark(tt) -> active(tt) 5.04/5.10 mark(u) -> active(u) 5.04/5.10 ->Strongly Connected Components: 5.04/5.10 There is no strongly connected component 5.04/5.10 5.04/5.10 The problem is finite. 5.04/5.10 5.04/5.10 Problem 1.17: 5.04/5.10 5.04/5.10 Subterm Processor: 5.04/5.10 -> Pairs: 5.04/5.10 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 5.04/5.10 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 5.04/5.10 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 5.04/5.10 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 5.04/5.10 -> Rules: 5.04/5.10 U11(active(X:S)) -> U11(X:S) 5.04/5.10 U11(mark(X:S)) -> U11(X:S) 5.04/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.10 U22(active(X:S)) -> U22(X:S) 5.04/5.10 U22(mark(X:S)) -> U22(X:S) 5.04/5.10 U31(active(X:S)) -> U31(X:S) 5.04/5.10 U31(mark(X:S)) -> U31(X:S) 5.04/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.10 U42(active(X:S)) -> U42(X:S) 5.04/5.10 U42(mark(X:S)) -> U42(X:S) 5.04/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.10 U52(active(X:S)) -> U52(X:S) 5.04/5.10 U52(mark(X:S)) -> U52(X:S) 5.04/5.10 U61(active(X:S)) -> U61(X:S) 5.04/5.10 U61(mark(X:S)) -> U61(X:S) 5.04/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.10 U72(active(X:S)) -> U72(X:S) 5.04/5.10 U72(mark(X:S)) -> U72(X:S) 5.04/5.10 U81(active(X:S)) -> U81(X:S) 5.04/5.10 U81(mark(X:S)) -> U81(X:S) 5.04/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.10 active(U11(tt)) -> mark(tt) 5.04/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.10 active(U22(tt)) -> mark(tt) 5.04/5.10 active(U31(tt)) -> mark(tt) 5.04/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.10 active(U42(tt)) -> mark(tt) 5.04/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.10 active(U52(tt)) -> mark(tt) 5.04/5.10 active(U61(tt)) -> mark(tt) 5.04/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.10 active(U72(tt)) -> mark(tt) 5.04/5.10 active(U81(tt)) -> mark(tt) 5.04/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.10 active(__(nil,X:S)) -> mark(X:S) 5.04/5.10 active(__(X:S,nil)) -> mark(X:S) 5.04/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.04/5.10 active(isList(nil)) -> mark(tt) 5.04/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.04/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.04/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.04/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.04/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.04/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.04/5.10 active(isPal(nil)) -> mark(tt) 5.04/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.04/5.10 active(isQid(a)) -> mark(tt) 5.04/5.10 active(isQid(e)) -> mark(tt) 5.04/5.10 active(isQid(i)) -> mark(tt) 5.04/5.10 active(isQid(o)) -> mark(tt) 5.04/5.10 active(isQid(u)) -> mark(tt) 5.04/5.10 isList(active(X:S)) -> isList(X:S) 5.04/5.10 isList(mark(X:S)) -> isList(X:S) 5.04/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.04/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.04/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.04/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.04/5.10 isPal(active(X:S)) -> isPal(X:S) 5.04/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.04/5.10 isQid(active(X:S)) -> isQid(X:S) 5.04/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.04/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.04/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.04/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.04/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.04/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.04/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.04/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.04/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.04/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.04/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.04/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.04/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.04/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.04/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.04/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.04/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.04/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.04/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.04/5.10 mark(a) -> active(a) 5.04/5.10 mark(e) -> active(e) 5.04/5.10 mark(i) -> active(i) 5.04/5.10 mark(nil) -> active(nil) 5.04/5.10 mark(o) -> active(o) 5.04/5.10 mark(tt) -> active(tt) 5.04/5.10 mark(u) -> active(u) 5.04/5.10 ->Projection: 5.04/5.10 pi(U21#) = 1 5.04/5.10 5.04/5.10 Problem 1.17: 5.04/5.10 5.04/5.10 SCC Processor: 5.04/5.10 -> Pairs: 5.04/5.10 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 5.04/5.10 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 5.04/5.10 -> Rules: 5.04/5.10 U11(active(X:S)) -> U11(X:S) 5.04/5.10 U11(mark(X:S)) -> U11(X:S) 5.04/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.04/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.04/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.04/5.10 U22(active(X:S)) -> U22(X:S) 5.04/5.10 U22(mark(X:S)) -> U22(X:S) 5.04/5.10 U31(active(X:S)) -> U31(X:S) 5.04/5.10 U31(mark(X:S)) -> U31(X:S) 5.04/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.04/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.04/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.04/5.10 U42(active(X:S)) -> U42(X:S) 5.04/5.10 U42(mark(X:S)) -> U42(X:S) 5.04/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.04/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.04/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.04/5.10 U52(active(X:S)) -> U52(X:S) 5.04/5.10 U52(mark(X:S)) -> U52(X:S) 5.04/5.10 U61(active(X:S)) -> U61(X:S) 5.04/5.10 U61(mark(X:S)) -> U61(X:S) 5.04/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.04/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.04/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.04/5.10 U72(active(X:S)) -> U72(X:S) 5.04/5.10 U72(mark(X:S)) -> U72(X:S) 5.04/5.10 U81(active(X:S)) -> U81(X:S) 5.04/5.10 U81(mark(X:S)) -> U81(X:S) 5.04/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.04/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.04/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.04/5.10 active(U11(tt)) -> mark(tt) 5.04/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.04/5.10 active(U22(tt)) -> mark(tt) 5.04/5.10 active(U31(tt)) -> mark(tt) 5.04/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.04/5.10 active(U42(tt)) -> mark(tt) 5.04/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.04/5.10 active(U52(tt)) -> mark(tt) 5.04/5.10 active(U61(tt)) -> mark(tt) 5.04/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.04/5.10 active(U72(tt)) -> mark(tt) 5.04/5.10 active(U81(tt)) -> mark(tt) 5.04/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.04/5.10 active(__(nil,X:S)) -> mark(X:S) 5.04/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Strongly Connected Components: 5.05/5.10 ->->Cycle: 5.05/5.10 ->->-> Pairs: 5.05/5.10 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 5.05/5.10 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 5.05/5.10 ->->-> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 5.05/5.10 Problem 1.17: 5.05/5.10 5.05/5.10 Subterm Processor: 5.05/5.10 -> Pairs: 5.05/5.10 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 5.05/5.10 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Projection: 5.05/5.10 pi(U21#) = 2 5.05/5.10 5.05/5.10 Problem 1.17: 5.05/5.10 5.05/5.10 SCC Processor: 5.05/5.10 -> Pairs: 5.05/5.10 Empty 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Strongly Connected Components: 5.05/5.10 There is no strongly connected component 5.05/5.10 5.05/5.10 The problem is finite. 5.05/5.10 5.05/5.10 Problem 1.18: 5.05/5.10 5.05/5.10 Subterm Processor: 5.05/5.10 -> Pairs: 5.05/5.10 U11#(active(X:S)) -> U11#(X:S) 5.05/5.10 U11#(mark(X:S)) -> U11#(X:S) 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Projection: 5.05/5.10 pi(U11#) = 1 5.05/5.10 5.05/5.10 Problem 1.18: 5.05/5.10 5.05/5.10 SCC Processor: 5.05/5.10 -> Pairs: 5.05/5.10 Empty 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Strongly Connected Components: 5.05/5.10 There is no strongly connected component 5.05/5.10 5.05/5.10 The problem is finite. 5.05/5.10 5.05/5.10 Problem 1.19: 5.05/5.10 5.05/5.10 Reduction Pairs Processor: 5.05/5.10 -> Pairs: 5.05/5.10 ACTIVE(U21(tt,V2:S)) -> MARK(U22(isList(V2:S))) 5.05/5.10 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 5.05/5.10 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.10 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.10 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.10 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.10 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.10 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.10 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.10 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.10 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.10 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.10 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.10 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.10 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.10 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.10 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.10 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.10 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.10 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.10 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.10 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.10 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 -> Usable rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Interpretation type: 5.05/5.10 Linear 5.05/5.10 ->Coefficients: 5.05/5.10 Natural Numbers 5.05/5.10 ->Dimension: 5.05/5.10 1 5.05/5.10 ->Bound: 5.05/5.10 2 5.05/5.10 ->Interpretation: 5.05/5.10 5.05/5.10 [U11](X) = X 5.05/5.10 [U21](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.10 [U22](X) = X + 2 5.05/5.10 [U31](X) = X 5.05/5.10 [U41](X1,X2) = 2.X1 + 2.X2 + 1 5.05/5.10 [U42](X) = X 5.05/5.10 [U51](X1,X2) = X1 + 2.X2 + 2 5.05/5.10 [U52](X) = X + 1 5.05/5.10 [U61](X) = X 5.05/5.10 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.10 [U72](X) = X + 2 5.05/5.10 [U81](X) = X 5.05/5.10 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.10 [active](X) = X 5.05/5.10 [isList](X) = 2.X + 2 5.05/5.10 [isNeList](X) = 2.X + 2 5.05/5.10 [isNePal](X) = 2.X + 2 5.05/5.10 [isPal](X) = 2.X + 2 5.05/5.10 [isQid](X) = 2.X + 2 5.05/5.10 [mark](X) = X 5.05/5.10 [a] = 2 5.05/5.10 [e] = 2 5.05/5.10 [fSNonEmpty] = 0 5.05/5.10 [i] = 2 5.05/5.10 [nil] = 1 5.05/5.10 [o] = 2 5.05/5.10 [tt] = 2 5.05/5.10 [u] = 1 5.05/5.10 [U11#](X) = 0 5.05/5.10 [U21#](X1,X2) = 0 5.05/5.10 [U22#](X) = 0 5.05/5.10 [U31#](X) = 0 5.05/5.10 [U41#](X1,X2) = 0 5.05/5.10 [U42#](X) = 0 5.05/5.10 [U51#](X1,X2) = 0 5.05/5.10 [U52#](X) = 0 5.05/5.10 [U61#](X) = 0 5.05/5.10 [U71#](X1,X2) = 0 5.05/5.10 [U72#](X) = 0 5.05/5.10 [U81#](X) = 0 5.05/5.10 [__#](X1,X2) = 0 5.05/5.10 [ACTIVE](X) = 2.X + 2 5.05/5.10 [ISLIST](X) = 0 5.05/5.10 [ISNELIST](X) = 0 5.05/5.10 [ISNEPAL](X) = 0 5.05/5.10 [ISPAL](X) = 0 5.05/5.10 [ISQID](X) = 0 5.05/5.10 [MARK](X) = 2.X + 2 5.05/5.10 5.05/5.10 Problem 1.19: 5.05/5.10 5.05/5.10 SCC Processor: 5.05/5.10 -> Pairs: 5.05/5.10 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 5.05/5.10 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.10 