118.39/124.31 YES 118.39/124.31 118.39/124.31 Problem 1: 118.39/124.31 118.39/124.31 (VAR v_NonEmpty:S M:S N:S V1:S V2:S X:S X1:S X2:S X3:S) 118.39/124.31 (RULES 118.39/124.31 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.31 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.31 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.31 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.31 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.31 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.31 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.31 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.31 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.31 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.31 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.31 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.31 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.31 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.31 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.31 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.31 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.31 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.31 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.31 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.31 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.31 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.31 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.31 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.31 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.31 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.31 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.31 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.31 U16(active(X:S)) -> U16(X:S) 118.39/124.31 U16(mark(X:S)) -> U16(X:S) 118.39/124.31 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.31 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.31 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.31 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.31 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.31 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.31 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.31 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.31 U23(active(X:S)) -> U23(X:S) 118.39/124.31 U23(mark(X:S)) -> U23(X:S) 118.39/124.31 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.31 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.31 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.31 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.31 U32(active(X:S)) -> U32(X:S) 118.39/124.31 U32(mark(X:S)) -> U32(X:S) 118.39/124.31 U41(active(X:S)) -> U41(X:S) 118.39/124.31 U41(mark(X:S)) -> U41(X:S) 118.39/124.31 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.31 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.31 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.31 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.31 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.31 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.31 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.31 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.31 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.31 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.31 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.31 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.31 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.31 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.31 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.31 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.31 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.31 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.31 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.31 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.31 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.31 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.31 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.31 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.31 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.31 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.31 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.31 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.31 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.31 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.31 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.31 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.31 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.31 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.31 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.31 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.31 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.31 active(U16(tt)) -> mark(tt) 118.39/124.31 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.31 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.31 active(U23(tt)) -> mark(tt) 118.39/124.31 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.31 active(U32(tt)) -> mark(tt) 118.39/124.31 active(U41(tt)) -> mark(tt) 118.39/124.31 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.31 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.31 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.31 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.31 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.31 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.31 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.31 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.31 active(isNat(0)) -> mark(tt) 118.39/124.31 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.31 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.31 active(isNatKind(0)) -> mark(tt) 118.39/124.31 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.31 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.31 isNat(active(X:S)) -> isNat(X:S) 118.39/124.31 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.31 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.31 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.31 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.31 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.31 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.31 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.31 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.31 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.31 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.31 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.31 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.31 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.31 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.31 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.31 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.31 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.31 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.31 mark(0) -> active(0) 118.39/124.31 mark(tt) -> active(tt) 118.39/124.31 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.31 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.31 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.31 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.31 s(active(X:S)) -> s(X:S) 118.39/124.31 s(mark(X:S)) -> s(X:S) 118.39/124.31 ) 118.39/124.31 (STRATEGY INNERMOST) 118.39/124.31 118.39/124.31 Problem 1: 118.39/124.31 118.39/124.31 Dependency Pairs Processor: 118.39/124.31 -> Pairs: 118.39/124.31 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.31 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.31 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.31 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.31 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.39/124.31 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.39/124.31 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.31 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.31 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.31 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.31 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.39/124.31 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.39/124.31 U13#(active(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.31 U13#(mark(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.31 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.31 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.31 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.39/124.31 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.39/124.31 U14#(active(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.31 U14#(mark(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.31 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.31 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.31 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.39/124.31 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.39/124.31 U15#(active(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.39/124.31 U15#(mark(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.39/124.31 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.39/124.31 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.39/124.31 U16#(active(X:S)) -> U16#(X:S) 118.39/124.31 U16#(mark(X:S)) -> U16#(X:S) 118.39/124.31 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.39/124.31 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.39/124.32 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.39/124.32 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.39/124.32 U22#(active(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.39/124.32 U22#(mark(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.39/124.32 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.39/124.32 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.39/124.32 U23#(active(X:S)) -> U23#(X:S) 118.39/124.32 U23#(mark(X:S)) -> U23#(X:S) 118.39/124.32 U31#(active(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.39/124.32 U31#(mark(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.39/124.32 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.39/124.32 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.39/124.32 U32#(active(X:S)) -> U32#(X:S) 118.39/124.32 U32#(mark(X:S)) -> U32#(X:S) 118.39/124.32 U41#(active(X:S)) -> U41#(X:S) 118.39/124.32 U41#(mark(X:S)) -> U41#(X:S) 118.39/124.32 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.39/124.32 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.39/124.32 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.39/124.32 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.39/124.32 U52#(active(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(mark(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.39/124.32 U61#(active(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(mark(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(active(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(mark(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(active(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(mark(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(active(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(mark(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 ACTIVE(U11(tt,V1:S,V2:S)) -> U12#(isNatKind(V1:S),V1:S,V2:S) 118.39/124.32 ACTIVE(U11(tt,V1:S,V2:S)) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(U12(tt,V1:S,V2:S)) -> U13#(isNatKind(V2:S),V1:S,V2:S) 118.39/124.32 ACTIVE(U12(tt,V1:S,V2:S)) -> ISNATKIND(V2:S) 118.39/124.32 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(U13(tt,V1:S,V2:S)) -> U14#(isNatKind(V2:S),V1:S,V2:S) 118.39/124.32 ACTIVE(U13(tt,V1:S,V2:S)) -> ISNATKIND(V2:S) 118.39/124.32 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(U14(tt,V1:S,V2:S)) -> U15#(isNat(V1:S),V2:S) 118.39/124.32 ACTIVE(U14(tt,V1:S,V2:S)) -> ISNAT(V1:S) 118.39/124.32 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.39/124.32 ACTIVE(U15(tt,V2:S)) -> U16#(isNat(V2:S)) 118.39/124.32 ACTIVE(U15(tt,V2:S)) -> ISNAT(V2:S) 118.39/124.32 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.39/124.32 ACTIVE(U16(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U21(tt,V1:S)) -> U22#(isNatKind(V1:S),V1:S) 118.39/124.32 ACTIVE(U21(tt,V1:S)) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 ACTIVE(U22(tt,V1:S)) -> U23#(isNat(V1:S)) 118.39/124.32 ACTIVE(U22(tt,V1:S)) -> ISNAT(V1:S) 118.39/124.32 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.39/124.32 ACTIVE(U23(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U31(tt,V2:S)) -> U32#(isNatKind(V2:S)) 118.39/124.32 ACTIVE(U31(tt,V2:S)) -> ISNATKIND(V2:S) 118.39/124.32 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.39/124.32 ACTIVE(U32(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U41(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U51(tt,N:S)) -> U52#(isNatKind(N:S),N:S) 118.39/124.32 ACTIVE(U51(tt,N:S)) -> ISNATKIND(N:S) 118.39/124.32 ACTIVE(U51(tt,N:S)) -> MARK(U52(isNatKind(N:S),N:S)) 118.39/124.32 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.39/124.32 ACTIVE(U61(tt,M:S,N:S)) -> U62#(isNatKind(M:S),M:S,N:S) 118.39/124.32 ACTIVE(U61(tt,M:S,N:S)) -> ISNATKIND(M:S) 118.39/124.32 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 ACTIVE(U62(tt,M:S,N:S)) -> U63#(isNat(N:S),M:S,N:S) 118.39/124.32 ACTIVE(U62(tt,M:S,N:S)) -> ISNAT(N:S) 118.39/124.32 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 ACTIVE(U63(tt,M:S,N:S)) -> U64#(isNatKind(N:S),M:S,N:S) 118.39/124.32 ACTIVE(U63(tt,M:S,N:S)) -> ISNATKIND(N:S) 118.39/124.32 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.39/124.32 ACTIVE(U64(tt,M:S,N:S)) -> PLUS(N:S,M:S) 118.39/124.32 ACTIVE(U64(tt,M:S,N:S)) -> S(plus(N:S,M:S)) 118.39/124.32 ACTIVE(isNat(plus(V1:S,V2:S))) -> U11#(isNatKind(V1:S),V1:S,V2:S) 118.39/124.32 ACTIVE(isNat(plus(V1:S,V2:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(isNat(s(V1:S))) -> U21#(isNatKind(V1:S),V1:S) 118.39/124.32 ACTIVE(isNat(s(V1:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 ACTIVE(isNat(0)) -> MARK(tt) 118.39/124.32 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> U31#(isNatKind(V1:S),V2:S) 118.39/124.32 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 ACTIVE(isNatKind(s(V1:S))) -> U41#(isNatKind(V1:S)) 118.39/124.32 ACTIVE(isNatKind(s(V1:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.39/124.32 ACTIVE(isNatKind(0)) -> MARK(tt) 118.39/124.32 ACTIVE(plus(N:S,s(M:S))) -> U61#(isNat(M:S),M:S,N:S) 118.39/124.32 ACTIVE(plus(N:S,s(M:S))) -> ISNAT(M:S) 118.39/124.32 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 ACTIVE(plus(N:S,0)) -> U51#(isNat(N:S),N:S) 118.39/124.32 ACTIVE(plus(N:S,0)) -> ISNAT(N:S) 118.39/124.32 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.39/124.32 ISNAT(active(X:S)) -> ISNAT(X:S) 118.39/124.32 ISNAT(mark(X:S)) -> ISNAT(X:S) 118.39/124.32 ISNATKIND(active(X:S)) -> ISNATKIND(X:S) 118.39/124.32 ISNATKIND(mark(X:S)) -> ISNATKIND(X:S) 118.39/124.32 MARK(U11(X1:S,X2:S,X3:S)) -> U11#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U12(X1:S,X2:S,X3:S)) -> U12#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U13(X1:S,X2:S,X3:S)) -> U13#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U14(X1:S,X2:S,X3:S)) -> U14#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U15(X1:S,X2:S)) -> U15#(mark(X1:S),X2:S) 118.39/124.32 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.39/124.32 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U16(X:S)) -> U16#(mark(X:S)) 118.39/124.32 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.39/124.32 MARK(U16(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U21(X1:S,X2:S)) -> U21#(mark(X1:S),X2:S) 118.39/124.32 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.39/124.32 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U22(X1:S,X2:S)) -> U22#(mark(X1:S),X2:S) 118.39/124.32 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.39/124.32 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U23(X:S)) -> U23#(mark(X:S)) 118.39/124.32 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.39/124.32 MARK(U23(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U31(X1:S,X2:S)) -> U31#(mark(X1:S),X2:S) 118.39/124.32 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.39/124.32 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U32(X:S)) -> U32#(mark(X:S)) 118.39/124.32 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.39/124.32 MARK(U32(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U41(X:S)) -> U41#(mark(X:S)) 118.39/124.32 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.39/124.32 MARK(U41(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U51(X1:S,X2:S)) -> U51#(mark(X1:S),X2:S) 118.39/124.32 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.39/124.32 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U52(X1:S,X2:S)) -> U52#(mark(X1:S),X2:S) 118.39/124.32 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.39/124.32 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U61(X1:S,X2:S,X3:S)) -> U61#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U62(X1:S,X2:S,X3:S)) -> U62#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U63(X1:S,X2:S,X3:S)) -> U63#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U64(X1:S,X2:S,X3:S)) -> U64#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.39/124.32 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> PLUS(mark(X1:S),mark(X2:S)) 118.39/124.32 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.39/124.32 MARK(s(X:S)) -> MARK(X:S) 118.39/124.32 MARK(s(X:S)) -> S(mark(X:S)) 118.39/124.32 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.39/124.32 S(active(X:S)) -> S(X:S) 118.39/124.32 S(mark(X:S)) -> S(X:S) 118.39/124.32 -> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 118.39/124.32 Problem 1: 118.39/124.32 118.39/124.32 SCC Processor: 118.39/124.32 -> Pairs: 118.39/124.32 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.32 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.32 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.32 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.39/124.32 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.39/124.32 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.39/124.32 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.32 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.32 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.32 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.39/124.32 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.39/124.32 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.39/124.32 U13#(active(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.32 U13#(mark(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.32 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.32 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.39/124.32 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.39/124.32 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.39/124.32 U14#(active(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.32 U14#(mark(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.32 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.32 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.39/124.32 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.39/124.32 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.39/124.32 U15#(active(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.39/124.32 U15#(mark(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.39/124.32 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.39/124.32 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.39/124.32 U16#(active(X:S)) -> U16#(X:S) 118.39/124.32 U16#(mark(X:S)) -> U16#(X:S) 118.39/124.32 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.39/124.32 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.39/124.32 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.39/124.32 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.39/124.32 U22#(active(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.39/124.32 U22#(mark(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.39/124.32 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.39/124.32 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.39/124.32 U23#(active(X:S)) -> U23#(X:S) 118.39/124.32 U23#(mark(X:S)) -> U23#(X:S) 118.39/124.32 U31#(active(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.39/124.32 U31#(mark(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.39/124.32 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.39/124.32 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.39/124.32 U32#(active(X:S)) -> U32#(X:S) 118.39/124.32 U32#(mark(X:S)) -> U32#(X:S) 118.39/124.32 U41#(active(X:S)) -> U41#(X:S) 118.39/124.32 U41#(mark(X:S)) -> U41#(X:S) 118.39/124.32 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.39/124.32 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.39/124.32 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.39/124.32 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.39/124.32 U52#(active(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(mark(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.39/124.32 U61#(active(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(mark(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(active(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(mark(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(active(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(mark(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(active(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(mark(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 ACTIVE(U11(tt,V1:S,V2:S)) -> U12#(isNatKind(V1:S),V1:S,V2:S) 118.39/124.32 ACTIVE(U11(tt,V1:S,V2:S)) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(U12(tt,V1:S,V2:S)) -> U13#(isNatKind(V2:S),V1:S,V2:S) 118.39/124.32 ACTIVE(U12(tt,V1:S,V2:S)) -> ISNATKIND(V2:S) 118.39/124.32 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(U13(tt,V1:S,V2:S)) -> U14#(isNatKind(V2:S),V1:S,V2:S) 118.39/124.32 ACTIVE(U13(tt,V1:S,V2:S)) -> ISNATKIND(V2:S) 118.39/124.32 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(U14(tt,V1:S,V2:S)) -> U15#(isNat(V1:S),V2:S) 118.39/124.32 ACTIVE(U14(tt,V1:S,V2:S)) -> ISNAT(V1:S) 118.39/124.32 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.39/124.32 ACTIVE(U15(tt,V2:S)) -> U16#(isNat(V2:S)) 118.39/124.32 ACTIVE(U15(tt,V2:S)) -> ISNAT(V2:S) 118.39/124.32 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.39/124.32 ACTIVE(U16(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U21(tt,V1:S)) -> U22#(isNatKind(V1:S),V1:S) 118.39/124.32 ACTIVE(U21(tt,V1:S)) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 ACTIVE(U22(tt,V1:S)) -> U23#(isNat(V1:S)) 118.39/124.32 ACTIVE(U22(tt,V1:S)) -> ISNAT(V1:S) 118.39/124.32 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.39/124.32 ACTIVE(U23(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U31(tt,V2:S)) -> U32#(isNatKind(V2:S)) 118.39/124.32 ACTIVE(U31(tt,V2:S)) -> ISNATKIND(V2:S) 118.39/124.32 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.39/124.32 ACTIVE(U32(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U41(tt)) -> MARK(tt) 118.39/124.32 ACTIVE(U51(tt,N:S)) -> U52#(isNatKind(N:S),N:S) 118.39/124.32 ACTIVE(U51(tt,N:S)) -> ISNATKIND(N:S) 118.39/124.32 ACTIVE(U51(tt,N:S)) -> MARK(U52(isNatKind(N:S),N:S)) 118.39/124.32 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.39/124.32 ACTIVE(U61(tt,M:S,N:S)) -> U62#(isNatKind(M:S),M:S,N:S) 118.39/124.32 ACTIVE(U61(tt,M:S,N:S)) -> ISNATKIND(M:S) 118.39/124.32 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 ACTIVE(U62(tt,M:S,N:S)) -> U63#(isNat(N:S),M:S,N:S) 118.39/124.32 ACTIVE(U62(tt,M:S,N:S)) -> ISNAT(N:S) 118.39/124.32 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 ACTIVE(U63(tt,M:S,N:S)) -> U64#(isNatKind(N:S),M:S,N:S) 118.39/124.32 ACTIVE(U63(tt,M:S,N:S)) -> ISNATKIND(N:S) 118.39/124.32 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.39/124.32 ACTIVE(U64(tt,M:S,N:S)) -> PLUS(N:S,M:S) 118.39/124.32 ACTIVE(U64(tt,M:S,N:S)) -> S(plus(N:S,M:S)) 118.39/124.32 ACTIVE(isNat(plus(V1:S,V2:S))) -> U11#(isNatKind(V1:S),V1:S,V2:S) 118.39/124.32 ACTIVE(isNat(plus(V1:S,V2:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 ACTIVE(isNat(s(V1:S))) -> U21#(isNatKind(V1:S),V1:S) 118.39/124.32 ACTIVE(isNat(s(V1:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 ACTIVE(isNat(0)) -> MARK(tt) 118.39/124.32 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> U31#(isNatKind(V1:S),V2:S) 118.39/124.32 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 ACTIVE(isNatKind(s(V1:S))) -> U41#(isNatKind(V1:S)) 118.39/124.32 ACTIVE(isNatKind(s(V1:S))) -> ISNATKIND(V1:S) 118.39/124.32 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.39/124.32 ACTIVE(isNatKind(0)) -> MARK(tt) 118.39/124.32 ACTIVE(plus(N:S,s(M:S))) -> U61#(isNat(M:S),M:S,N:S) 118.39/124.32 ACTIVE(plus(N:S,s(M:S))) -> ISNAT(M:S) 118.39/124.32 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 ACTIVE(plus(N:S,0)) -> U51#(isNat(N:S),N:S) 118.39/124.32 ACTIVE(plus(N:S,0)) -> ISNAT(N:S) 118.39/124.32 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.39/124.32 ISNAT(active(X:S)) -> ISNAT(X:S) 118.39/124.32 ISNAT(mark(X:S)) -> ISNAT(X:S) 118.39/124.32 ISNATKIND(active(X:S)) -> ISNATKIND(X:S) 118.39/124.32 ISNATKIND(mark(X:S)) -> ISNATKIND(X:S) 118.39/124.32 MARK(U11(X1:S,X2:S,X3:S)) -> U11#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U12(X1:S,X2:S,X3:S)) -> U12#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U13(X1:S,X2:S,X3:S)) -> U13#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U14(X1:S,X2:S,X3:S)) -> U14#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U15(X1:S,X2:S)) -> U15#(mark(X1:S),X2:S) 118.39/124.32 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.39/124.32 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U16(X:S)) -> U16#(mark(X:S)) 118.39/124.32 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.39/124.32 MARK(U16(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U21(X1:S,X2:S)) -> U21#(mark(X1:S),X2:S) 118.39/124.32 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.39/124.32 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U22(X1:S,X2:S)) -> U22#(mark(X1:S),X2:S) 118.39/124.32 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.39/124.32 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U23(X:S)) -> U23#(mark(X:S)) 118.39/124.32 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.39/124.32 MARK(U23(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U31(X1:S,X2:S)) -> U31#(mark(X1:S),X2:S) 118.39/124.32 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.39/124.32 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U32(X:S)) -> U32#(mark(X:S)) 118.39/124.32 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.39/124.32 MARK(U32(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U41(X:S)) -> U41#(mark(X:S)) 118.39/124.32 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.39/124.32 MARK(U41(X:S)) -> MARK(X:S) 118.39/124.32 MARK(U51(X1:S,X2:S)) -> U51#(mark(X1:S),X2:S) 118.39/124.32 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.39/124.32 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U52(X1:S,X2:S)) -> U52#(mark(X1:S),X2:S) 118.39/124.32 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.39/124.32 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(U61(X1:S,X2:S,X3:S)) -> U61#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U62(X1:S,X2:S,X3:S)) -> U62#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U63(X1:S,X2:S,X3:S)) -> U63#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(U64(X1:S,X2:S,X3:S)) -> U64#(mark(X1:S),X2:S,X3:S) 118.39/124.32 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.39/124.32 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.39/124.32 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.39/124.32 MARK(plus(X1:S,X2:S)) -> PLUS(mark(X1:S),mark(X2:S)) 118.39/124.32 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.39/124.32 MARK(s(X:S)) -> MARK(X:S) 118.39/124.32 MARK(s(X:S)) -> S(mark(X:S)) 118.39/124.32 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.39/124.32 S(active(X:S)) -> S(X:S) 118.39/124.32 S(mark(X:S)) -> S(X:S) 118.39/124.32 -> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->Strongly Connected Components: 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 S(active(X:S)) -> S(X:S) 118.39/124.32 S(mark(X:S)) -> S(X:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.39/124.32 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 ISNATKIND(active(X:S)) -> ISNATKIND(X:S) 118.39/124.32 ISNATKIND(mark(X:S)) -> ISNATKIND(X:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 ISNAT(active(X:S)) -> ISNAT(X:S) 118.39/124.32 ISNAT(mark(X:S)) -> ISNAT(X:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 U64#(active(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(mark(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 U63#(active(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(mark(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 U62#(active(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(mark(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 U61#(active(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(mark(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.32 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.32 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.32 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.32 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.32 mark(0) -> active(0) 118.39/124.32 mark(tt) -> active(tt) 118.39/124.32 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.32 s(active(X:S)) -> s(X:S) 118.39/124.32 s(mark(X:S)) -> s(X:S) 118.39/124.32 ->->Cycle: 118.39/124.32 ->->-> Pairs: 118.39/124.32 U52#(active(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(mark(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.39/124.32 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.39/124.32 ->->-> Rules: 118.39/124.32 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.32 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.32 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.32 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.32 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.32 U16(active(X:S)) -> U16(X:S) 118.39/124.32 U16(mark(X:S)) -> U16(X:S) 118.39/124.32 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.32 