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.10 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.10 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.10 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.10 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.10 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.10 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.10 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.10 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.10 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.10 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.10 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.10 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.10 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.10 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.10 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.10 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.10 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.10 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.10 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Strongly Connected Components: 5.05/5.10 ->->Cycle: 5.05/5.10 ->->-> Pairs: 5.05/5.10 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 5.05/5.10 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.10 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.10 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.10 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.10 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.10 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.10 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.10 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.10 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.10 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.10 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.10 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.10 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.10 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.10 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.10 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.10 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.10 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.10 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.10 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.10 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.10 ->->-> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 5.05/5.10 Problem 1.19: 5.05/5.10 5.05/5.10 Reduction Pairs Processor: 5.05/5.10 -> Pairs: 5.05/5.10 ACTIVE(U41(tt,V2:S)) -> MARK(U42(isNeList(V2:S))) 5.05/5.10 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.10 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.10 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.10 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.10 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.10 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.10 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.10 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.10 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.10 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.10 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.10 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.10 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.10 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.10 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.10 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.10 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.10 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.10 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.10 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.10 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 -> Usable rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Interpretation type: 5.05/5.10 Linear 5.05/5.10 ->Coefficients: 5.05/5.10 Natural Numbers 5.05/5.10 ->Dimension: 5.05/5.10 1 5.05/5.10 ->Bound: 5.05/5.10 2 5.05/5.10 ->Interpretation: 5.05/5.10 5.05/5.10 [U11](X) = X 5.05/5.10 [U21](X1,X2) = X1 + 2.X2 + 2 5.05/5.10 [U22](X) = X 5.05/5.10 [U31](X) = X + 1 5.05/5.10 [U41](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.10 [U42](X) = X 5.05/5.10 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.10 [U52](X) = X + 2 5.05/5.10 [U61](X) = X + 1 5.05/5.10 [U71](X1,X2) = 2.X1 + 2.X2 5.05/5.10 [U72](X) = X + 2 5.05/5.10 [U81](X) = X 5.05/5.10 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.10 [active](X) = X 5.05/5.10 [isList](X) = 2.X + 2 5.05/5.10 [isNeList](X) = 2.X + 2 5.05/5.10 [isNePal](X) = 2.X + 2 5.05/5.10 [isPal](X) = 2.X + 2 5.05/5.10 [isQid](X) = 2.X + 1 5.05/5.10 [mark](X) = X 5.05/5.10 [a] = 2 5.05/5.10 [e] = 1 5.05/5.10 [fSNonEmpty] = 0 5.05/5.10 [i] = 1 5.05/5.10 [nil] = 0 5.05/5.10 [o] = 2 5.05/5.10 [tt] = 2 5.05/5.10 [u] = 2 5.05/5.10 [U11#](X) = 0 5.05/5.10 [U21#](X1,X2) = 0 5.05/5.10 [U22#](X) = 0 5.05/5.10 [U31#](X) = 0 5.05/5.10 [U41#](X1,X2) = 0 5.05/5.10 [U42#](X) = 0 5.05/5.10 [U51#](X1,X2) = 0 5.05/5.10 [U52#](X) = 0 5.05/5.10 [U61#](X) = 0 5.05/5.10 [U71#](X1,X2) = 0 5.05/5.10 [U72#](X) = 0 5.05/5.10 [U81#](X) = 0 5.05/5.10 [__#](X1,X2) = 0 5.05/5.10 [ACTIVE](X) = 2.X + 2 5.05/5.10 [ISLIST](X) = 0 5.05/5.10 [ISNELIST](X) = 0 5.05/5.10 [ISNEPAL](X) = 0 5.05/5.10 [ISPAL](X) = 0 5.05/5.10 [ISQID](X) = 0 5.05/5.10 [MARK](X) = 2.X + 2 5.05/5.10 5.05/5.10 Problem 1.19: 5.05/5.10 5.05/5.10 SCC Processor: 5.05/5.10 -> Pairs: 5.05/5.10 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.10 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.10 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.10 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.10 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.10 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.10 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.10 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.10 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.10 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.10 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.10 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.10 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.10 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.10 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.10 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.10 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.10 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.10 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.10 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.10 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.10 -> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.10 U61(active(X:S)) -> U61(X:S) 5.05/5.10 U61(mark(X:S)) -> U61(X:S) 5.05/5.10 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.10 U72(active(X:S)) -> U72(X:S) 5.05/5.10 U72(mark(X:S)) -> U72(X:S) 5.05/5.10 U81(active(X:S)) -> U81(X:S) 5.05/5.10 U81(mark(X:S)) -> U81(X:S) 5.05/5.10 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.10 active(U11(tt)) -> mark(tt) 5.05/5.10 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.10 active(U22(tt)) -> mark(tt) 5.05/5.10 active(U31(tt)) -> mark(tt) 5.05/5.10 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.10 active(U42(tt)) -> mark(tt) 5.05/5.10 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.10 active(U52(tt)) -> mark(tt) 5.05/5.10 active(U61(tt)) -> mark(tt) 5.05/5.10 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.10 active(U72(tt)) -> mark(tt) 5.05/5.10 active(U81(tt)) -> mark(tt) 5.05/5.10 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.10 active(__(nil,X:S)) -> mark(X:S) 5.05/5.10 active(__(X:S,nil)) -> mark(X:S) 5.05/5.10 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.10 active(isList(nil)) -> mark(tt) 5.05/5.10 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.10 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.10 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.10 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.10 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.10 active(isPal(nil)) -> mark(tt) 5.05/5.10 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.10 active(isQid(a)) -> mark(tt) 5.05/5.10 active(isQid(e)) -> mark(tt) 5.05/5.10 active(isQid(i)) -> mark(tt) 5.05/5.10 active(isQid(o)) -> mark(tt) 5.05/5.10 active(isQid(u)) -> mark(tt) 5.05/5.10 isList(active(X:S)) -> isList(X:S) 5.05/5.10 isList(mark(X:S)) -> isList(X:S) 5.05/5.10 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.10 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.10 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.10 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.10 isPal(active(X:S)) -> isPal(X:S) 5.05/5.10 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.10 isQid(active(X:S)) -> isQid(X:S) 5.05/5.10 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.10 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.10 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.10 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.10 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.10 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.10 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.10 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.10 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.10 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.10 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.10 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.10 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.10 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.10 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.10 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.10 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.10 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.10 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.10 mark(a) -> active(a) 5.05/5.10 mark(e) -> active(e) 5.05/5.10 mark(i) -> active(i) 5.05/5.10 mark(nil) -> active(nil) 5.05/5.10 mark(o) -> active(o) 5.05/5.10 mark(tt) -> active(tt) 5.05/5.10 mark(u) -> active(u) 5.05/5.10 ->Strongly Connected Components: 5.05/5.10 ->->Cycle: 5.05/5.10 ->->-> Pairs: 5.05/5.10 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.10 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.10 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.10 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.10 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.10 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.10 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.10 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.10 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.10 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.10 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.10 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.10 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.10 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.10 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.10 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.10 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.10 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.10 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.10 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.10 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.10 