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.32 U23(active(X:S)) -> U23(X:S) 118.39/124.32 U23(mark(X:S)) -> U23(X:S) 118.39/124.32 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.32 U32(active(X:S)) -> U32(X:S) 118.39/124.32 U32(mark(X:S)) -> U32(X:S) 118.39/124.32 U41(active(X:S)) -> U41(X:S) 118.39/124.32 U41(mark(X:S)) -> U41(X:S) 118.39/124.32 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.32 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.32 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.32 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.32 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.32 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.32 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.32 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.32 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.32 active(U16(tt)) -> mark(tt) 118.39/124.32 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.32 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.32 active(U23(tt)) -> mark(tt) 118.39/124.32 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.32 active(U32(tt)) -> mark(tt) 118.39/124.32 active(U41(tt)) -> mark(tt) 118.39/124.32 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.32 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.32 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.32 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.32 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.32 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.32 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.32 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.32 active(isNat(0)) -> mark(tt) 118.39/124.32 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.32 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.32 active(isNatKind(0)) -> mark(tt) 118.39/124.32 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.32 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.32 isNat(active(X:S)) -> isNat(X:S) 118.39/124.32 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.32 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.32 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.32 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.32 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.32 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.32 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.32 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.32 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.32 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.32 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.32 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.32 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.32 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.33 mark(0) -> active(0) 118.39/124.33 mark(tt) -> active(tt) 118.39/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.33 s(active(X:S)) -> s(X:S) 118.39/124.33 s(mark(X:S)) -> s(X:S) 118.39/124.33 ->->Cycle: 118.39/124.33 ->->-> Pairs: 118.39/124.33 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.39/124.33 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.39/124.33 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.39/124.33 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.39/124.33 ->->-> Rules: 118.39/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.33 U16(active(X:S)) -> U16(X:S) 118.39/124.33 U16(mark(X:S)) -> U16(X:S) 118.39/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.33 U23(active(X:S)) -> U23(X:S) 118.39/124.33 U23(mark(X:S)) -> U23(X:S) 118.39/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.33 U32(active(X:S)) -> U32(X:S) 118.39/124.33 U32(mark(X:S)) -> U32(X:S) 118.39/124.33 U41(active(X:S)) -> U41(X:S) 118.39/124.33 U41(mark(X:S)) -> U41(X:S) 118.39/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.33 active(U16(tt)) -> mark(tt) 118.39/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.33 active(U23(tt)) -> mark(tt) 118.39/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.33 active(U32(tt)) -> mark(tt) 118.39/124.33 active(U41(tt)) -> mark(tt) 118.39/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.33 active(isNat(0)) -> mark(tt) 118.39/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.33 active(isNatKind(0)) -> mark(tt) 118.39/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.33 isNat(active(X:S)) -> isNat(X:S) 118.39/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.33 mark(0) -> active(0) 118.39/124.33 mark(tt) -> active(tt) 118.39/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.33 s(active(X:S)) -> s(X:S) 118.39/124.33 s(mark(X:S)) -> s(X:S) 118.39/124.33 ->->Cycle: 118.39/124.33 ->->-> Pairs: 118.39/124.33 U41#(active(X:S)) -> U41#(X:S) 118.39/124.33 U41#(mark(X:S)) -> U41#(X:S) 118.39/124.33 ->->-> Rules: 118.39/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.33 U16(active(X:S)) -> U16(X:S) 118.39/124.33 U16(mark(X:S)) -> U16(X:S) 118.39/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.33 U23(active(X:S)) -> U23(X:S) 118.39/124.33 U23(mark(X:S)) -> U23(X:S) 118.39/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.33 U32(active(X:S)) -> U32(X:S) 118.39/124.33 U32(mark(X:S)) -> U32(X:S) 118.39/124.33 U41(active(X:S)) -> U41(X:S) 118.39/124.33 U41(mark(X:S)) -> U41(X:S) 118.39/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.33 active(U16(tt)) -> mark(tt) 118.39/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.33 active(U23(tt)) -> mark(tt) 118.39/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.33 active(U32(tt)) -> mark(tt) 118.39/124.33 active(U41(tt)) -> mark(tt) 118.39/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.33 active(isNat(0)) -> mark(tt) 118.39/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.33 active(isNatKind(0)) -> mark(tt) 118.39/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.33 isNat(active(X:S)) -> isNat(X:S) 118.39/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.39/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.39/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.39/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.39/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.39/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.39/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.39/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.39/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.39/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.39/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.39/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.39/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.39/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.39/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.39/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.39/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.39/124.33 mark(0) -> active(0) 118.39/124.33 mark(tt) -> active(tt) 118.39/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.39/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.39/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.39/124.33 s(active(X:S)) -> s(X:S) 118.39/124.33 s(mark(X:S)) -> s(X:S) 118.39/124.33 ->->Cycle: 118.39/124.33 ->->-> Pairs: 118.39/124.33 U32#(active(X:S)) -> U32#(X:S) 118.39/124.33 U32#(mark(X:S)) -> U32#(X:S) 118.39/124.33 ->->-> Rules: 118.39/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.39/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.39/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.39/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.39/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.39/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.39/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.39/124.33 U16(active(X:S)) -> U16(X:S) 118.39/124.33 U16(mark(X:S)) -> U16(X:S) 118.39/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.39/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.39/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.39/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.39/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.39/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.39/124.33 U23(active(X:S)) -> U23(X:S) 118.39/124.33 U23(mark(X:S)) -> U23(X:S) 118.39/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.39/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.39/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.39/124.33 U32(active(X:S)) -> U32(X:S) 118.39/124.33 U32(mark(X:S)) -> U32(X:S) 118.39/124.33 U41(active(X:S)) -> U41(X:S) 118.39/124.33 U41(mark(X:S)) -> U41(X:S) 118.39/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.39/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.39/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.39/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.39/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.39/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.39/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.39/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.39/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.39/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.39/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.39/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.39/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.39/124.33 active(U16(tt)) -> mark(tt) 118.39/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.39/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.39/124.33 active(U23(tt)) -> mark(tt) 118.39/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.39/124.33 active(U32(tt)) -> mark(tt) 118.39/124.33 active(U41(tt)) -> mark(tt) 118.39/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.39/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.39/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.39/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.39/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.39/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.39/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.39/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.39/124.33 active(isNat(0)) -> mark(tt) 118.39/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.39/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.39/124.33 active(isNatKind(0)) -> mark(tt) 118.39/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.39/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.39/124.33 isNat(active(X:S)) -> isNat(X:S) 118.39/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.39/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U31#(active(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.48/124.33 U31#(mark(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.48/124.33 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.33 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U23#(active(X:S)) -> U23#(X:S) 118.48/124.33 U23#(mark(X:S)) -> U23#(X:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U22#(active(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.48/124.33 U22#(mark(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.48/124.33 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.33 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.48/124.33 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.48/124.33 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.33 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U16#(active(X:S)) -> U16#(X:S) 118.48/124.33 U16#(mark(X:S)) -> U16#(X:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U15#(active(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.48/124.33 U15#(mark(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.48/124.33 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.48/124.33 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U14#(active(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.48/124.33 U14#(mark(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.48/124.33 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.48/124.33 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.48/124.33 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.48/124.33 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U13#(active(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.48/124.33 U13#(mark(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.48/124.33 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.48/124.33 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.48/124.33 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.48/124.33 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.48/124.33 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.48/124.33 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.48/124.33 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.48/124.33 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.48/124.33 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.48/124.33 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.48/124.33 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.48/124.33 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.48/124.33 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.48/124.33 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.48/124.33 ->->-> Rules: 118.48/124.33 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.33 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.33 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.33 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.33 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.33 U16(active(X:S)) -> U16(X:S) 118.48/124.33 U16(mark(X:S)) -> U16(X:S) 118.48/124.33 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.33 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.33 U23(active(X:S)) -> U23(X:S) 118.48/124.33 U23(mark(X:S)) -> U23(X:S) 118.48/124.33 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.33 U32(active(X:S)) -> U32(X:S) 118.48/124.33 U32(mark(X:S)) -> U32(X:S) 118.48/124.33 U41(active(X:S)) -> U41(X:S) 118.48/124.33 U41(mark(X:S)) -> U41(X:S) 118.48/124.33 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.33 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.33 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.33 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.33 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.33 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.33 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.33 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.33 active(U16(tt)) -> mark(tt) 118.48/124.33 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.33 active(U23(tt)) -> mark(tt) 118.48/124.33 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.33 active(U32(tt)) -> mark(tt) 118.48/124.33 active(U41(tt)) -> mark(tt) 118.48/124.33 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.33 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.33 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.33 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 active(isNat(0)) -> mark(tt) 118.48/124.33 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.33 active(isNatKind(0)) -> mark(tt) 118.48/124.33 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.33 isNat(active(X:S)) -> isNat(X:S) 118.48/124.33 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.33 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.33 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.33 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.33 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.33 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.33 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.33 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.33 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.33 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.33 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.33 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.33 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.33 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.33 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.33 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.33 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.33 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.33 mark(0) -> active(0) 118.48/124.33 mark(tt) -> active(tt) 118.48/124.33 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.33 s(active(X:S)) -> s(X:S) 118.48/124.33 s(mark(X:S)) -> s(X:S) 118.48/124.33 ->->Cycle: 118.48/124.33 ->->-> Pairs: 118.48/124.33 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.33 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.48/124.33 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.48/124.33 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.48/124.33 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.48/124.33 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.48/124.33 ACTIVE(U51(tt,N:S)) -> MARK(U52(isNatKind(N:S),N:S)) 118.48/124.33 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.48/124.33 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.33 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.48/124.33 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.33 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.48/124.33 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.33 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.48/124.33 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.48/124.33 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.48/124.33 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.48/124.33 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.48/124.33 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.33 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.33 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.33 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.33 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.33 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.33 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.33 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.33 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.48/124.33 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.33 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.48/124.33 MARK(U16(X:S)) -> MARK(X:S) 118.48/124.33 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.48/124.33 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.33 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.48/124.33 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.33 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.48/124.33 MARK(U23(X:S)) -> MARK(X:S) 118.48/124.33 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.48/124.33 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.33 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.48/124.33 MARK(U32(X:S)) -> MARK(X:S) 118.48/124.33 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.48/124.33 MARK(U41(X:S)) -> MARK(X:S) 118.48/124.33 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.48/124.33 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.33 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.48/124.33 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.33 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.33 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.33 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.33 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.33 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.34 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.48/124.34 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.48/124.34 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.48/124.34 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.48/124.34 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.48/124.34 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.48/124.34 MARK(s(X:S)) -> MARK(X:S) 118.48/124.34 ->->-> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 118.48/124.34 118.48/124.34 The problem is decomposed in 23 subproblems. 118.48/124.34 118.48/124.34 Problem 1.1: 118.48/124.34 118.48/124.34 Subterm Processor: 118.48/124.34 -> Pairs: 118.48/124.34 S(active(X:S)) -> S(X:S) 118.48/124.34 S(mark(X:S)) -> S(X:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Projection: 118.48/124.34 pi(S) = 1 118.48/124.34 118.48/124.34 Problem 1.1: 118.48/124.34 118.48/124.34 SCC Processor: 118.48/124.34 -> Pairs: 118.48/124.34 Empty 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Strongly Connected Components: 118.48/124.34 There is no strongly connected component 118.48/124.34 118.48/124.34 The problem is finite. 118.48/124.34 118.48/124.34 Problem 1.2: 118.48/124.34 118.48/124.34 Subterm Processor: 118.48/124.34 -> Pairs: 118.48/124.34 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.48/124.34 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 118.48/124.34 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Projection: 118.48/124.34 pi(PLUS) = 1 118.48/124.34 118.48/124.34 Problem 1.2: 118.48/124.34 118.48/124.34 SCC Processor: 118.48/124.34 -> Pairs: 118.48/124.34 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Strongly Connected Components: 118.48/124.34 ->->Cycle: 118.48/124.34 ->->-> Pairs: 118.48/124.34 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 ->->-> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 118.48/124.34 Problem 1.2: 118.48/124.34 118.48/124.34 Subterm Processor: 118.48/124.34 -> Pairs: 118.48/124.34 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Projection: 118.48/124.34 pi(PLUS) = 2 118.48/124.34 118.48/124.34 Problem 1.2: 118.48/124.34 118.48/124.34 SCC Processor: 118.48/124.34 -> Pairs: 118.48/124.34 Empty 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Strongly Connected Components: 118.48/124.34 There is no strongly connected component 118.48/124.34 118.48/124.34 The problem is finite. 118.48/124.34 118.48/124.34 Problem 1.3: 118.48/124.34 118.48/124.34 Subterm Processor: 118.48/124.34 -> Pairs: 118.48/124.34 ISNATKIND(active(X:S)) -> ISNATKIND(X:S) 118.48/124.34 ISNATKIND(mark(X:S)) -> ISNATKIND(X:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Projection: 118.48/124.34 pi(ISNATKIND) = 1 118.48/124.34 118.48/124.34 Problem 1.3: 118.48/124.34 118.48/124.34 SCC Processor: 118.48/124.34 -> Pairs: 118.48/124.34 Empty 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Strongly Connected Components: 118.48/124.34 There is no strongly connected component 118.48/124.34 118.48/124.34 The problem is finite. 118.48/124.34 118.48/124.34 Problem 1.4: 118.48/124.34 118.48/124.34 Subterm Processor: 118.48/124.34 -> Pairs: 118.48/124.34 ISNAT(active(X:S)) -> ISNAT(X:S) 118.48/124.34 ISNAT(mark(X:S)) -> ISNAT(X:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Projection: 118.48/124.34 pi(ISNAT) = 1 118.48/124.34 118.48/124.34 Problem 1.4: 118.48/124.34 118.48/124.34 SCC Processor: 118.48/124.34 -> Pairs: 118.48/124.34 Empty 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Strongly Connected Components: 118.48/124.34 There is no strongly connected component 118.48/124.34 118.48/124.34 The problem is finite. 118.48/124.34 118.48/124.34 Problem 1.5: 118.48/124.34 118.48/124.34 Subterm Processor: 118.48/124.34 -> Pairs: 118.48/124.34 U64#(active(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(mark(X1:S),X2:S,X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.34 U16(active(X:S)) -> U16(X:S) 118.48/124.34 U16(mark(X:S)) -> U16(X:S) 118.48/124.34 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.34 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.34 U23(active(X:S)) -> U23(X:S) 118.48/124.34 U23(mark(X:S)) -> U23(X:S) 118.48/124.34 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.34 U32(active(X:S)) -> U32(X:S) 118.48/124.34 U32(mark(X:S)) -> U32(X:S) 118.48/124.34 U41(active(X:S)) -> U41(X:S) 118.48/124.34 U41(mark(X:S)) -> U41(X:S) 118.48/124.34 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.34 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.34 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.34 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.34 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.34 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.34 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.34 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.34 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.34 active(U16(tt)) -> mark(tt) 118.48/124.34 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.34 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.34 active(U23(tt)) -> mark(tt) 118.48/124.34 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.34 active(U32(tt)) -> mark(tt) 118.48/124.34 active(U41(tt)) -> mark(tt) 118.48/124.34 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.34 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.34 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.34 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.34 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.34 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.34 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.34 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.34 active(isNat(0)) -> mark(tt) 118.48/124.34 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.34 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.34 active(isNatKind(0)) -> mark(tt) 118.48/124.34 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.34 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.34 isNat(active(X:S)) -> isNat(X:S) 118.48/124.34 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.34 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.34 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.34 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.34 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.34 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.34 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.34 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.34 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.34 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.34 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.34 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.34 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.34 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.34 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.34 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.34 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.34 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.34 mark(0) -> active(0) 118.48/124.34 mark(tt) -> active(tt) 118.48/124.34 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.34 s(active(X:S)) -> s(X:S) 118.48/124.34 s(mark(X:S)) -> s(X:S) 118.48/124.34 ->Projection: 118.48/124.34 pi(U64#) = 1 118.48/124.34 118.48/124.34 Problem 1.5: 118.48/124.34 118.48/124.34 SCC Processor: 118.48/124.34 -> Pairs: 118.48/124.34 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.34 -> Rules: 118.48/124.34 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.34 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.34 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.34 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.34 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Strongly Connected Components: 118.48/124.35 ->->Cycle: 118.48/124.35 ->->-> Pairs: 118.48/124.35 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 ->->-> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 118.48/124.35 Problem 1.5: 118.48/124.35 118.48/124.35 Subterm Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U64#(X1:S,active(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,mark(X2:S),X3:S) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Projection: 118.48/124.35 pi(U64#) = 2 118.48/124.35 118.48/124.35 Problem 1.5: 118.48/124.35 118.48/124.35 SCC Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Strongly Connected Components: 118.48/124.35 ->->Cycle: 118.48/124.35 ->->-> Pairs: 118.48/124.35 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 ->->-> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 118.48/124.35 Problem 1.5: 118.48/124.35 118.48/124.35 Subterm Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U64#(X1:S,X2:S,active(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 U64#(X1:S,X2:S,mark(X3:S)) -> U64#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Projection: 118.48/124.35 pi(U64#) = 3 118.48/124.35 118.48/124.35 Problem 1.5: 118.48/124.35 118.48/124.35 SCC Processor: 118.48/124.35 -> Pairs: 118.48/124.35 Empty 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Strongly Connected Components: 118.48/124.35 There is no strongly connected component 118.48/124.35 118.48/124.35 The problem is finite. 