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.10 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.10 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.10 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.10 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.10 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.10 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.10 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.10 ->->-> Rules: 5.05/5.10 U11(active(X:S)) -> U11(X:S) 5.05/5.10 U11(mark(X:S)) -> U11(X:S) 5.05/5.10 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.10 U22(active(X:S)) -> U22(X:S) 5.05/5.10 U22(mark(X:S)) -> U22(X:S) 5.05/5.10 U31(active(X:S)) -> U31(X:S) 5.05/5.10 U31(mark(X:S)) -> U31(X:S) 5.05/5.10 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.10 U42(active(X:S)) -> U42(X:S) 5.05/5.10 U42(mark(X:S)) -> U42(X:S) 5.05/5.10 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.10 U52(active(X:S)) -> U52(X:S) 5.05/5.10 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 Reduction Pairs Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(U51(tt,V2:S)) -> MARK(U52(isList(V2:S))) 5.05/5.11 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 -> Usable rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 ->Interpretation type: 5.05/5.11 Linear 5.05/5.11 ->Coefficients: 5.05/5.11 Natural Numbers 5.05/5.11 ->Dimension: 5.05/5.11 1 5.05/5.11 ->Bound: 5.05/5.11 2 5.05/5.11 ->Interpretation: 5.05/5.11 5.05/5.11 [U11](X) = X 5.05/5.11 [U21](X1,X2) = 2.X1 + 2.X2 + 1 5.05/5.11 [U22](X) = X + 2 5.05/5.11 [U31](X) = 2.X 5.05/5.11 [U41](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.11 [U42](X) = X + 2 5.05/5.11 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.11 [U52](X) = X 5.05/5.11 [U61](X) = 2.X 5.05/5.11 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.11 [U72](X) = X + 2 5.05/5.11 [U81](X) = X 5.05/5.11 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.11 [active](X) = X 5.05/5.11 [isList](X) = 2.X + 2 5.05/5.11 [isNeList](X) = 2.X + 2 5.05/5.11 [isNePal](X) = 2.X + 2 5.05/5.11 [isPal](X) = 2.X + 2 5.05/5.11 [isQid](X) = X + 1 5.05/5.11 [mark](X) = X 5.05/5.11 [a] = 2 5.05/5.11 [e] = 2 5.05/5.11 [fSNonEmpty] = 0 5.05/5.11 [i] = 2 5.05/5.11 [nil] = 2 5.05/5.11 [o] = 2 5.05/5.11 [tt] = 2 5.05/5.11 [u] = 2 5.05/5.11 [U11#](X) = 0 5.05/5.11 [U21#](X1,X2) = 0 5.05/5.11 [U22#](X) = 0 5.05/5.11 [U31#](X) = 0 5.05/5.11 [U41#](X1,X2) = 0 5.05/5.11 [U42#](X) = 0 5.05/5.11 [U51#](X1,X2) = 0 5.05/5.11 [U52#](X) = 0 5.05/5.11 [U61#](X) = 0 5.05/5.11 [U71#](X1,X2) = 0 5.05/5.11 [U72#](X) = 0 5.05/5.11 [U81#](X) = 0 5.05/5.11 [__#](X1,X2) = 0 5.05/5.11 [ACTIVE](X) = 2.X + 2 5.05/5.11 [ISLIST](X) = 0 5.05/5.11 [ISNELIST](X) = 0 5.05/5.11 [ISNEPAL](X) = 0 5.05/5.11 [ISPAL](X) = 0 5.05/5.11 [ISQID](X) = 0 5.05/5.11 [MARK](X) = 2.X + 2 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 SCC Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 ->Strongly Connected Components: 5.05/5.11 ->->Cycle: 5.05/5.11 ->->-> Pairs: 5.05/5.11 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 ->->-> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 Reduction Pairs Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(U71(tt,P:S)) -> MARK(U72(isPal(P:S))) 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 -> Usable rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 ->Interpretation type: 5.05/5.11 Linear 5.05/5.11 ->Coefficients: 5.05/5.11 Natural Numbers 5.05/5.11 ->Dimension: 5.05/5.11 1 5.05/5.11 ->Bound: 5.05/5.11 2 5.05/5.11 ->Interpretation: 5.05/5.11 5.05/5.11 [U11](X) = X 5.05/5.11 [U21](X1,X2) = X1 + 2.X2 + 2 5.05/5.11 [U22](X) = X + 1 5.05/5.11 [U31](X) = 2.X 5.05/5.11 [U41](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.11 [U42](X) = X + 2 5.05/5.11 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.11 [U52](X) = X + 1 5.05/5.11 [U61](X) = 2.X 5.05/5.11 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.11 [U72](X) = X + 2 5.05/5.11 [U81](X) = X 5.05/5.11 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.11 [active](X) = X 5.05/5.11 [isList](X) = 2.X + 2 5.05/5.11 [isNeList](X) = 2.X + 2 5.05/5.11 [isNePal](X) = 2.X + 2 5.05/5.11 [isPal](X) = 2.X + 2 5.05/5.11 [isQid](X) = X + 1 5.05/5.11 [mark](X) = X 5.05/5.11 [a] = 2 5.05/5.11 [e] = 2 5.05/5.11 [fSNonEmpty] = 0 5.05/5.11 [i] = 2 5.05/5.11 [nil] = 2 5.05/5.11 [o] = 2 5.05/5.11 [tt] = 2 5.05/5.11 [u] = 2 5.05/5.11 [U11#](X) = 0 5.05/5.11 [U21#](X1,X2) = 0 5.05/5.11 [U22#](X) = 0 5.05/5.11 [U31#](X) = 0 5.05/5.11 [U41#](X1,X2) = 0 5.05/5.11 [U42#](X) = 0 5.05/5.11 [U51#](X1,X2) = 0 5.05/5.11 [U52#](X) = 0 5.05/5.11 [U61#](X) = 0 5.05/5.11 [U71#](X1,X2) = 0 5.05/5.11 [U72#](X) = 0 5.05/5.11 [U81#](X) = 0 5.05/5.11 [__#](X1,X2) = 0 5.05/5.11 [ACTIVE](X) = 2.X + 2 5.05/5.11 [ISLIST](X) = 0 5.05/5.11 [ISNELIST](X) = 0 5.05/5.11 [ISNEPAL](X) = 0 5.05/5.11 [ISPAL](X) = 0 5.05/5.11 [ISQID](X) = 0 5.05/5.11 [MARK](X) = 2.X + 2 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 SCC Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 ->Strongly Connected Components: 5.05/5.11 ->->Cycle: 5.05/5.11 ->->-> Pairs: 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 ->->-> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 Reduction Pairs Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S))) 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 -> Usable rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 ->Interpretation type: 5.05/5.11 Linear 5.05/5.11 ->Coefficients: 5.05/5.11 Natural Numbers 5.05/5.11 ->Dimension: 5.05/5.11 1 5.05/5.11 ->Bound: 5.05/5.11 2 5.05/5.11 ->Interpretation: 5.05/5.11 5.05/5.11 [U11](X) = X 5.05/5.11 [U21](X1,X2) = 2.X1 + X2 5.05/5.11 [U22](X) = X + 2 5.05/5.11 [U31](X) = X 5.05/5.11 [U41](X1,X2) = X1 + X2 + 2 5.05/5.11 [U42](X) = X + 2 5.05/5.11 [U51](X1,X2) = 2.X1 + X2 5.05/5.11 [U52](X) = X + 2 5.05/5.11 [U61](X) = X 5.05/5.11 [U71](X1,X2) = 2.X1 + 2.X2 5.05/5.11 [U72](X) = X + 1 5.05/5.11 [U81](X) = X 5.05/5.11 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.11 [active](X) = X 5.05/5.11 [isList](X) = X + 2 5.05/5.11 [isNeList](X) = X + 2 5.05/5.11 [isNePal](X) = 2.X + 2 5.05/5.11 [isPal](X) = 2.X + 2 5.05/5.11 [isQid](X) = X + 2 5.05/5.11 [mark](X) = X 5.05/5.11 [a] = 0 5.05/5.11 [e] = 2 5.05/5.11 [fSNonEmpty] = 0 5.05/5.11 [i] = 2 5.05/5.11 [nil] = 2 5.05/5.11 [o] = 2 5.05/5.11 [tt] = 2 5.05/5.11 [u] = 2 5.05/5.11 [U11#](X) = 0 5.05/5.11 [U21#](X1,X2) = 0 5.05/5.11 [U22#](X) = 0 5.05/5.11 [U31#](X) = 0 5.05/5.11 [U41#](X1,X2) = 0 5.05/5.11 [U42#](X) = 0 5.05/5.11 [U51#](X1,X2) = 0 5.05/5.11 [U52#](X) = 0 5.05/5.11 [U61#](X) = 0 5.05/5.11 [U71#](X1,X2) = 0 5.05/5.11 [U72#](X) = 0 5.05/5.11 [U81#](X) = 0 5.05/5.11 [__#](X1,X2) = 0 5.05/5.11 [ACTIVE](X) = 2.X + 2 5.05/5.11 [ISLIST](X) = 0 5.05/5.11 [ISNELIST](X) = 0 5.05/5.11 [ISNEPAL](X) = 0 5.05/5.11 [ISPAL](X) = 0 5.05/5.11 [ISQID](X) = 0 5.05/5.11 [MARK](X) = 2.X + 2 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 SCC Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 ->Strongly Connected Components: 5.05/5.11 ->->Cycle: 5.05/5.11 ->->-> Pairs: 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 ->->-> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 5.05/5.11 Problem 1.19: 5.05/5.11 5.05/5.11 Reduction Pairs Processor: 5.05/5.11 -> Pairs: 5.05/5.11 ACTIVE(__(nil,X:S)) -> MARK(X:S) 5.05/5.11 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.11 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.11 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.11 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.11 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.11 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.11 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.11 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.11 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.11 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.11 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.11 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.11 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.11 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.11 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.11 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.11 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.11 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.11 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.11 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.11 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.11 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.11 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.11 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.11 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.11 -> Rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.11 U31(mark(X:S)) -> U31(X:S) 5.05/5.11 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.11 U42(active(X:S)) -> U42(X:S) 5.05/5.11 U42(mark(X:S)) -> U42(X:S) 5.05/5.11 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.11 U52(active(X:S)) -> U52(X:S) 5.05/5.11 U52(mark(X:S)) -> U52(X:S) 5.05/5.11 U61(active(X:S)) -> U61(X:S) 5.05/5.11 U61(mark(X:S)) -> U61(X:S) 5.05/5.11 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.11 U72(active(X:S)) -> U72(X:S) 5.05/5.11 U72(mark(X:S)) -> U72(X:S) 5.05/5.11 U81(active(X:S)) -> U81(X:S) 5.05/5.11 U81(mark(X:S)) -> U81(X:S) 5.05/5.11 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.11 active(U11(tt)) -> mark(tt) 5.05/5.11 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.11 active(U22(tt)) -> mark(tt) 5.05/5.11 active(U31(tt)) -> mark(tt) 5.05/5.11 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.11 active(U42(tt)) -> mark(tt) 5.05/5.11 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.11 active(U52(tt)) -> mark(tt) 5.05/5.11 active(U61(tt)) -> mark(tt) 5.05/5.11 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.11 active(U72(tt)) -> mark(tt) 5.05/5.11 active(U81(tt)) -> mark(tt) 5.05/5.11 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.11 active(__(nil,X:S)) -> mark(X:S) 5.05/5.11 active(__(X:S,nil)) -> mark(X:S) 5.05/5.11 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.11 active(isList(nil)) -> mark(tt) 5.05/5.11 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.11 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.11 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.11 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.11 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.11 active(isPal(nil)) -> mark(tt) 5.05/5.11 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.11 active(isQid(a)) -> mark(tt) 5.05/5.11 active(isQid(e)) -> mark(tt) 5.05/5.11 active(isQid(i)) -> mark(tt) 5.05/5.11 active(isQid(o)) -> mark(tt) 5.05/5.11 active(isQid(u)) -> mark(tt) 5.05/5.11 isList(active(X:S)) -> isList(X:S) 5.05/5.11 isList(mark(X:S)) -> isList(X:S) 5.05/5.11 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.11 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.11 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.11 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.11 isPal(active(X:S)) -> isPal(X:S) 5.05/5.11 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.11 isQid(active(X:S)) -> isQid(X:S) 5.05/5.11 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.11 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.11 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.11 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.11 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.11 