118.48/124.35 118.48/124.35 Problem 1.6: 118.48/124.35 118.48/124.35 Subterm Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U63#(active(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(mark(X1:S),X2:S,X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Projection: 118.48/124.35 pi(U63#) = 1 118.48/124.35 118.48/124.35 Problem 1.6: 118.48/124.35 118.48/124.35 SCC Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Strongly Connected Components: 118.48/124.35 ->->Cycle: 118.48/124.35 ->->-> Pairs: 118.48/124.35 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 ->->-> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 118.48/124.35 Problem 1.6: 118.48/124.35 118.48/124.35 Subterm Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U63#(X1:S,active(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,mark(X2:S),X3:S) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Projection: 118.48/124.35 pi(U63#) = 2 118.48/124.35 118.48/124.35 Problem 1.6: 118.48/124.35 118.48/124.35 SCC Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 ->Strongly Connected Components: 118.48/124.35 ->->Cycle: 118.48/124.35 ->->-> Pairs: 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 ->->-> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.35 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.35 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.35 active(U16(tt)) -> mark(tt) 118.48/124.35 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.35 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.35 active(U23(tt)) -> mark(tt) 118.48/124.35 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.35 active(U32(tt)) -> mark(tt) 118.48/124.35 active(U41(tt)) -> mark(tt) 118.48/124.35 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.35 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.35 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.35 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.35 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.35 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.35 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.35 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.35 active(isNat(0)) -> mark(tt) 118.48/124.35 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.35 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.35 active(isNatKind(0)) -> mark(tt) 118.48/124.35 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.35 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.35 isNat(active(X:S)) -> isNat(X:S) 118.48/124.35 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.35 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.35 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.35 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.35 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.35 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.35 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.35 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.35 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.35 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.35 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.35 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.35 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.35 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.35 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.35 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.35 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.35 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.35 mark(0) -> active(0) 118.48/124.35 mark(tt) -> active(tt) 118.48/124.35 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.35 s(active(X:S)) -> s(X:S) 118.48/124.35 s(mark(X:S)) -> s(X:S) 118.48/124.35 118.48/124.35 Problem 1.6: 118.48/124.35 118.48/124.35 Subterm Processor: 118.48/124.35 -> Pairs: 118.48/124.35 U63#(X1:S,X2:S,active(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 U63#(X1:S,X2:S,mark(X3:S)) -> U63#(X1:S,X2:S,X3:S) 118.48/124.35 -> Rules: 118.48/124.35 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.35 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.35 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.35 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.35 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.35 U16(active(X:S)) -> U16(X:S) 118.48/124.35 U16(mark(X:S)) -> U16(X:S) 118.48/124.35 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.35 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.35 U23(active(X:S)) -> U23(X:S) 118.48/124.35 U23(mark(X:S)) -> U23(X:S) 118.48/124.35 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.35 U32(active(X:S)) -> U32(X:S) 118.48/124.35 U32(mark(X:S)) -> U32(X:S) 118.48/124.35 U41(active(X:S)) -> U41(X:S) 118.48/124.35 U41(mark(X:S)) -> U41(X:S) 118.48/124.35 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.35 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.35 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.35 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.35 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.35 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.35 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Projection: 118.48/124.36 pi(U63#) = 3 118.48/124.36 118.48/124.36 Problem 1.6: 118.48/124.36 118.48/124.36 SCC Processor: 118.48/124.36 -> Pairs: 118.48/124.36 Empty 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Strongly Connected Components: 118.48/124.36 There is no strongly connected component 118.48/124.36 118.48/124.36 The problem is finite. 118.48/124.36 118.48/124.36 Problem 1.7: 118.48/124.36 118.48/124.36 Subterm Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U62#(active(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(mark(X1:S),X2:S,X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Projection: 118.48/124.36 pi(U62#) = 1 118.48/124.36 118.48/124.36 Problem 1.7: 118.48/124.36 118.48/124.36 SCC Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Strongly Connected Components: 118.48/124.36 ->->Cycle: 118.48/124.36 ->->-> Pairs: 118.48/124.36 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 ->->-> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 118.48/124.36 Problem 1.7: 118.48/124.36 118.48/124.36 Subterm Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U62#(X1:S,active(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,mark(X2:S),X3:S) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Projection: 118.48/124.36 pi(U62#) = 2 118.48/124.36 118.48/124.36 Problem 1.7: 118.48/124.36 118.48/124.36 SCC Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Strongly Connected Components: 118.48/124.36 ->->Cycle: 118.48/124.36 ->->-> Pairs: 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 ->->-> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 118.48/124.36 Problem 1.7: 118.48/124.36 118.48/124.36 Subterm Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U62#(X1:S,X2:S,active(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 U62#(X1:S,X2:S,mark(X3:S)) -> U62#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Projection: 118.48/124.36 pi(U62#) = 3 118.48/124.36 118.48/124.36 Problem 1.7: 118.48/124.36 118.48/124.36 SCC Processor: 118.48/124.36 -> Pairs: 118.48/124.36 Empty 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Strongly Connected Components: 118.48/124.36 There is no strongly connected component 118.48/124.36 118.48/124.36 The problem is finite. 118.48/124.36 118.48/124.36 Problem 1.8: 118.48/124.36 118.48/124.36 Subterm Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U61#(active(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(mark(X1:S),X2:S,X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Projection: 118.48/124.36 pi(U61#) = 1 118.48/124.36 118.48/124.36 Problem 1.8: 118.48/124.36 118.48/124.36 SCC Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 ->Strongly Connected Components: 118.48/124.36 ->->Cycle: 118.48/124.36 ->->-> Pairs: 118.48/124.36 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 ->->-> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.36 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.36 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.36 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.36 active(isNat(0)) -> mark(tt) 118.48/124.36 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.36 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.36 active(isNatKind(0)) -> mark(tt) 118.48/124.36 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.36 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.36 isNat(active(X:S)) -> isNat(X:S) 118.48/124.36 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.36 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.36 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.36 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.36 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.36 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.36 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.36 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.36 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.36 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.36 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.36 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.36 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.36 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.36 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.36 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.36 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.36 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.36 mark(0) -> active(0) 118.48/124.36 mark(tt) -> active(tt) 118.48/124.36 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.36 s(active(X:S)) -> s(X:S) 118.48/124.36 s(mark(X:S)) -> s(X:S) 118.48/124.36 118.48/124.36 Problem 1.8: 118.48/124.36 118.48/124.36 Subterm Processor: 118.48/124.36 -> Pairs: 118.48/124.36 U61#(X1:S,active(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,mark(X2:S),X3:S) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.36 -> Rules: 118.48/124.36 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.36 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.36 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.36 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.36 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.36 U16(active(X:S)) -> U16(X:S) 118.48/124.36 U16(mark(X:S)) -> U16(X:S) 118.48/124.36 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.36 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.36 U23(active(X:S)) -> U23(X:S) 118.48/124.36 U23(mark(X:S)) -> U23(X:S) 118.48/124.36 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.36 U32(active(X:S)) -> U32(X:S) 118.48/124.36 U32(mark(X:S)) -> U32(X:S) 118.48/124.36 U41(active(X:S)) -> U41(X:S) 118.48/124.36 U41(mark(X:S)) -> U41(X:S) 118.48/124.36 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.36 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.36 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.36 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.36 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.36 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.36 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.36 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.36 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.36 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.36 active(U16(tt)) -> mark(tt) 118.48/124.36 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.36 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.36 active(U23(tt)) -> mark(tt) 118.48/124.36 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.36 active(U32(tt)) -> mark(tt) 118.48/124.36 active(U41(tt)) -> mark(tt) 118.48/124.36 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.36 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.36 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.36 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Projection: 118.48/124.37 pi(U61#) = 2 118.48/124.37 118.48/124.37 Problem 1.8: 118.48/124.37 118.48/124.37 SCC Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.37 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Strongly Connected Components: 118.48/124.37 ->->Cycle: 118.48/124.37 ->->-> Pairs: 118.48/124.37 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.37 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.37 ->->-> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 118.48/124.37 Problem 1.8: 118.48/124.37 118.48/124.37 Subterm Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U61#(X1:S,X2:S,active(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.37 U61#(X1:S,X2:S,mark(X3:S)) -> U61#(X1:S,X2:S,X3:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Projection: 118.48/124.37 pi(U61#) = 3 118.48/124.37 118.48/124.37 Problem 1.8: 118.48/124.37 118.48/124.37 SCC Processor: 118.48/124.37 -> Pairs: 118.48/124.37 Empty 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Strongly Connected Components: 118.48/124.37 There is no strongly connected component 118.48/124.37 118.48/124.37 The problem is finite. 118.48/124.37 118.48/124.37 Problem 1.9: 118.48/124.37 118.48/124.37 Subterm Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U52#(active(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.48/124.37 U52#(mark(X1:S),X2:S) -> U52#(X1:S,X2:S) 118.48/124.37 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Projection: 118.48/124.37 pi(U52#) = 1 118.48/124.37 118.48/124.37 Problem 1.9: 118.48/124.37 118.48/124.37 SCC Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Strongly Connected Components: 118.48/124.37 ->->Cycle: 118.48/124.37 ->->-> Pairs: 118.48/124.37 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 ->->-> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 118.48/124.37 Problem 1.9: 118.48/124.37 118.48/124.37 Subterm Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U52#(X1:S,active(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 U52#(X1:S,mark(X2:S)) -> U52#(X1:S,X2:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Projection: 118.48/124.37 pi(U52#) = 2 118.48/124.37 118.48/124.37 Problem 1.9: 118.48/124.37 118.48/124.37 SCC Processor: 118.48/124.37 -> Pairs: 118.48/124.37 Empty 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Strongly Connected Components: 118.48/124.37 There is no strongly connected component 118.48/124.37 118.48/124.37 The problem is finite. 118.48/124.37 118.48/124.37 Problem 1.10: 118.48/124.37 118.48/124.37 Subterm Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U51#(active(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.48/124.37 U51#(mark(X1:S),X2:S) -> U51#(X1:S,X2:S) 118.48/124.37 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Projection: 118.48/124.37 pi(U51#) = 1 118.48/124.37 118.48/124.37 Problem 1.10: 118.48/124.37 118.48/124.37 SCC Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Strongly Connected Components: 118.48/124.37 ->->Cycle: 118.48/124.37 ->->-> Pairs: 118.48/124.37 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 ->->-> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 118.48/124.37 Problem 1.10: 118.48/124.37 118.48/124.37 Subterm Processor: 118.48/124.37 -> Pairs: 118.48/124.37 U51#(X1:S,active(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 U51#(X1:S,mark(X2:S)) -> U51#(X1:S,X2:S) 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.37 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.37 U16(active(X:S)) -> U16(X:S) 118.48/124.37 U16(mark(X:S)) -> U16(X:S) 118.48/124.37 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.37 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.37 U23(active(X:S)) -> U23(X:S) 118.48/124.37 U23(mark(X:S)) -> U23(X:S) 118.48/124.37 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.37 U32(active(X:S)) -> U32(X:S) 118.48/124.37 U32(mark(X:S)) -> U32(X:S) 118.48/124.37 U41(active(X:S)) -> U41(X:S) 118.48/124.37 U41(mark(X:S)) -> U41(X:S) 118.48/124.37 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.37 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.37 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.37 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.37 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.37 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.37 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.37 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.37 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.37 active(U16(tt)) -> mark(tt) 118.48/124.37 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.37 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.37 active(U23(tt)) -> mark(tt) 118.48/124.37 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.37 active(U32(tt)) -> mark(tt) 118.48/124.37 active(U41(tt)) -> mark(tt) 118.48/124.37 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.37 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.37 