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.11 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.11 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.11 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.11 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.11 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.11 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.11 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.11 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.11 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.11 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.11 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.11 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.11 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.11 mark(a) -> active(a) 5.05/5.11 mark(e) -> active(e) 5.05/5.11 mark(i) -> active(i) 5.05/5.11 mark(nil) -> active(nil) 5.05/5.11 mark(o) -> active(o) 5.05/5.11 mark(tt) -> active(tt) 5.05/5.11 mark(u) -> active(u) 5.05/5.11 -> Usable rules: 5.05/5.11 U11(active(X:S)) -> U11(X:S) 5.05/5.11 U11(mark(X:S)) -> U11(X:S) 5.05/5.11 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.11 U22(active(X:S)) -> U22(X:S) 5.05/5.11 U22(mark(X:S)) -> U22(X:S) 5.05/5.11 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 ->Interpretation type: 5.05/5.12 Linear 5.05/5.12 ->Coefficients: 5.05/5.12 Natural Numbers 5.05/5.12 ->Dimension: 5.05/5.12 1 5.05/5.12 ->Bound: 5.05/5.12 2 5.05/5.12 ->Interpretation: 5.05/5.12 5.05/5.12 [U11](X) = X 5.05/5.12 [U21](X1,X2) = X1 + 2.X2 + 2 5.05/5.12 [U22](X) = X + 2 5.05/5.12 [U31](X) = X + 1 5.05/5.12 [U41](X1,X2) = 2.X1 + 2.X2 + 1 5.05/5.12 [U42](X) = X + 2 5.05/5.12 [U51](X1,X2) = X1 + 2.X2 + 2 5.05/5.12 [U52](X) = X 5.05/5.12 [U61](X) = X + 2 5.05/5.12 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.12 [U72](X) = X + 1 5.05/5.12 [U81](X) = X 5.05/5.12 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.12 [active](X) = X 5.05/5.12 [isList](X) = 2.X + 2 5.05/5.12 [isNeList](X) = 2.X + 2 5.05/5.12 [isNePal](X) = 2.X + 2 5.05/5.12 [isPal](X) = 2.X + 2 5.05/5.12 [isQid](X) = 2.X 5.05/5.12 [mark](X) = X 5.05/5.12 [a] = 2 5.05/5.12 [e] = 1 5.05/5.12 [fSNonEmpty] = 0 5.05/5.12 [i] = 2 5.05/5.12 [nil] = 2 5.05/5.12 [o] = 2 5.05/5.12 [tt] = 2 5.05/5.12 [u] = 2 5.05/5.12 [U11#](X) = 0 5.05/5.12 [U21#](X1,X2) = 0 5.05/5.12 [U22#](X) = 0 5.05/5.12 [U31#](X) = 0 5.05/5.12 [U41#](X1,X2) = 0 5.05/5.12 [U42#](X) = 0 5.05/5.12 [U51#](X1,X2) = 0 5.05/5.12 [U52#](X) = 0 5.05/5.12 [U61#](X) = 0 5.05/5.12 [U71#](X1,X2) = 0 5.05/5.12 [U72#](X) = 0 5.05/5.12 [U81#](X) = 0 5.05/5.12 [__#](X1,X2) = 0 5.05/5.12 [ACTIVE](X) = 2.X + 2 5.05/5.12 [ISLIST](X) = 0 5.05/5.12 [ISNELIST](X) = 0 5.05/5.12 [ISNEPAL](X) = 0 5.05/5.12 [ISPAL](X) = 0 5.05/5.12 [ISQID](X) = 0 5.05/5.12 [MARK](X) = 2.X + 2 5.05/5.12 5.05/5.12 Problem 1.19: 5.05/5.12 5.05/5.12 SCC Processor: 5.05/5.12 -> Pairs: 5.05/5.12 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.12 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.12 -> Rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.05/5.12 U11(mark(X:S)) -> U11(X:S) 5.05/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U22(active(X:S)) -> U22(X:S) 5.05/5.12 U22(mark(X:S)) -> U22(X:S) 5.05/5.12 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 ->Strongly Connected Components: 5.05/5.12 ->->Cycle: 5.05/5.12 ->->-> Pairs: 5.05/5.12 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.12 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.12 ->->-> Rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.05/5.12 U11(mark(X:S)) -> U11(X:S) 5.05/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U22(active(X:S)) -> U22(X:S) 5.05/5.12 U22(mark(X:S)) -> U22(X:S) 5.05/5.12 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 5.05/5.12 Problem 1.19: 5.05/5.12 5.05/5.12 Reduction Pairs Processor: 5.05/5.12 -> Pairs: 5.05/5.12 ACTIVE(__(X:S,nil)) -> MARK(X:S) 5.05/5.12 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.12 -> Rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.05/5.12 U11(mark(X:S)) -> U11(X:S) 5.05/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U22(active(X:S)) -> U22(X:S) 5.05/5.12 U22(mark(X:S)) -> U22(X:S) 5.05/5.12 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 -> Usable rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.05/5.12 U11(mark(X:S)) -> U11(X:S) 5.05/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U22(active(X:S)) -> U22(X:S) 5.05/5.12 U22(mark(X:S)) -> U22(X:S) 5.05/5.12 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 ->Interpretation type: 5.05/5.12 Linear 5.05/5.12 ->Coefficients: 5.05/5.12 Natural Numbers 5.05/5.12 ->Dimension: 5.05/5.12 1 5.05/5.12 ->Bound: 5.05/5.12 2 5.05/5.12 ->Interpretation: 5.05/5.12 5.05/5.12 [U11](X) = X 5.05/5.12 [U21](X1,X2) = X1 5.05/5.12 [U22](X) = X 5.05/5.12 [U31](X) = X 5.05/5.12 [U41](X1,X2) = X1 5.05/5.12 [U42](X) = X 5.05/5.12 [U51](X1,X2) = X1 5.05/5.12 [U52](X) = X 5.05/5.12 [U61](X) = X 5.05/5.12 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.05/5.12 [U72](X) = 2.X 5.05/5.12 [U81](X) = X 5.05/5.12 [__](X1,X2) = 2.X1 + X2 + 2 5.05/5.12 [active](X) = X 5.05/5.12 [isList](X) = 2 5.05/5.12 [isNeList](X) = 2 5.05/5.12 [isNePal](X) = X + 2 5.05/5.12 [isPal](X) = X + 2 5.05/5.12 [isQid](X) = 2 5.05/5.12 [mark](X) = X 5.05/5.12 [a] = 2 5.05/5.12 [e] = 2 5.05/5.12 [fSNonEmpty] = 0 5.05/5.12 [i] = 1 5.05/5.12 [nil] = 2 5.05/5.12 [o] = 0 5.05/5.12 [tt] = 2 5.05/5.12 [u] = 2 5.05/5.12 [U11#](X) = 0 5.05/5.12 [U21#](X1,X2) = 0 5.05/5.12 [U22#](X) = 0 5.05/5.12 [U31#](X) = 0 5.05/5.12 [U41#](X1,X2) = 0 5.05/5.12 [U42#](X) = 0 5.05/5.12 [U51#](X1,X2) = 0 5.05/5.12 [U52#](X) = 0 5.05/5.12 [U61#](X) = 0 5.05/5.12 [U71#](X1,X2) = 0 5.05/5.12 [U72#](X) = 0 5.05/5.12 [U81#](X) = 0 5.05/5.12 [__#](X1,X2) = 0 5.05/5.12 [ACTIVE](X) = 2.X + 1 5.05/5.12 [ISLIST](X) = 0 5.05/5.12 [ISNELIST](X) = 0 5.05/5.12 [ISNEPAL](X) = 0 5.05/5.12 [ISPAL](X) = 0 5.05/5.12 [ISQID](X) = 0 5.05/5.12 [MARK](X) = 2.X + 1 5.05/5.12 5.05/5.12 Problem 1.19: 5.05/5.12 5.05/5.12 SCC Processor: 5.05/5.12 -> Pairs: 5.05/5.12 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.12 -> Rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.05/5.12 U11(mark(X:S)) -> U11(X:S) 5.05/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U22(active(X:S)) -> U22(X:S) 5.05/5.12 U22(mark(X:S)) -> U22(X:S) 5.05/5.12 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 ->Strongly Connected Components: 5.05/5.12 ->->Cycle: 5.05/5.12 ->->-> Pairs: 5.05/5.12 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.12 ->->-> Rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.05/5.12 U11(mark(X:S)) -> U11(X:S) 5.05/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.05/5.12 U22(active(X:S)) -> U22(X:S) 5.05/5.12 U22(mark(X:S)) -> U22(X:S) 5.05/5.12 U31(active(X:S)) -> U31(X:S) 5.05/5.12 U31(mark(X:S)) -> U31(X:S) 5.05/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.05/5.12 U42(active(X:S)) -> U42(X:S) 5.05/5.12 U42(mark(X:S)) -> U42(X:S) 5.05/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.05/5.12 U52(active(X:S)) -> U52(X:S) 5.05/5.12 U52(mark(X:S)) -> U52(X:S) 5.05/5.12 U61(active(X:S)) -> U61(X:S) 5.05/5.12 U61(mark(X:S)) -> U61(X:S) 5.05/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.05/5.12 U72(active(X:S)) -> U72(X:S) 5.05/5.12 U72(mark(X:S)) -> U72(X:S) 5.05/5.12 U81(active(X:S)) -> U81(X:S) 5.05/5.12 U81(mark(X:S)) -> U81(X:S) 5.05/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.05/5.12 active(U11(tt)) -> mark(tt) 5.05/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.05/5.12 active(U22(tt)) -> mark(tt) 5.05/5.12 active(U31(tt)) -> mark(tt) 5.05/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.05/5.12 active(U42(tt)) -> mark(tt) 5.05/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.05/5.12 active(U52(tt)) -> mark(tt) 5.05/5.12 active(U61(tt)) -> mark(tt) 5.05/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.05/5.12 active(U72(tt)) -> mark(tt) 5.05/5.12 active(U81(tt)) -> mark(tt) 5.05/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.05/5.12 active(__(nil,X:S)) -> mark(X:S) 5.05/5.12 active(__(X:S,nil)) -> mark(X:S) 5.05/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.05/5.12 active(isList(nil)) -> mark(tt) 5.05/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.05/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.05/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.05/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.05/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.05/5.12 active(isPal(nil)) -> mark(tt) 5.05/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.05/5.12 active(isQid(a)) -> mark(tt) 5.05/5.12 active(isQid(e)) -> mark(tt) 5.05/5.12 active(isQid(i)) -> mark(tt) 5.05/5.12 active(isQid(o)) -> mark(tt) 5.05/5.12 active(isQid(u)) -> mark(tt) 5.05/5.12 isList(active(X:S)) -> isList(X:S) 5.05/5.12 isList(mark(X:S)) -> isList(X:S) 5.05/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.05/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.05/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.05/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.05/5.12 isPal(active(X:S)) -> isPal(X:S) 5.05/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.05/5.12 isQid(active(X:S)) -> isQid(X:S) 5.05/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.05/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.05/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.05/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.05/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.05/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.05/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.05/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.05/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.05/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.05/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.05/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.05/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.05/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.05/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.05/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.05/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.05/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.05/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.05/5.12 mark(a) -> active(a) 5.05/5.12 mark(e) -> active(e) 5.05/5.12 mark(i) -> active(i) 5.05/5.12 mark(nil) -> active(nil) 5.05/5.12 mark(o) -> active(o) 5.05/5.12 mark(tt) -> active(tt) 5.05/5.12 mark(u) -> active(u) 5.05/5.12 5.05/5.12 Problem 1.19: 5.05/5.12 5.05/5.12 Reduction Pairs Processor: 5.05/5.12 -> Pairs: 5.05/5.12 ACTIVE(isList(__(V1:S,V2:S))) -> MARK(U21(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.05/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.05/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.05/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.05/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.05/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.05/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.05/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.05/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.05/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.05/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.05/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.05/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.05/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.05/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.05/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.05/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.05/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.05/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.05/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.05/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.05/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.05/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.05/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.05/5.12 -> Rules: 5.05/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.12 U22(mark(X:S)) -> U22(X:S) 5.07/5.12 U31(active(X:S)) -> U31(X:S) 5.07/5.12 U31(mark(X:S)) -> U31(X:S) 5.07/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U42(active(X:S)) -> U42(X:S) 5.07/5.12 U42(mark(X:S)) -> U42(X:S) 5.07/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U52(active(X:S)) -> U52(X:S) 5.07/5.12 U52(mark(X:S)) -> U52(X:S) 5.07/5.12 U61(active(X:S)) -> U61(X:S) 5.07/5.12 U61(mark(X:S)) -> U61(X:S) 5.07/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U72(active(X:S)) -> U72(X:S) 5.07/5.12 U72(mark(X:S)) -> U72(X:S) 5.07/5.12 U81(active(X:S)) -> U81(X:S) 5.07/5.12 U81(mark(X:S)) -> U81(X:S) 5.07/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 active(U11(tt)) -> mark(tt) 5.07/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.12 active(U22(tt)) -> mark(tt) 5.07/5.12 active(U31(tt)) -> mark(tt) 5.07/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.12 active(U42(tt)) -> mark(tt) 5.07/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.12 active(U52(tt)) -> mark(tt) 5.07/5.12 active(U61(tt)) -> mark(tt) 5.07/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.12 active(U72(tt)) -> mark(tt) 5.07/5.12 active(U81(tt)) -> mark(tt) 5.07/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.12 active(__(nil,X:S)) -> mark(X:S) 5.07/5.12 active(__(X:S,nil)) -> mark(X:S) 5.07/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.12 active(isList(nil)) -> mark(tt) 5.07/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.12 active(isPal(nil)) -> mark(tt) 5.07/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.12 active(isQid(a)) -> mark(tt) 5.07/5.12 active(isQid(e)) -> mark(tt) 5.07/5.12 active(isQid(i)) -> mark(tt) 5.07/5.12 active(isQid(o)) -> mark(tt) 5.07/5.12 active(isQid(u)) -> mark(tt) 5.07/5.12 isList(active(X:S)) -> isList(X:S) 5.07/5.12 isList(mark(X:S)) -> isList(X:S) 5.07/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.12 isPal(active(X:S)) -> isPal(X:S) 5.07/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.12 isQid(active(X:S)) -> isQid(X:S) 5.07/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.12 mark(a) -> active(a) 5.07/5.12 mark(e) -> active(e) 5.07/5.12 mark(i) -> active(i) 5.07/5.12 mark(nil) -> active(nil) 5.07/5.12 mark(o) -> active(o) 5.07/5.12 mark(tt) -> active(tt) 5.07/5.12 mark(u) -> active(u) 5.07/5.12 -> Usable rules: 5.07/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.12 U22(mark(X:S)) -> U22(X:S) 5.07/5.12 U31(active(X:S)) -> U31(X:S) 5.07/5.12 U31(mark(X:S)) -> U31(X:S) 5.07/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U42(active(X:S)) -> U42(X:S) 5.07/5.12 U42(mark(X:S)) -> U42(X:S) 5.07/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U52(active(X:S)) -> U52(X:S) 5.07/5.12 U52(mark(X:S)) -> U52(X:S) 5.07/5.12 U61(active(X:S)) -> U61(X:S) 5.07/5.12 U61(mark(X:S)) -> U61(X:S) 5.07/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U72(active(X:S)) -> U72(X:S) 5.07/5.12 U72(mark(X:S)) -> U72(X:S) 5.07/5.12 U81(active(X:S)) -> U81(X:S) 5.07/5.12 U81(mark(X:S)) -> U81(X:S) 5.07/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 active(U11(tt)) -> mark(tt) 5.07/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.12 active(U22(tt)) -> mark(tt) 5.07/5.12 active(U31(tt)) -> mark(tt) 5.07/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.12 active(U42(tt)) -> mark(tt) 5.07/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.12 active(U52(tt)) -> mark(tt) 5.07/5.12 active(U61(tt)) -> mark(tt) 5.07/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.12 active(U72(tt)) -> mark(tt) 5.07/5.12 active(U81(tt)) -> mark(tt) 5.07/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.12 active(__(nil,X:S)) -> mark(X:S) 5.07/5.12 active(__(X:S,nil)) -> mark(X:S) 5.07/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.12 active(isList(nil)) -> mark(tt) 5.07/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.12 active(isPal(nil)) -> mark(tt) 5.07/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.12 active(isQid(a)) -> mark(tt) 5.07/5.12 active(isQid(e)) -> mark(tt) 5.07/5.12 active(isQid(i)) -> mark(tt) 5.07/5.12 active(isQid(o)) -> mark(tt) 5.07/5.12 active(isQid(u)) -> mark(tt) 5.07/5.12 isList(active(X:S)) -> isList(X:S) 5.07/5.12 isList(mark(X:S)) -> isList(X:S) 5.07/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.12 isPal(active(X:S)) -> isPal(X:S) 5.07/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.12 isQid(active(X:S)) -> isQid(X:S) 5.07/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.12 mark(a) -> active(a) 5.07/5.12 mark(e) -> active(e) 5.07/5.12 mark(i) -> active(i) 5.07/5.12 mark(nil) -> active(nil) 5.07/5.12 mark(o) -> active(o) 5.07/5.12 mark(tt) -> active(tt) 5.07/5.12 mark(u) -> active(u) 5.07/5.12 ->Interpretation type: 5.07/5.12 Linear 5.07/5.12 ->Coefficients: 5.07/5.12 Natural Numbers 5.07/5.12 ->Dimension: 5.07/5.12 1 5.07/5.12 ->Bound: 5.07/5.12 2 5.07/5.12 ->Interpretation: 5.07/5.12 5.07/5.12 [U11](X) = X + 2 5.07/5.12 [U21](X1,X2) = X1 + 2.X2 + 2 5.07/5.12 [U22](X) = X + 2 5.07/5.12 [U31](X) = 2.X 5.07/5.12 [U41](X1,X2) = X1 + 2.X2 + 2 5.07/5.12 [U42](X) = X + 2 5.07/5.12 [U51](X1,X2) = 2.X1 + 2.X2 5.07/5.12 [U52](X) = X + 2 5.07/5.12 [U61](X) = 2.X 5.07/5.12 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.12 [U72](X) = X + 2 5.07/5.12 [U81](X) = X + 2 5.07/5.12 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.12 [active](X) = X 5.07/5.12 [isList](X) = 2.X + 2 5.07/5.12 [isNeList](X) = 2.X 5.07/5.12 [isNePal](X) = 2.X 5.07/5.12 [isPal](X) = 2.X + 2 5.07/5.12 [isQid](X) = X 5.07/5.12 [mark](X) = X 5.07/5.12 [a] = 2 5.07/5.12 [e] = 2 5.07/5.12 [fSNonEmpty] = 0 5.07/5.12 [i] = 2 5.07/5.12 [nil] = 1 5.07/5.12 [o] = 2 5.07/5.12 [tt] = 2 5.07/5.12 [u] = 2 5.07/5.12 [U11#](X) = 0 5.07/5.12 [U21#](X1,X2) = 0 5.07/5.12 [U22#](X) = 0 5.07/5.12 [U31#](X) = 0 5.07/5.12 [U41#](X1,X2) = 0 5.07/5.12 [U42#](X) = 0 5.07/5.12 [U51#](X1,X2) = 0 5.07/5.12 [U52#](X) = 0 5.07/5.12 [U61#](X) = 0 5.07/5.12 [U71#](X1,X2) = 0 5.07/5.12 [U72#](X) = 0 5.07/5.12 [U81#](X) = 0 5.07/5.12 [__#](X1,X2) = 0 5.07/5.12 [ACTIVE](X) = X + 2 5.07/5.12 [ISLIST](X) = 0 5.07/5.12 [ISNELIST](X) = 0 5.07/5.12 [ISNEPAL](X) = 0 5.07/5.12 [ISPAL](X) = 0 5.07/5.12 [ISQID](X) = 0 5.07/5.12 [MARK](X) = X + 2 5.07/5.12 5.07/5.12 Problem 1.19: 5.07/5.12 5.07/5.12 SCC Processor: 5.07/5.12 -> Pairs: 5.07/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.07/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.12 -> Rules: 5.07/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.12 U22(mark(X:S)) -> U22(X:S) 5.07/5.12 U31(active(X:S)) -> U31(X:S) 5.07/5.12 U31(mark(X:S)) -> U31(X:S) 5.07/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U42(active(X:S)) -> U42(X:S) 5.07/5.12 U42(mark(X:S)) -> U42(X:S) 5.07/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U52(active(X:S)) -> U52(X:S) 5.07/5.12 U52(mark(X:S)) -> U52(X:S) 5.07/5.12 U61(active(X:S)) -> U61(X:S) 5.07/5.12 U61(mark(X:S)) -> U61(X:S) 5.07/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U72(active(X:S)) -> U72(X:S) 5.07/5.12 U72(mark(X:S)) -> U72(X:S) 5.07/5.12 U81(active(X:S)) -> U81(X:S) 5.07/5.12 U81(mark(X:S)) -> U81(X:S) 5.07/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 active(U11(tt)) -> mark(tt) 5.07/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.12 active(U22(tt)) -> mark(tt) 5.07/5.12 active(U31(tt)) -> mark(tt) 5.07/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.12 active(U42(tt)) -> mark(tt) 5.07/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.12 active(U52(tt)) -> mark(tt) 5.07/5.12 active(U61(tt)) -> mark(tt) 5.07/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.12 active(U72(tt)) -> mark(tt) 5.07/5.12 active(U81(tt)) -> mark(tt) 5.07/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.12 active(__(nil,X:S)) -> mark(X:S) 5.07/5.12 active(__(X:S,nil)) -> mark(X:S) 5.07/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.12 active(isList(nil)) -> mark(tt) 5.07/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.12 active(isPal(nil)) -> mark(tt) 5.07/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.12 active(isQid(a)) -> mark(tt) 5.07/5.12 active(isQid(e)) -> mark(tt) 5.07/5.12 active(isQid(i)) -> mark(tt) 5.07/5.12 active(isQid(o)) -> mark(tt) 5.07/5.12 active(isQid(u)) -> mark(tt) 5.07/5.12 isList(active(X:S)) -> isList(X:S) 5.07/5.12 isList(mark(X:S)) -> isList(X:S) 5.07/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.12 isPal(active(X:S)) -> isPal(X:S) 5.07/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.12 isQid(active(X:S)) -> isQid(X:S) 5.07/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.12 mark(a) -> active(a) 5.07/5.12 mark(e) -> active(e) 5.07/5.12 mark(i) -> active(i) 5.07/5.12 mark(nil) -> active(nil) 5.07/5.12 mark(o) -> active(o) 5.07/5.12 mark(tt) -> active(tt) 5.07/5.12 mark(u) -> active(u) 5.07/5.12 ->Strongly Connected Components: 5.07/5.12 ->->Cycle: 5.07/5.12 ->->-> Pairs: 5.07/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.07/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.12 ->->-> Rules: 5.07/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.12 U22(mark(X:S)) -> U22(X:S) 5.07/5.12 U31(active(X:S)) -> U31(X:S) 5.07/5.12 U31(mark(X:S)) -> U31(X:S) 5.07/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U42(active(X:S)) -> U42(X:S) 5.07/5.12 U42(mark(X:S)) -> U42(X:S) 5.07/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U52(active(X:S)) -> U52(X:S) 5.07/5.12 U52(mark(X:S)) -> U52(X:S) 5.07/5.12 U61(active(X:S)) -> U61(X:S) 5.07/5.12 U61(mark(X:S)) -> U61(X:S) 5.07/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U72(active(X:S)) -> U72(X:S) 5.07/5.12 U72(mark(X:S)) -> U72(X:S) 5.07/5.12 U81(active(X:S)) -> U81(X:S) 5.07/5.12 U81(mark(X:S)) -> U81(X:S) 5.07/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 active(U11(tt)) -> mark(tt) 5.07/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.12 active(U22(tt)) -> mark(tt) 5.07/5.12 active(U31(tt)) -> mark(tt) 5.07/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.12 active(U42(tt)) -> mark(tt) 5.07/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.12 active(U52(tt)) -> mark(tt) 5.07/5.12 active(U61(tt)) -> mark(tt) 5.07/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.12 active(U72(tt)) -> mark(tt) 5.07/5.12 active(U81(tt)) -> mark(tt) 5.07/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.12 active(__(nil,X:S)) -> mark(X:S) 5.07/5.12 active(__(X:S,nil)) -> mark(X:S) 5.07/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.12 active(isList(nil)) -> mark(tt) 5.07/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.12 active(isPal(nil)) -> mark(tt) 5.07/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.12 active(isQid(a)) -> mark(tt) 5.07/5.12 active(isQid(e)) -> mark(tt) 5.07/5.12 active(isQid(i)) -> mark(tt) 5.07/5.12 active(isQid(o)) -> mark(tt) 5.07/5.12 active(isQid(u)) -> mark(tt) 5.07/5.12 isList(active(X:S)) -> isList(X:S) 5.07/5.12 isList(mark(X:S)) -> isList(X:S) 