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.37 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.37 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.37 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.37 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.37 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.37 active(isNat(0)) -> mark(tt) 118.48/124.37 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.37 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.37 active(isNatKind(0)) -> mark(tt) 118.48/124.37 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.37 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.37 isNat(active(X:S)) -> isNat(X:S) 118.48/124.37 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.37 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.37 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.37 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.37 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.37 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.37 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.37 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.37 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.37 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.37 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.37 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.37 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.37 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.37 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.37 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.37 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.37 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.37 mark(0) -> active(0) 118.48/124.37 mark(tt) -> active(tt) 118.48/124.37 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.37 s(active(X:S)) -> s(X:S) 118.48/124.37 s(mark(X:S)) -> s(X:S) 118.48/124.37 ->Projection: 118.48/124.37 pi(U51#) = 2 118.48/124.37 118.48/124.37 Problem 1.10: 118.48/124.37 118.48/124.37 SCC Processor: 118.48/124.37 -> Pairs: 118.48/124.37 Empty 118.48/124.37 -> Rules: 118.48/124.37 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.37 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.37 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.37 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Strongly Connected Components: 118.48/124.38 There is no strongly connected component 118.48/124.38 118.48/124.38 The problem is finite. 118.48/124.38 118.48/124.38 Problem 1.11: 118.48/124.38 118.48/124.38 Subterm Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U41#(active(X:S)) -> U41#(X:S) 118.48/124.38 U41#(mark(X:S)) -> U41#(X:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Projection: 118.48/124.38 pi(U41#) = 1 118.48/124.38 118.48/124.38 Problem 1.11: 118.48/124.38 118.48/124.38 SCC Processor: 118.48/124.38 -> Pairs: 118.48/124.38 Empty 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Strongly Connected Components: 118.48/124.38 There is no strongly connected component 118.48/124.38 118.48/124.38 The problem is finite. 118.48/124.38 118.48/124.38 Problem 1.12: 118.48/124.38 118.48/124.38 Subterm Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U32#(active(X:S)) -> U32#(X:S) 118.48/124.38 U32#(mark(X:S)) -> U32#(X:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Projection: 118.48/124.38 pi(U32#) = 1 118.48/124.38 118.48/124.38 Problem 1.12: 118.48/124.38 118.48/124.38 SCC Processor: 118.48/124.38 -> Pairs: 118.48/124.38 Empty 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Strongly Connected Components: 118.48/124.38 There is no strongly connected component 118.48/124.38 118.48/124.38 The problem is finite. 118.48/124.38 118.48/124.38 Problem 1.13: 118.48/124.38 118.48/124.38 Subterm Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U31#(active(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.48/124.38 U31#(mark(X1:S),X2:S) -> U31#(X1:S,X2:S) 118.48/124.38 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Projection: 118.48/124.38 pi(U31#) = 1 118.48/124.38 118.48/124.38 Problem 1.13: 118.48/124.38 118.48/124.38 SCC Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Strongly Connected Components: 118.48/124.38 ->->Cycle: 118.48/124.38 ->->-> Pairs: 118.48/124.38 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 ->->-> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 118.48/124.38 Problem 1.13: 118.48/124.38 118.48/124.38 Subterm Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U31#(X1:S,active(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 U31#(X1:S,mark(X2:S)) -> U31#(X1:S,X2:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Projection: 118.48/124.38 pi(U31#) = 2 118.48/124.38 118.48/124.38 Problem 1.13: 118.48/124.38 118.48/124.38 SCC Processor: 118.48/124.38 -> Pairs: 118.48/124.38 Empty 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Strongly Connected Components: 118.48/124.38 There is no strongly connected component 118.48/124.38 118.48/124.38 The problem is finite. 118.48/124.38 118.48/124.38 Problem 1.14: 118.48/124.38 118.48/124.38 Subterm Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U23#(active(X:S)) -> U23#(X:S) 118.48/124.38 U23#(mark(X:S)) -> U23#(X:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Projection: 118.48/124.38 pi(U23#) = 1 118.48/124.38 118.48/124.38 Problem 1.14: 118.48/124.38 118.48/124.38 SCC Processor: 118.48/124.38 -> Pairs: 118.48/124.38 Empty 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Strongly Connected Components: 118.48/124.38 There is no strongly connected component 118.48/124.38 118.48/124.38 The problem is finite. 118.48/124.38 118.48/124.38 Problem 1.15: 118.48/124.38 118.48/124.38 Subterm Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U22#(active(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.48/124.38 U22#(mark(X1:S),X2:S) -> U22#(X1:S,X2:S) 118.48/124.38 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.38 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.38 U23(active(X:S)) -> U23(X:S) 118.48/124.38 U23(mark(X:S)) -> U23(X:S) 118.48/124.38 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.38 U32(active(X:S)) -> U32(X:S) 118.48/124.38 U32(mark(X:S)) -> U32(X:S) 118.48/124.38 U41(active(X:S)) -> U41(X:S) 118.48/124.38 U41(mark(X:S)) -> U41(X:S) 118.48/124.38 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.38 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.38 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.38 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.38 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.38 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.38 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.38 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.38 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.38 active(U16(tt)) -> mark(tt) 118.48/124.38 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.38 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.38 active(U23(tt)) -> mark(tt) 118.48/124.38 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.38 active(U32(tt)) -> mark(tt) 118.48/124.38 active(U41(tt)) -> mark(tt) 118.48/124.38 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.38 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.38 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.38 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.38 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.38 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.38 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.38 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.38 active(isNat(0)) -> mark(tt) 118.48/124.38 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.38 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.38 active(isNatKind(0)) -> mark(tt) 118.48/124.38 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.38 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.38 isNat(active(X:S)) -> isNat(X:S) 118.48/124.38 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.38 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.38 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.38 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.38 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.38 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.38 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.38 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.38 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.38 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.38 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.38 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.38 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.38 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.38 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.38 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.38 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.38 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.38 mark(0) -> active(0) 118.48/124.38 mark(tt) -> active(tt) 118.48/124.38 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.38 s(active(X:S)) -> s(X:S) 118.48/124.38 s(mark(X:S)) -> s(X:S) 118.48/124.38 ->Projection: 118.48/124.38 pi(U22#) = 1 118.48/124.38 118.48/124.38 Problem 1.15: 118.48/124.38 118.48/124.38 SCC Processor: 118.48/124.38 -> Pairs: 118.48/124.38 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.38 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.38 -> Rules: 118.48/124.38 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.38 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.38 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.38 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.38 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.38 U16(active(X:S)) -> U16(X:S) 118.48/124.38 U16(mark(X:S)) -> U16(X:S) 118.48/124.38 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.38 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Strongly Connected Components: 118.48/124.39 ->->Cycle: 118.48/124.39 ->->-> Pairs: 118.48/124.39 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.39 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.39 ->->-> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 118.48/124.39 Problem 1.15: 118.48/124.39 118.48/124.39 Subterm Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U22#(X1:S,active(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.39 U22#(X1:S,mark(X2:S)) -> U22#(X1:S,X2:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Projection: 118.48/124.39 pi(U22#) = 2 118.48/124.39 118.48/124.39 Problem 1.15: 118.48/124.39 118.48/124.39 SCC Processor: 118.48/124.39 -> Pairs: 118.48/124.39 Empty 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Strongly Connected Components: 118.48/124.39 There is no strongly connected component 118.48/124.39 118.48/124.39 The problem is finite. 118.48/124.39 118.48/124.39 Problem 1.16: 118.48/124.39 118.48/124.39 Subterm Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U21#(active(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.48/124.39 U21#(mark(X1:S),X2:S) -> U21#(X1:S,X2:S) 118.48/124.39 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Projection: 118.48/124.39 pi(U21#) = 1 118.48/124.39 118.48/124.39 Problem 1.16: 118.48/124.39 118.48/124.39 SCC Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Strongly Connected Components: 118.48/124.39 ->->Cycle: 118.48/124.39 ->->-> Pairs: 118.48/124.39 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 ->->-> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 118.48/124.39 Problem 1.16: 118.48/124.39 118.48/124.39 Subterm Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U21#(X1:S,active(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 U21#(X1:S,mark(X2:S)) -> U21#(X1:S,X2:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Projection: 118.48/124.39 pi(U21#) = 2 118.48/124.39 118.48/124.39 Problem 1.16: 118.48/124.39 118.48/124.39 SCC Processor: 118.48/124.39 -> Pairs: 118.48/124.39 Empty 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Strongly Connected Components: 118.48/124.39 There is no strongly connected component 118.48/124.39 118.48/124.39 The problem is finite. 118.48/124.39 118.48/124.39 Problem 1.17: 118.48/124.39 118.48/124.39 Subterm Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U16#(active(X:S)) -> U16#(X:S) 118.48/124.39 U16#(mark(X:S)) -> U16#(X:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Projection: 118.48/124.39 pi(U16#) = 1 118.48/124.39 118.48/124.39 Problem 1.17: 118.48/124.39 118.48/124.39 SCC Processor: 118.48/124.39 -> Pairs: 118.48/124.39 Empty 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Strongly Connected Components: 118.48/124.39 There is no strongly connected component 118.48/124.39 118.48/124.39 The problem is finite. 118.48/124.39 118.48/124.39 Problem 1.18: 118.48/124.39 118.48/124.39 Subterm Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U15#(active(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.48/124.39 U15#(mark(X1:S),X2:S) -> U15#(X1:S,X2:S) 118.48/124.39 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.48/124.39 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.48/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.48/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.48/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.48/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.48/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.48/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.48/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.48/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.48/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.48/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.48/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.48/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.48/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.48/124.39 mark(0) -> active(0) 118.48/124.39 mark(tt) -> active(tt) 118.48/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.48/124.39 s(active(X:S)) -> s(X:S) 118.48/124.39 s(mark(X:S)) -> s(X:S) 118.48/124.39 ->Projection: 118.48/124.39 pi(U15#) = 1 118.48/124.39 118.48/124.39 Problem 1.18: 118.48/124.39 118.48/124.39 SCC Processor: 118.48/124.39 -> Pairs: 118.48/124.39 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.48/124.39 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.48/124.39 -> Rules: 118.48/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.48/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.48/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.48/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.48/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.48/124.39 U16(active(X:S)) -> U16(X:S) 118.48/124.39 U16(mark(X:S)) -> U16(X:S) 118.48/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.48/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.48/124.39 U23(active(X:S)) -> U23(X:S) 118.48/124.39 U23(mark(X:S)) -> U23(X:S) 118.48/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.48/124.39 U32(active(X:S)) -> U32(X:S) 118.48/124.39 U32(mark(X:S)) -> U32(X:S) 118.48/124.39 U41(active(X:S)) -> U41(X:S) 118.48/124.39 U41(mark(X:S)) -> U41(X:S) 118.48/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.48/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.48/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.48/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.48/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.48/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.48/124.39 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.48/124.39 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.48/124.39 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.48/124.39 active(U16(tt)) -> mark(tt) 118.48/124.39 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.48/124.39 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.48/124.39 active(U23(tt)) -> mark(tt) 118.48/124.39 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.48/124.39 active(U32(tt)) -> mark(tt) 118.48/124.39 active(U41(tt)) -> mark(tt) 118.48/124.39 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.48/124.39 active(U52(tt,N:S)) -> mark(N:S) 118.48/124.39 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.48/124.39 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.48/124.39 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.48/124.39 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.48/124.39 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.48/124.39 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.48/124.39 active(isNat(0)) -> mark(tt) 118.48/124.39 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.48/124.39 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.48/124.39 active(isNatKind(0)) -> mark(tt) 118.48/124.39 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.48/124.39 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.48/124.39 isNat(active(X:S)) -> isNat(X:S) 118.48/124.39 isNat(mark(X:S)) -> isNat(X:S) 118.48/124.39 isNatKind(active(X:S)) -> isNatKind(X:S) 118.48/124.39 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.48/124.39 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.48/124.39 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.39 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.39 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.39 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.39 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.39 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.39 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.39 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.39 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.39 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.39 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.39 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.39 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.39 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.39 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.39 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.39 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.39 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.39 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.39 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.39 mark(0) -> active(0) 118.52/124.39 mark(tt) -> active(tt) 118.52/124.39 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.39 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.39 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.39 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.39 s(active(X:S)) -> s(X:S) 118.52/124.39 s(mark(X:S)) -> s(X:S) 118.52/124.39 ->Strongly Connected Components: 118.52/124.39 ->->Cycle: 118.52/124.39 ->->-> Pairs: 118.52/124.39 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.52/124.39 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.52/124.39 ->->-> Rules: 118.52/124.39 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.39 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.39 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.39 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.39 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.39 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.39 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.39 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.39 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.39 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.39 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.39 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.39 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.39 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.39 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.39 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.39 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.39 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.39 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.39 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.39 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.39 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.39 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.39 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.39 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.39 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.39 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.39 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.39 U16(active(X:S)) -> U16(X:S) 118.52/124.39 U16(mark(X:S)) -> U16(X:S) 118.52/124.39 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.39 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.39 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.39 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.39 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.39 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.39 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.39 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.39 U23(active(X:S)) -> U23(X:S) 118.52/124.39 U23(mark(X:S)) -> U23(X:S) 118.52/124.39 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.39 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.39 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.39 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.39 U32(active(X:S)) -> U32(X:S) 118.52/124.39 U32(mark(X:S)) -> U32(X:S) 118.52/124.39 U41(active(X:S)) -> U41(X:S) 118.52/124.39 U41(mark(X:S)) -> U41(X:S) 118.52/124.39 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.39 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.39 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.39 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.39 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.39 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.39 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.39 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.39 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.39 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.39 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.39 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.39 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.39 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.39 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.39 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.39 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.39 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.39 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.39 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.39 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.39 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.39 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.39 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.39 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.39 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.39 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.39 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.39 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.39 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.39 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.39 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 118.52/124.40 Problem 1.18: 118.52/124.40 118.52/124.40 Subterm Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U15#(X1:S,active(X2:S)) -> U15#(X1:S,X2:S) 118.52/124.40 U15#(X1:S,mark(X2:S)) -> U15#(X1:S,X2:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Projection: 118.52/124.40 pi(U15#) = 2 118.52/124.40 118.52/124.40 Problem 1.18: 118.52/124.40 118.52/124.40 SCC Processor: 118.52/124.40 -> Pairs: 118.52/124.40 Empty 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Strongly Connected Components: 118.52/124.40 There is no strongly connected component 118.52/124.40 118.52/124.40 The problem is finite. 118.52/124.40 118.52/124.40 Problem 1.19: 118.52/124.40 118.52/124.40 Subterm Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U14#(active(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(mark(X1:S),X2:S,X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Projection: 118.52/124.40 pi(U14#) = 1 118.52/124.40 118.52/124.40 Problem 1.19: 118.52/124.40 118.52/124.40 SCC Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Strongly Connected Components: 118.52/124.40 ->->Cycle: 118.52/124.40 ->->-> Pairs: 118.52/124.40 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 ->->-> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 118.52/124.40 Problem 1.19: 118.52/124.40 118.52/124.40 Subterm Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U14#(X1:S,active(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,mark(X2:S),X3:S) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Projection: 118.52/124.40 pi(U14#) = 2 118.52/124.40 118.52/124.40 Problem 1.19: 118.52/124.40 118.52/124.40 SCC Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Strongly Connected Components: 118.52/124.40 ->->Cycle: 118.52/124.40 ->->-> Pairs: 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 ->->-> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 118.52/124.40 Problem 1.19: 118.52/124.40 118.52/124.40 Subterm Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U14#(X1:S,X2:S,active(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 U14#(X1:S,X2:S,mark(X3:S)) -> U14#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Projection: 118.52/124.40 pi(U14#) = 3 118.52/124.40 118.52/124.40 Problem 1.19: 118.52/124.40 118.52/124.40 SCC Processor: 118.52/124.40 -> Pairs: 118.52/124.40 Empty 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Strongly Connected Components: 118.52/124.40 There is no strongly connected component 118.52/124.40 118.52/124.40 The problem is finite. 118.52/124.40 118.52/124.40 Problem 1.20: 118.52/124.40 118.52/124.40 Subterm Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U13#(active(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(mark(X1:S),X2:S,X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Projection: 118.52/124.40 pi(U13#) = 1 118.52/124.40 118.52/124.40 Problem 1.20: 118.52/124.40 118.52/124.40 SCC Processor: 118.52/124.40 -> Pairs: 118.52/124.40 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 -> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.40 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.40 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.40 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.40 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.40 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.40 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.40 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.40 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.40 mark(0) -> active(0) 118.52/124.40 mark(tt) -> active(tt) 118.52/124.40 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.40 s(active(X:S)) -> s(X:S) 118.52/124.40 s(mark(X:S)) -> s(X:S) 118.52/124.40 ->Strongly Connected Components: 118.52/124.40 ->->Cycle: 118.52/124.40 ->->-> Pairs: 118.52/124.40 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.40 ->->-> Rules: 118.52/124.40 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.40 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.40 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.40 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.40 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.40 U16(active(X:S)) -> U16(X:S) 118.52/124.40 U16(mark(X:S)) -> U16(X:S) 118.52/124.40 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.40 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.40 U23(active(X:S)) -> U23(X:S) 118.52/124.40 U23(mark(X:S)) -> U23(X:S) 118.52/124.40 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.40 U32(active(X:S)) -> U32(X:S) 118.52/124.40 U32(mark(X:S)) -> U32(X:S) 118.52/124.40 U41(active(X:S)) -> U41(X:S) 118.52/124.40 U41(mark(X:S)) -> U41(X:S) 118.52/124.40 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.40 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.40 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.40 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.40 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.40 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.40 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.40 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.40 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.40 active(U16(tt)) -> mark(tt) 118.52/124.40 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.40 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.40 active(U23(tt)) -> mark(tt) 118.52/124.40 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.40 active(U32(tt)) -> mark(tt) 118.52/124.40 active(U41(tt)) -> mark(tt) 118.52/124.40 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.40 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.40 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.40 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.40 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.40 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.40 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.40 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.40 active(isNat(0)) -> mark(tt) 118.52/124.40 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.40 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.40 active(isNatKind(0)) -> mark(tt) 118.52/124.40 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.40 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.40 isNat(active(X:S)) -> isNat(X:S) 118.52/124.40 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.40 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.40 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.40 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.40 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.40 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.40 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.40 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.40 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.40 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 118.52/124.41 Problem 1.20: 118.52/124.41 118.52/124.41 Subterm Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U13#(X1:S,active(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 U13#(X1:S,mark(X2:S),X3:S) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Projection: 118.52/124.41 pi(U13#) = 2 118.52/124.41 118.52/124.41 Problem 1.20: 118.52/124.41 118.52/124.41 SCC Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Strongly Connected Components: 118.52/124.41 ->->Cycle: 118.52/124.41 ->->-> Pairs: 118.52/124.41 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 ->->-> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 118.52/124.41 Problem 1.20: 118.52/124.41 118.52/124.41 Subterm Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U13#(X1:S,X2:S,active(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 U13#(X1:S,X2:S,mark(X3:S)) -> U13#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Projection: 118.52/124.41 pi(U13#) = 3 118.52/124.41 118.52/124.41 Problem 1.20: 118.52/124.41 118.52/124.41 SCC Processor: 118.52/124.41 -> Pairs: 118.52/124.41 Empty 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Strongly Connected Components: 118.52/124.41 There is no strongly connected component 118.52/124.41 118.52/124.41 The problem is finite. 