5.07/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.12 isPal(active(X:S)) -> isPal(X:S) 5.07/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.12 isQid(active(X:S)) -> isQid(X:S) 5.07/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.12 mark(a) -> active(a) 5.07/5.12 mark(e) -> active(e) 5.07/5.12 mark(i) -> active(i) 5.07/5.12 mark(nil) -> active(nil) 5.07/5.12 mark(o) -> active(o) 5.07/5.12 mark(tt) -> active(tt) 5.07/5.12 mark(u) -> active(u) 5.07/5.12 5.07/5.12 Problem 1.19: 5.07/5.12 5.07/5.12 Reduction Pairs Processor: 5.07/5.12 -> Pairs: 5.07/5.12 ACTIVE(isList(V:S)) -> MARK(U11(isNeList(V:S))) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.07/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.12 -> Rules: 5.07/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.12 U22(mark(X:S)) -> U22(X:S) 5.07/5.12 U31(active(X:S)) -> U31(X:S) 5.07/5.12 U31(mark(X:S)) -> U31(X:S) 5.07/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U42(active(X:S)) -> U42(X:S) 5.07/5.12 U42(mark(X:S)) -> U42(X:S) 5.07/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U52(active(X:S)) -> U52(X:S) 5.07/5.12 U52(mark(X:S)) -> U52(X:S) 5.07/5.12 U61(active(X:S)) -> U61(X:S) 5.07/5.12 U61(mark(X:S)) -> U61(X:S) 5.07/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U72(active(X:S)) -> U72(X:S) 5.07/5.12 U72(mark(X:S)) -> U72(X:S) 5.07/5.12 U81(active(X:S)) -> U81(X:S) 5.07/5.12 U81(mark(X:S)) -> U81(X:S) 5.07/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 active(U11(tt)) -> mark(tt) 5.07/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.12 active(U22(tt)) -> mark(tt) 5.07/5.12 active(U31(tt)) -> mark(tt) 5.07/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.12 active(U42(tt)) -> mark(tt) 5.07/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.12 active(U52(tt)) -> mark(tt) 5.07/5.12 active(U61(tt)) -> mark(tt) 5.07/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.12 active(U72(tt)) -> mark(tt) 5.07/5.12 active(U81(tt)) -> mark(tt) 5.07/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.12 active(__(nil,X:S)) -> mark(X:S) 5.07/5.12 active(__(X:S,nil)) -> mark(X:S) 5.07/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.12 active(isList(nil)) -> mark(tt) 5.07/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.12 active(isPal(nil)) -> mark(tt) 5.07/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.12 active(isQid(a)) -> mark(tt) 5.07/5.12 active(isQid(e)) -> mark(tt) 5.07/5.12 active(isQid(i)) -> mark(tt) 5.07/5.12 active(isQid(o)) -> mark(tt) 5.07/5.12 active(isQid(u)) -> mark(tt) 5.07/5.12 isList(active(X:S)) -> isList(X:S) 5.07/5.12 isList(mark(X:S)) -> isList(X:S) 5.07/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.12 isPal(active(X:S)) -> isPal(X:S) 5.07/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.12 isQid(active(X:S)) -> isQid(X:S) 5.07/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.12 mark(a) -> active(a) 5.07/5.12 mark(e) -> active(e) 5.07/5.12 mark(i) -> active(i) 5.07/5.12 mark(nil) -> active(nil) 5.07/5.12 mark(o) -> active(o) 5.07/5.12 mark(tt) -> active(tt) 5.07/5.12 mark(u) -> active(u) 5.07/5.12 -> Usable rules: 5.07/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.12 U22(mark(X:S)) -> U22(X:S) 5.07/5.12 U31(active(X:S)) -> U31(X:S) 5.07/5.12 U31(mark(X:S)) -> U31(X:S) 5.07/5.12 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.12 U42(active(X:S)) -> U42(X:S) 5.07/5.12 U42(mark(X:S)) -> U42(X:S) 5.07/5.12 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.12 U52(active(X:S)) -> U52(X:S) 5.07/5.12 U52(mark(X:S)) -> U52(X:S) 5.07/5.12 U61(active(X:S)) -> U61(X:S) 5.07/5.12 U61(mark(X:S)) -> U61(X:S) 5.07/5.12 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.12 U72(active(X:S)) -> U72(X:S) 5.07/5.12 U72(mark(X:S)) -> U72(X:S) 5.07/5.12 U81(active(X:S)) -> U81(X:S) 5.07/5.12 U81(mark(X:S)) -> U81(X:S) 5.07/5.12 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.12 active(U11(tt)) -> mark(tt) 5.07/5.12 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.12 active(U22(tt)) -> mark(tt) 5.07/5.12 active(U31(tt)) -> mark(tt) 5.07/5.12 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.12 active(U42(tt)) -> mark(tt) 5.07/5.12 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.12 active(U52(tt)) -> mark(tt) 5.07/5.12 active(U61(tt)) -> mark(tt) 5.07/5.12 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.12 active(U72(tt)) -> mark(tt) 5.07/5.12 active(U81(tt)) -> mark(tt) 5.07/5.12 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.12 active(__(nil,X:S)) -> mark(X:S) 5.07/5.12 active(__(X:S,nil)) -> mark(X:S) 5.07/5.12 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.12 active(isList(nil)) -> mark(tt) 5.07/5.12 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.12 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.12 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.12 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.12 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.12 active(isPal(nil)) -> mark(tt) 5.07/5.12 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.12 active(isQid(a)) -> mark(tt) 5.07/5.12 active(isQid(e)) -> mark(tt) 5.07/5.12 active(isQid(i)) -> mark(tt) 5.07/5.12 active(isQid(o)) -> mark(tt) 5.07/5.12 active(isQid(u)) -> mark(tt) 5.07/5.12 isList(active(X:S)) -> isList(X:S) 5.07/5.12 isList(mark(X:S)) -> isList(X:S) 5.07/5.12 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.12 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.12 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.12 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.12 isPal(active(X:S)) -> isPal(X:S) 5.07/5.12 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.12 isQid(active(X:S)) -> isQid(X:S) 5.07/5.12 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.12 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.12 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.12 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.12 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.12 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.12 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.12 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.12 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.12 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.12 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.12 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.12 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.12 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.12 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.12 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.12 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.12 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.12 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.12 mark(a) -> active(a) 5.07/5.12 mark(e) -> active(e) 5.07/5.12 mark(i) -> active(i) 5.07/5.12 mark(nil) -> active(nil) 5.07/5.12 mark(o) -> active(o) 5.07/5.12 mark(tt) -> active(tt) 5.07/5.12 mark(u) -> active(u) 5.07/5.12 ->Interpretation type: 5.07/5.12 Linear 5.07/5.12 ->Coefficients: 5.07/5.12 Natural Numbers 5.07/5.12 ->Dimension: 5.07/5.12 1 5.07/5.12 ->Bound: 5.07/5.12 2 5.07/5.12 ->Interpretation: 5.07/5.12 5.07/5.12 [U11](X) = X 5.07/5.12 [U21](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.12 [U22](X) = X + 2 5.07/5.12 [U31](X) = X 5.07/5.12 [U41](X1,X2) = X1 + 2.X2 + 2 5.07/5.12 [U42](X) = X + 2 5.07/5.12 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.12 [U52](X) = X 5.07/5.12 [U61](X) = X + 1 5.07/5.12 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.12 [U72](X) = 2.X 5.07/5.12 [U81](X) = X 5.07/5.12 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.12 [active](X) = X 5.07/5.12 [isList](X) = 2.X + 2 5.07/5.12 [isNeList](X) = 2.X + 1 5.07/5.12 [isNePal](X) = X + 2 5.07/5.12 [isPal](X) = X + 2 5.07/5.12 [isQid](X) = X + 1 5.07/5.12 [mark](X) = X 5.07/5.12 [a] = 2 5.07/5.12 [e] = 1 5.07/5.12 [fSNonEmpty] = 0 5.07/5.12 [i] = 2 5.07/5.12 [nil] = 2 5.07/5.12 [o] = 1 5.07/5.12 [tt] = 2 5.07/5.12 [u] = 1 5.07/5.12 [U11#](X) = 0 5.07/5.12 [U21#](X1,X2) = 0 5.07/5.12 [U22#](X) = 0 5.07/5.12 [U31#](X) = 0 5.07/5.12 [U41#](X1,X2) = 0 5.07/5.12 [U42#](X) = 0 5.07/5.12 [U51#](X1,X2) = 0 5.07/5.12 [U52#](X) = 0 5.07/5.12 [U61#](X) = 0 5.07/5.12 [U71#](X1,X2) = 0 5.07/5.12 [U72#](X) = 0 5.07/5.12 [U81#](X) = 0 5.07/5.12 [__#](X1,X2) = 0 5.07/5.12 [ACTIVE](X) = 2.X + 2 5.07/5.12 [ISLIST](X) = 0 5.07/5.12 [ISNELIST](X) = 0 5.07/5.12 [ISNEPAL](X) = 0 5.07/5.12 [ISPAL](X) = 0 5.07/5.12 [ISQID](X) = 0 5.07/5.12 [MARK](X) = 2.X + 2 5.07/5.12 5.07/5.12 Problem 1.19: 5.07/5.12 5.07/5.12 SCC Processor: 5.07/5.12 -> Pairs: 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.12 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.12 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.12 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.12 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.12 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.12 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.12 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.12 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.12 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.12 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.12 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.12 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.12 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.12 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.12 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.12 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.12 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.12 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.12 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.12 MARK(isList(X:S)) -> ACTIVE(isList(X:S)) 5.07/5.12 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.12 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.12 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.12 -> Rules: 5.07/5.12 U11(active(X:S)) -> U11(X:S) 5.07/5.12 U11(mark(X:S)) -> U11(X:S) 5.07/5.12 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.12 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Strongly Connected Components: 5.07/5.13 ->->Cycle: 5.07/5.13 ->->-> Pairs: 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 ->->-> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 Reduction Pairs Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U41(isList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 -> Usable rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Interpretation type: 5.07/5.13 Linear 5.07/5.13 ->Coefficients: 5.07/5.13 Natural Numbers 5.07/5.13 ->Dimension: 5.07/5.13 1 5.07/5.13 ->Bound: 5.07/5.13 2 5.07/5.13 ->Interpretation: 5.07/5.13 5.07/5.13 [U11](X) = X 5.07/5.13 [U21](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.13 [U22](X) = X 5.07/5.13 [U31](X) = X + 1 5.07/5.13 [U41](X1,X2) = 2.X1 + 2.X2 + 1 5.07/5.13 [U42](X) = X + 2 5.07/5.13 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.13 [U52](X) = X + 1 5.07/5.13 [U61](X) = X 5.07/5.13 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.13 [U72](X) = X 5.07/5.13 [U81](X) = 2.X 5.07/5.13 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.13 [active](X) = X 5.07/5.13 [isList](X) = 2.X + 2 5.07/5.13 [isNeList](X) = 2.X + 2 5.07/5.13 [isNePal](X) = X + 1 5.07/5.13 [isPal](X) = 2.X + 2 5.07/5.13 [isQid](X) = X + 1 5.07/5.13 [mark](X) = X 5.07/5.13 [a] = 2 5.07/5.13 [e] = 2 5.07/5.13 [fSNonEmpty] = 0 5.07/5.13 [i] = 2 5.07/5.13 [nil] = 2 5.07/5.13 [o] = 2 5.07/5.13 [tt] = 2 5.07/5.13 [u] = 2 5.07/5.13 [U11#](X) = 0 5.07/5.13 [U21#](X1,X2) = 0 5.07/5.13 [U22#](X) = 0 5.07/5.13 [U31#](X) = 0 5.07/5.13 [U41#](X1,X2) = 0 5.07/5.13 [U42#](X) = 0 5.07/5.13 [U51#](X1,X2) = 0 5.07/5.13 [U52#](X) = 0 5.07/5.13 [U61#](X) = 0 5.07/5.13 [U71#](X1,X2) = 0 5.07/5.13 [U72#](X) = 0 5.07/5.13 [U81#](X) = 0 5.07/5.13 [__#](X1,X2) = 0 5.07/5.13 [ACTIVE](X) = 2.X 5.07/5.13 [ISLIST](X) = 0 5.07/5.13 [ISNELIST](X) = 0 5.07/5.13 [ISNEPAL](X) = 0 5.07/5.13 [ISPAL](X) = 0 5.07/5.13 [ISQID](X) = 0 5.07/5.13 [MARK](X) = 2.X 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 SCC Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Strongly Connected Components: 5.07/5.13 ->->Cycle: 5.07/5.13 ->->-> Pairs: 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 ->->-> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 Reduction Pairs Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNeList(__(V1:S,V2:S))) -> MARK(U51(isNeList(V1:S),V2:S)) 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 -> Usable rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Interpretation type: 5.07/5.13 Linear 5.07/5.13 ->Coefficients: 5.07/5.13 Natural Numbers 5.07/5.13 ->Dimension: 5.07/5.13 1 5.07/5.13 ->Bound: 5.07/5.13 2 5.07/5.13 ->Interpretation: 5.07/5.13 5.07/5.13 [U11](X) = X 5.07/5.13 [U21](X1,X2) = X1 + 2.X2 + 2 5.07/5.13 [U22](X) = X + 1 5.07/5.13 [U31](X) = X + 1 5.07/5.13 [U41](X1,X2) = X1 + 2.X2 + 2 5.07/5.13 [U42](X) = X + 1 5.07/5.13 [U51](X1,X2) = 2.X1 + 2.X2 + 1 5.07/5.13 [U52](X) = X + 1 5.07/5.13 [U61](X) = X 5.07/5.13 [U71](X1,X2) = 2.X1 + 2.X2 5.07/5.13 [U72](X) = X + 2 5.07/5.13 [U81](X) = X + 1 5.07/5.13 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.13 [active](X) = X 5.07/5.13 [isList](X) = 2.X + 2 5.07/5.13 [isNeList](X) = 2.X + 2 5.07/5.13 [isNePal](X) = 2.X + 1 5.07/5.13 [isPal](X) = 2.X + 2 5.07/5.13 [isQid](X) = 2.X + 1 5.07/5.13 [mark](X) = X 5.07/5.13 [a] = 1 5.07/5.13 [e] = 2 5.07/5.13 [fSNonEmpty] = 0 5.07/5.13 [i] = 2 5.07/5.13 [nil] = 2 5.07/5.13 [o] = 2 5.07/5.13 [tt] = 2 5.07/5.13 [u] = 2 5.07/5.13 [U11#](X) = 0 5.07/5.13 [U21#](X1,X2) = 0 5.07/5.13 [U22#](X) = 0 5.07/5.13 [U31#](X) = 0 5.07/5.13 [U41#](X1,X2) = 0 5.07/5.13 [U42#](X) = 0 5.07/5.13 [U51#](X1,X2) = 0 5.07/5.13 [U52#](X) = 0 5.07/5.13 [U61#](X) = 0 5.07/5.13 [U71#](X1,X2) = 0 5.07/5.13 [U72#](X) = 0 5.07/5.13 [U81#](X) = 0 5.07/5.13 [__#](X1,X2) = 0 5.07/5.13 [ACTIVE](X) = 2.X + 2 5.07/5.13 [ISLIST](X) = 0 5.07/5.13 [ISNELIST](X) = 0 5.07/5.13 [ISNEPAL](X) = 0 5.07/5.13 [ISPAL](X) = 0 5.07/5.13 [ISQID](X) = 0 5.07/5.13 [MARK](X) = 2.X + 2 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 SCC Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Strongly Connected Components: 5.07/5.13 ->->Cycle: 5.07/5.13 ->->-> Pairs: 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 ->->-> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 Reduction Pairs Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNeList(V:S)) -> MARK(U31(isQid(V:S))) 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 -> Usable rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Interpretation type: 5.07/5.13 Linear 5.07/5.13 ->Coefficients: 5.07/5.13 Natural Numbers 5.07/5.13 ->Dimension: 5.07/5.13 1 5.07/5.13 ->Bound: 5.07/5.13 2 5.07/5.13 ->Interpretation: 5.07/5.13 5.07/5.13 [U11](X) = X 5.07/5.13 [U21](X1,X2) = 2.X1 + 2.X2 + 1 5.07/5.13 [U22](X) = X + 2 5.07/5.13 [U31](X) = X 5.07/5.13 [U41](X1,X2) = X1 + 2.X2 + 2 5.07/5.13 [U42](X) = X + 2 5.07/5.13 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.13 [U52](X) = X + 2 5.07/5.13 [U61](X) = X + 1 5.07/5.13 [U71](X1,X2) = 2.X1 + 2.X2 5.07/5.13 [U72](X) = X + 2 5.07/5.13 [U81](X) = X 5.07/5.13 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.13 [active](X) = X 5.07/5.13 [isList](X) = 2.X + 2 5.07/5.13 [isNeList](X) = 2.X + 2 5.07/5.13 [isNePal](X) = X + 2 5.07/5.13 [isPal](X) = 2.X + 2 5.07/5.13 [isQid](X) = X + 1 5.07/5.13 [mark](X) = X 5.07/5.13 [a] = 2 5.07/5.13 [e] = 2 5.07/5.13 [fSNonEmpty] = 0 5.07/5.13 [i] = 2 5.07/5.13 [nil] = 2 5.07/5.13 [o] = 1 5.07/5.13 [tt] = 2 5.07/5.13 [u] = 2 5.07/5.13 [U11#](X) = 0 5.07/5.13 [U21#](X1,X2) = 0 5.07/5.13 [U22#](X) = 0 5.07/5.13 [U31#](X) = 0 5.07/5.13 [U41#](X1,X2) = 0 5.07/5.13 [U42#](X) = 0 5.07/5.13 [U51#](X1,X2) = 0 5.07/5.13 [U52#](X) = 0 5.07/5.13 [U61#](X) = 0 5.07/5.13 [U71#](X1,X2) = 0 5.07/5.13 [U72#](X) = 0 5.07/5.13 [U81#](X) = 0 5.07/5.13 [__#](X1,X2) = 0 5.07/5.13 [ACTIVE](X) = 2.X + 1 5.07/5.13 [ISLIST](X) = 0 5.07/5.13 [ISNELIST](X) = 0 5.07/5.13 [ISNEPAL](X) = 0 5.07/5.13 [ISPAL](X) = 0 5.07/5.13 [ISQID](X) = 0 5.07/5.13 [MARK](X) = 2.X + 1 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 SCC Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNeList(X:S)) -> ACTIVE(isNeList(X:S)) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 ->Strongly Connected Components: 5.07/5.13 ->->Cycle: 5.07/5.13 ->->-> Pairs: 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 ->->-> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.13 active(isPal(nil)) -> mark(tt) 5.07/5.13 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.13 active(isQid(a)) -> mark(tt) 5.07/5.13 active(isQid(e)) -> mark(tt) 5.07/5.13 active(isQid(i)) -> mark(tt) 5.07/5.13 active(isQid(o)) -> mark(tt) 5.07/5.13 active(isQid(u)) -> mark(tt) 5.07/5.13 isList(active(X:S)) -> isList(X:S) 5.07/5.13 isList(mark(X:S)) -> isList(X:S) 5.07/5.13 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.13 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.13 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.13 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.13 isPal(active(X:S)) -> isPal(X:S) 5.07/5.13 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.13 isQid(active(X:S)) -> isQid(X:S) 5.07/5.13 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.13 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.13 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.13 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.13 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.13 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.13 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.13 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.13 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.13 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.13 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.13 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.13 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.13 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.13 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.13 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.13 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.13 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.13 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.13 mark(a) -> active(a) 5.07/5.13 mark(e) -> active(e) 5.07/5.13 mark(i) -> active(i) 5.07/5.13 mark(nil) -> active(nil) 5.07/5.13 mark(o) -> active(o) 5.07/5.13 mark(tt) -> active(tt) 5.07/5.13 mark(u) -> active(u) 5.07/5.13 5.07/5.13 Problem 1.19: 5.07/5.13 5.07/5.13 Reduction Pairs Processor: 5.07/5.13 -> Pairs: 5.07/5.13 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U71(isQid(I:S),P:S)) 5.07/5.13 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.13 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.13 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.13 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.13 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.13 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.13 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.13 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.13 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.13 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.13 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.13 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.13 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.13 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.13 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.13 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.13 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.13 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.13 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.13 -> Rules: 5.07/5.13 U11(active(X:S)) -> U11(X:S) 5.07/5.13 U11(mark(X:S)) -> U11(X:S) 5.07/5.13 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.13 U22(active(X:S)) -> U22(X:S) 5.07/5.13 U22(mark(X:S)) -> U22(X:S) 5.07/5.13 U31(active(X:S)) -> U31(X:S) 5.07/5.13 U31(mark(X:S)) -> U31(X:S) 5.07/5.13 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.13 U42(active(X:S)) -> U42(X:S) 5.07/5.13 U42(mark(X:S)) -> U42(X:S) 5.07/5.13 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.13 U52(active(X:S)) -> U52(X:S) 5.07/5.13 U52(mark(X:S)) -> U52(X:S) 5.07/5.13 U61(active(X:S)) -> U61(X:S) 5.07/5.13 U61(mark(X:S)) -> U61(X:S) 5.07/5.13 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.13 U72(active(X:S)) -> U72(X:S) 5.07/5.13 U72(mark(X:S)) -> U72(X:S) 5.07/5.13 U81(active(X:S)) -> U81(X:S) 5.07/5.13 U81(mark(X:S)) -> U81(X:S) 5.07/5.13 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.13 active(U11(tt)) -> mark(tt) 5.07/5.13 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.13 active(U22(tt)) -> mark(tt) 5.07/5.13 active(U31(tt)) -> mark(tt) 5.07/5.13 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.13 active(U42(tt)) -> mark(tt) 5.07/5.13 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.13 active(U52(tt)) -> mark(tt) 5.07/5.13 active(U61(tt)) -> mark(tt) 5.07/5.13 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.13 active(U72(tt)) -> mark(tt) 5.07/5.13 active(U81(tt)) -> mark(tt) 5.07/5.13 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.13 active(__(nil,X:S)) -> mark(X:S) 5.07/5.13 active(__(X:S,nil)) -> mark(X:S) 5.07/5.13 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.13 active(isList(nil)) -> mark(tt) 5.07/5.13 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.13 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.13 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.13 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.13 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 -> Usable rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Interpretation type: 5.07/5.14 Linear 5.07/5.14 ->Coefficients: 5.07/5.14 Natural Numbers 5.07/5.14 ->Dimension: 5.07/5.14 1 5.07/5.14 ->Bound: 5.07/5.14 2 5.07/5.14 ->Interpretation: 5.07/5.14 5.07/5.14 [U11](X) = X 5.07/5.14 [U21](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.14 [U22](X) = X + 2 5.07/5.14 [U31](X) = X 5.07/5.14 [U41](X1,X2) = X1 + 2.X2 + 2 5.07/5.14 [U42](X) = X + 2 5.07/5.14 [U51](X1,X2) = 2.X1 + 2.X2 5.07/5.14 [U52](X) = X + 2 5.07/5.14 [U61](X) = X 5.07/5.14 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.14 [U72](X) = X + 2 5.07/5.14 [U81](X) = X 5.07/5.14 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.14 [active](X) = X 5.07/5.14 [isList](X) = 2.X + 2 5.07/5.14 [isNeList](X) = 2.X + 2 5.07/5.14 [isNePal](X) = 2.X + 2 5.07/5.14 [isPal](X) = 2.X + 2 5.07/5.14 [isQid](X) = 2.X + 2 5.07/5.14 [mark](X) = X 5.07/5.14 [a] = 2 5.07/5.14 [e] = 2 5.07/5.14 [fSNonEmpty] = 0 5.07/5.14 [i] = 2 5.07/5.14 [nil] = 2 5.07/5.14 [o] = 1 5.07/5.14 [tt] = 2 5.07/5.14 [u] = 1 5.07/5.14 [U11#](X) = 0 5.07/5.14 [U21#](X1,X2) = 0 5.07/5.14 [U22#](X) = 0 5.07/5.14 [U31#](X) = 0 5.07/5.14 [U41#](X1,X2) = 0 5.07/5.14 [U42#](X) = 0 5.07/5.14 [U51#](X1,X2) = 0 5.07/5.14 [U52#](X) = 0 5.07/5.14 [U61#](X) = 0 5.07/5.14 [U71#](X1,X2) = 0 5.07/5.14 [U72#](X) = 0 5.07/5.14 [U81#](X) = 0 5.07/5.14 [__#](X1,X2) = 0 5.07/5.14 [ACTIVE](X) = 2.X + 2 5.07/5.14 [ISLIST](X) = 0 5.07/5.14 [ISNELIST](X) = 0 5.07/5.14 [ISNEPAL](X) = 0 5.07/5.14 [ISPAL](X) = 0 5.07/5.14 [ISQID](X) = 0 5.07/5.14 [MARK](X) = 2.X + 2 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 SCC Processor: 5.07/5.14 -> Pairs: 5.07/5.14 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.14 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Strongly Connected Components: 5.07/5.14 ->->Cycle: 5.07/5.14 ->->-> Pairs: 5.07/5.14 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.14 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 ->->-> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 Reduction Pairs Processor: 5.07/5.14 -> Pairs: 5.07/5.14 ACTIVE(isNePal(V:S)) -> MARK(U61(isQid(V:S))) 5.07/5.14 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 -> Usable rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Interpretation type: 5.07/5.14 Linear 5.07/5.14 ->Coefficients: 5.07/5.14 Natural Numbers 5.07/5.14 ->Dimension: 5.07/5.14 1 5.07/5.14 ->Bound: 5.07/5.14 2 5.07/5.14 ->Interpretation: 5.07/5.14 5.07/5.14 [U11](X) = X 5.07/5.14 [U21](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.14 [U22](X) = X + 2 5.07/5.14 [U31](X) = 2.X + 2 5.07/5.14 [U41](X1,X2) = 2.X1 + 2.X2 5.07/5.14 [U42](X) = X 5.07/5.14 [U51](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.14 [U52](X) = X + 2 5.07/5.14 [U61](X) = X 5.07/5.14 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.14 [U72](X) = X + 2 5.07/5.14 [U81](X) = X 5.07/5.14 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.14 [active](X) = X 5.07/5.14 [isList](X) = 2.X + 2 5.07/5.14 [isNeList](X) = 2.X + 2 5.07/5.14 [isNePal](X) = 2.X + 2 5.07/5.14 [isPal](X) = 2.X + 2 5.07/5.14 [isQid](X) = X 5.07/5.14 [mark](X) = X 5.07/5.14 [a] = 2 5.07/5.14 [e] = 2 5.07/5.14 [fSNonEmpty] = 0 5.07/5.14 [i] = 2 5.07/5.14 [nil] = 1 5.07/5.14 [o] = 2 5.07/5.14 [tt] = 2 5.07/5.14 [u] = 2 5.07/5.14 [U11#](X) = 0 5.07/5.14 [U21#](X1,X2) = 0 5.07/5.14 [U22#](X) = 0 5.07/5.14 [U31#](X) = 0 5.07/5.14 [U41#](X1,X2) = 0 5.07/5.14 [U42#](X) = 0 5.07/5.14 [U51#](X1,X2) = 0 5.07/5.14 [U52#](X) = 0 5.07/5.14 [U61#](X) = 0 5.07/5.14 [U71#](X1,X2) = 0 5.07/5.14 [U72#](X) = 0 5.07/5.14 [U81#](X) = 0 5.07/5.14 [__#](X1,X2) = 0 5.07/5.14 [ACTIVE](X) = 2.X 5.07/5.14 [ISLIST](X) = 0 5.07/5.14 [ISNELIST](X) = 0 5.07/5.14 [ISNEPAL](X) = 0 5.07/5.14 [ISPAL](X) = 0 5.07/5.14 [ISQID](X) = 0 5.07/5.14 [MARK](X) = 2.X 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 SCC Processor: 5.07/5.14 -> Pairs: 5.07/5.14 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isNePal(X:S)) -> ACTIVE(isNePal(X:S)) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Strongly Connected Components: 5.07/5.14 ->->Cycle: 5.07/5.14 ->->-> Pairs: 5.07/5.14 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 ->->-> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 Reduction Pairs Processor: 5.07/5.14 -> Pairs: 5.07/5.14 ACTIVE(isPal(V:S)) -> MARK(U81(isNePal(V:S))) 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 -> Usable rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Interpretation type: 5.07/5.14 Linear 5.07/5.14 ->Coefficients: 5.07/5.14 Natural Numbers 5.07/5.14 ->Dimension: 5.07/5.14 1 5.07/5.14 ->Bound: 5.07/5.14 2 5.07/5.14 ->Interpretation: 5.07/5.14 5.07/5.14 [U11](X) = X 5.07/5.14 [U21](X1,X2) = X1 + 2.X2 + 2 5.07/5.14 [U22](X) = X + 2 5.07/5.14 [U31](X) = X + 2 5.07/5.14 [U41](X1,X2) = 2.X1 + 2.X2 5.07/5.14 [U42](X) = X + 2 5.07/5.14 [U51](X1,X2) = 2.X1 + 2.X2 + 1 5.07/5.14 [U52](X) = X + 2 5.07/5.14 [U61](X) = X 5.07/5.14 [U71](X1,X2) = 2.X1 + 2.X2 + 2 5.07/5.14 [U72](X) = X + 1 5.07/5.14 [U81](X) = X + 1 5.07/5.14 [__](X1,X2) = 2.X1 + X2 + 2 5.07/5.14 [active](X) = X 5.07/5.14 [isList](X) = 2.X + 2 5.07/5.14 [isNeList](X) = 2.X + 2 5.07/5.14 [isNePal](X) = 2.X 5.07/5.14 [isPal](X) = 2.X + 2 5.07/5.14 [isQid](X) = 2.X 5.07/5.14 [mark](X) = X 5.07/5.14 [a] = 2 5.07/5.14 [e] = 1 5.07/5.14 [fSNonEmpty] = 0 5.07/5.14 [i] = 2 5.07/5.14 [nil] = 1 5.07/5.14 [o] = 2 5.07/5.14 [tt] = 2 5.07/5.14 [u] = 2 5.07/5.14 [U11#](X) = 0 5.07/5.14 [U21#](X1,X2) = 0 5.07/5.14 [U22#](X) = 0 5.07/5.14 [U31#](X) = 0 5.07/5.14 [U41#](X1,X2) = 0 5.07/5.14 [U42#](X) = 0 5.07/5.14 [U51#](X1,X2) = 0 5.07/5.14 [U52#](X) = 0 5.07/5.14 [U61#](X) = 0 5.07/5.14 [U71#](X1,X2) = 0 5.07/5.14 [U72#](X) = 0 5.07/5.14 [U81#](X) = 0 5.07/5.14 [__#](X1,X2) = 0 5.07/5.14 [ACTIVE](X) = X + 2 5.07/5.14 [ISLIST](X) = 0 5.07/5.14 [ISNELIST](X) = 0 5.07/5.14 [ISNEPAL](X) = 0 5.07/5.14 [ISPAL](X) = 0 5.07/5.14 [ISQID](X) = 0 5.07/5.14 [MARK](X) = X + 2 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 SCC Processor: 5.07/5.14 -> Pairs: 5.07/5.14 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S))) 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> ACTIVE(U22(mark(X:S))) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> ACTIVE(U31(mark(X:S))) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> ACTIVE(U41(mark(X1:S),X2:S)) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> ACTIVE(U42(mark(X:S))) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> ACTIVE(U52(mark(X:S))) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> ACTIVE(U61(mark(X:S))) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> ACTIVE(U71(mark(X1:S),X2:S)) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> ACTIVE(U72(mark(X:S))) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> ACTIVE(U81(mark(X:S))) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S))) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 MARK(isPal(X:S)) -> ACTIVE(isPal(X:S)) 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Strongly Connected Components: 5.07/5.14 ->->Cycle: 5.07/5.14 ->->-> Pairs: 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 ->->-> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 Subterm Processor: 5.07/5.14 -> Pairs: 5.07/5.14 MARK(U11(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U22(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U31(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U41(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U42(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U52(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U61(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U71(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(U72(X:S)) -> MARK(X:S) 5.07/5.14 MARK(U81(X:S)) -> MARK(X:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 5.07/5.14 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Projection: 5.07/5.14 pi(MARK) = 1 5.07/5.14 5.07/5.14 Problem 1.19: 5.07/5.14 5.07/5.14 SCC Processor: 5.07/5.14 -> Pairs: 5.07/5.14 Empty 5.07/5.14 -> Rules: 5.07/5.14 U11(active(X:S)) -> U11(X:S) 5.07/5.14 U11(mark(X:S)) -> U11(X:S) 5.07/5.14 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 5.07/5.14 U22(active(X:S)) -> U22(X:S) 5.07/5.14 U22(mark(X:S)) -> U22(X:S) 5.07/5.14 U31(active(X:S)) -> U31(X:S) 5.07/5.14 U31(mark(X:S)) -> U31(X:S) 5.07/5.14 U41(active(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(mark(X1:S),X2:S) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,active(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U41(X1:S,mark(X2:S)) -> U41(X1:S,X2:S) 5.07/5.14 U42(active(X:S)) -> U42(X:S) 5.07/5.14 U42(mark(X:S)) -> U42(X:S) 5.07/5.14 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 5.07/5.14 U52(active(X:S)) -> U52(X:S) 5.07/5.14 U52(mark(X:S)) -> U52(X:S) 5.07/5.14 U61(active(X:S)) -> U61(X:S) 5.07/5.14 U61(mark(X:S)) -> U61(X:S) 5.07/5.14 U71(active(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(mark(X1:S),X2:S) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,active(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U71(X1:S,mark(X2:S)) -> U71(X1:S,X2:S) 5.07/5.14 U72(active(X:S)) -> U72(X:S) 5.07/5.14 U72(mark(X:S)) -> U72(X:S) 5.07/5.14 U81(active(X:S)) -> U81(X:S) 5.07/5.14 U81(mark(X:S)) -> U81(X:S) 5.07/5.14 __(active(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(mark(X1:S),X2:S) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,active(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S) 5.07/5.14 active(U11(tt)) -> mark(tt) 5.07/5.14 active(U21(tt,V2:S)) -> mark(U22(isList(V2:S))) 5.07/5.14 active(U22(tt)) -> mark(tt) 5.07/5.14 active(U31(tt)) -> mark(tt) 5.07/5.14 active(U41(tt,V2:S)) -> mark(U42(isNeList(V2:S))) 5.07/5.14 active(U42(tt)) -> mark(tt) 5.07/5.14 active(U51(tt,V2:S)) -> mark(U52(isList(V2:S))) 5.07/5.14 active(U52(tt)) -> mark(tt) 5.07/5.14 active(U61(tt)) -> mark(tt) 5.07/5.14 active(U71(tt,P:S)) -> mark(U72(isPal(P:S))) 5.07/5.14 active(U72(tt)) -> mark(tt) 5.07/5.14 active(U81(tt)) -> mark(tt) 5.07/5.14 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S))) 5.07/5.14 active(__(nil,X:S)) -> mark(X:S) 5.07/5.14 active(__(X:S,nil)) -> mark(X:S) 5.07/5.14 active(isList(__(V1:S,V2:S))) -> mark(U21(isList(V1:S),V2:S)) 5.07/5.14 active(isList(nil)) -> mark(tt) 5.07/5.14 active(isList(V:S)) -> mark(U11(isNeList(V:S))) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U41(isList(V1:S),V2:S)) 5.07/5.14 active(isNeList(__(V1:S,V2:S))) -> mark(U51(isNeList(V1:S),V2:S)) 5.07/5.14 active(isNeList(V:S)) -> mark(U31(isQid(V:S))) 5.07/5.14 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U71(isQid(I:S),P:S)) 5.07/5.14 active(isNePal(V:S)) -> mark(U61(isQid(V:S))) 5.07/5.14 active(isPal(nil)) -> mark(tt) 5.07/5.14 active(isPal(V:S)) -> mark(U81(isNePal(V:S))) 5.07/5.14 active(isQid(a)) -> mark(tt) 5.07/5.14 active(isQid(e)) -> mark(tt) 5.07/5.14 active(isQid(i)) -> mark(tt) 5.07/5.14 active(isQid(o)) -> mark(tt) 5.07/5.14 active(isQid(u)) -> mark(tt) 5.07/5.14 isList(active(X:S)) -> isList(X:S) 5.07/5.14 isList(mark(X:S)) -> isList(X:S) 5.07/5.14 isNeList(active(X:S)) -> isNeList(X:S) 5.07/5.14 isNeList(mark(X:S)) -> isNeList(X:S) 5.07/5.14 isNePal(active(X:S)) -> isNePal(X:S) 5.07/5.14 isNePal(mark(X:S)) -> isNePal(X:S) 5.07/5.14 isPal(active(X:S)) -> isPal(X:S) 5.07/5.14 isPal(mark(X:S)) -> isPal(X:S) 5.07/5.14 isQid(active(X:S)) -> isQid(X:S) 5.07/5.14 isQid(mark(X:S)) -> isQid(X:S) 5.07/5.14 mark(U11(X:S)) -> active(U11(mark(X:S))) 5.07/5.14 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 5.07/5.14 mark(U22(X:S)) -> active(U22(mark(X:S))) 5.07/5.14 mark(U31(X:S)) -> active(U31(mark(X:S))) 5.07/5.14 mark(U41(X1:S,X2:S)) -> active(U41(mark(X1:S),X2:S)) 5.07/5.14 mark(U42(X:S)) -> active(U42(mark(X:S))) 5.07/5.14 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 5.07/5.14 mark(U52(X:S)) -> active(U52(mark(X:S))) 5.07/5.14 mark(U61(X:S)) -> active(U61(mark(X:S))) 5.07/5.14 mark(U71(X1:S,X2:S)) -> active(U71(mark(X1:S),X2:S)) 5.07/5.14 mark(U72(X:S)) -> active(U72(mark(X:S))) 5.07/5.14 mark(U81(X:S)) -> active(U81(mark(X:S))) 5.07/5.14 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S))) 5.07/5.14 mark(isList(X:S)) -> active(isList(X:S)) 5.07/5.14 mark(isNeList(X:S)) -> active(isNeList(X:S)) 5.07/5.14 mark(isNePal(X:S)) -> active(isNePal(X:S)) 5.07/5.14 mark(isPal(X:S)) -> active(isPal(X:S)) 5.07/5.14 mark(isQid(X:S)) -> active(isQid(X:S)) 5.07/5.14 mark(a) -> active(a) 5.07/5.14 mark(e) -> active(e) 5.07/5.14 mark(i) -> active(i) 5.07/5.14 mark(nil) -> active(nil) 5.07/5.14 mark(o) -> active(o) 5.07/5.14 mark(tt) -> active(tt) 5.07/5.14 mark(u) -> active(u) 5.07/5.14 ->Strongly Connected Components: 5.07/5.14 There is no strongly connected component 5.07/5.14 5.07/5.14 The problem is finite. 5.07/5.14 EOF