118.52/124.41 118.52/124.41 Problem 1.21: 118.52/124.41 118.52/124.41 Subterm Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Projection: 118.52/124.41 pi(U12#) = 1 118.52/124.41 118.52/124.41 Problem 1.21: 118.52/124.41 118.52/124.41 SCC Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Strongly Connected Components: 118.52/124.41 ->->Cycle: 118.52/124.41 ->->-> Pairs: 118.52/124.41 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 ->->-> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 118.52/124.41 Problem 1.21: 118.52/124.41 118.52/124.41 Subterm Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Projection: 118.52/124.41 pi(U12#) = 2 118.52/124.41 118.52/124.41 Problem 1.21: 118.52/124.41 118.52/124.41 SCC Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Strongly Connected Components: 118.52/124.41 ->->Cycle: 118.52/124.41 ->->-> Pairs: 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 ->->-> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 118.52/124.41 Problem 1.21: 118.52/124.41 118.52/124.41 Subterm Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Projection: 118.52/124.41 pi(U12#) = 3 118.52/124.41 118.52/124.41 Problem 1.21: 118.52/124.41 118.52/124.41 SCC Processor: 118.52/124.41 -> Pairs: 118.52/124.41 Empty 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.41 U16(active(X:S)) -> U16(X:S) 118.52/124.41 U16(mark(X:S)) -> U16(X:S) 118.52/124.41 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.41 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.41 U23(active(X:S)) -> U23(X:S) 118.52/124.41 U23(mark(X:S)) -> U23(X:S) 118.52/124.41 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.41 U32(active(X:S)) -> U32(X:S) 118.52/124.41 U32(mark(X:S)) -> U32(X:S) 118.52/124.41 U41(active(X:S)) -> U41(X:S) 118.52/124.41 U41(mark(X:S)) -> U41(X:S) 118.52/124.41 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.41 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.41 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.41 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.41 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.41 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.41 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.41 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.41 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.41 active(U16(tt)) -> mark(tt) 118.52/124.41 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.41 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.41 active(U23(tt)) -> mark(tt) 118.52/124.41 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.41 active(U32(tt)) -> mark(tt) 118.52/124.41 active(U41(tt)) -> mark(tt) 118.52/124.41 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.41 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.41 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.41 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.41 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.41 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.41 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.41 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.41 active(isNat(0)) -> mark(tt) 118.52/124.41 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.41 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.41 active(isNatKind(0)) -> mark(tt) 118.52/124.41 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.41 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.41 isNat(active(X:S)) -> isNat(X:S) 118.52/124.41 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.41 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.41 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.41 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.41 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.41 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.41 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.41 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.41 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.41 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.41 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.41 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.41 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.41 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.41 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.41 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.41 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.41 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.41 mark(0) -> active(0) 118.52/124.41 mark(tt) -> active(tt) 118.52/124.41 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.41 s(active(X:S)) -> s(X:S) 118.52/124.41 s(mark(X:S)) -> s(X:S) 118.52/124.41 ->Strongly Connected Components: 118.52/124.41 There is no strongly connected component 118.52/124.41 118.52/124.41 The problem is finite. 118.52/124.41 118.52/124.41 Problem 1.22: 118.52/124.41 118.52/124.41 Subterm Processor: 118.52/124.41 -> Pairs: 118.52/124.41 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.41 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.41 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.41 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.41 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.41 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.41 -> Rules: 118.52/124.41 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.41 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.41 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.41 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.41 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Projection: 118.52/124.42 pi(U11#) = 1 118.52/124.42 118.52/124.42 Problem 1.22: 118.52/124.42 118.52/124.42 SCC Processor: 118.52/124.42 -> Pairs: 118.52/124.42 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Strongly Connected Components: 118.52/124.42 ->->Cycle: 118.52/124.42 ->->-> Pairs: 118.52/124.42 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 ->->-> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 118.52/124.42 Problem 1.22: 118.52/124.42 118.52/124.42 Subterm Processor: 118.52/124.42 -> Pairs: 118.52/124.42 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Projection: 118.52/124.42 pi(U11#) = 2 118.52/124.42 118.52/124.42 Problem 1.22: 118.52/124.42 118.52/124.42 SCC Processor: 118.52/124.42 -> Pairs: 118.52/124.42 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Strongly Connected Components: 118.52/124.42 ->->Cycle: 118.52/124.42 ->->-> Pairs: 118.52/124.42 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 ->->-> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 118.52/124.42 Problem 1.22: 118.52/124.42 118.52/124.42 Subterm Processor: 118.52/124.42 -> Pairs: 118.52/124.42 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S) 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Projection: 118.52/124.42 pi(U11#) = 3 118.52/124.42 118.52/124.42 Problem 1.22: 118.52/124.42 118.52/124.42 SCC Processor: 118.52/124.42 -> Pairs: 118.52/124.42 Empty 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Strongly Connected Components: 118.52/124.42 There is no strongly connected component 118.52/124.42 118.52/124.42 The problem is finite. 118.52/124.42 118.52/124.42 Problem 1.23: 118.52/124.42 118.52/124.42 Reduction Pairs Processor: 118.52/124.42 -> Pairs: 118.52/124.42 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.42 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.42 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.42 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.42 ACTIVE(U51(tt,N:S)) -> MARK(U52(isNatKind(N:S),N:S)) 118.52/124.42 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.52/124.42 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.42 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.42 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.42 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.42 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.42 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.42 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.42 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.42 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.42 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.42 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.42 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.42 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.42 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.42 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.42 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.42 MARK(s(X:S)) -> MARK(X:S) 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 -> Usable rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Interpretation type: 118.52/124.42 Linear 118.52/124.42 ->Coefficients: 118.52/124.42 Natural Numbers 118.52/124.42 ->Dimension: 118.52/124.42 1 118.52/124.42 ->Bound: 118.52/124.42 2 118.52/124.42 ->Interpretation: 118.52/124.42 118.52/124.42 [U11](X1,X2,X3) = X1 118.52/124.42 [U12](X1,X2,X3) = X1 118.52/124.42 [U13](X1,X2,X3) = X1 118.52/124.42 [U14](X1,X2,X3) = X1 118.52/124.42 [U15](X1,X2) = X1 118.52/124.42 [U16](X) = X 118.52/124.42 [U21](X1,X2) = X1 118.52/124.42 [U22](X1,X2) = X1 118.52/124.42 [U23](X) = X 118.52/124.42 [U31](X1,X2) = X1 118.52/124.42 [U32](X) = X 118.52/124.42 [U41](X) = X 118.52/124.42 [U51](X1,X2) = 2.X1 + 2.X2 + 1 118.52/124.42 [U52](X1,X2) = X1 + X2 + 2 118.52/124.42 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.42 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.42 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.42 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.42 [active](X) = X 118.52/124.42 [isNat](X) = 2 118.52/124.42 [isNatKind](X) = 2 118.52/124.42 [mark](X) = X 118.52/124.42 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.42 [s](X) = X + 2 118.52/124.42 [0] = 2 118.52/124.42 [fSNonEmpty] = 0 118.52/124.42 [tt] = 2 118.52/124.42 [U11#](X1,X2,X3) = 0 118.52/124.42 [U12#](X1,X2,X3) = 0 118.52/124.42 [U13#](X1,X2,X3) = 0 118.52/124.42 [U14#](X1,X2,X3) = 0 118.52/124.42 [U15#](X1,X2) = 0 118.52/124.42 [U16#](X) = 0 118.52/124.42 [U21#](X1,X2) = 0 118.52/124.42 [U22#](X1,X2) = 0 118.52/124.42 [U23#](X) = 0 118.52/124.42 [U31#](X1,X2) = 0 118.52/124.42 [U32#](X) = 0 118.52/124.42 [U41#](X) = 0 118.52/124.42 [U51#](X1,X2) = 0 118.52/124.42 [U52#](X1,X2) = 0 118.52/124.42 [U61#](X1,X2,X3) = 0 118.52/124.42 [U62#](X1,X2,X3) = 0 118.52/124.42 [U63#](X1,X2,X3) = 0 118.52/124.42 [U64#](X1,X2,X3) = 0 118.52/124.42 [ACTIVE](X) = 2.X + 2 118.52/124.42 [ISNAT](X) = 0 118.52/124.42 [ISNATKIND](X) = 0 118.52/124.42 [MARK](X) = 2.X + 2 118.52/124.42 [PLUS](X1,X2) = 0 118.52/124.42 [S](X) = 0 118.52/124.42 118.52/124.42 Problem 1.23: 118.52/124.42 118.52/124.42 SCC Processor: 118.52/124.42 -> Pairs: 118.52/124.42 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.42 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.42 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.42 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.42 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.52/124.42 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.42 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.42 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.42 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.42 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.42 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.42 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.42 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.42 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.42 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.42 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.42 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.42 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.42 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.42 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.42 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.42 MARK(s(X:S)) -> MARK(X:S) 118.52/124.42 -> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.42 s(active(X:S)) -> s(X:S) 118.52/124.42 s(mark(X:S)) -> s(X:S) 118.52/124.42 ->Strongly Connected Components: 118.52/124.42 ->->Cycle: 118.52/124.42 ->->-> Pairs: 118.52/124.42 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.42 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.42 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.42 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.42 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.52/124.42 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.42 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.42 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.42 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.42 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.42 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.42 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.42 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.42 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.42 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.42 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.42 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.42 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.42 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.42 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.42 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.42 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.42 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.42 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.42 MARK(s(X:S)) -> MARK(X:S) 118.52/124.42 ->->-> Rules: 118.52/124.42 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.42 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.42 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.42 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.42 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.42 U16(active(X:S)) -> U16(X:S) 118.52/124.42 U16(mark(X:S)) -> U16(X:S) 118.52/124.42 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.42 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.42 U23(active(X:S)) -> U23(X:S) 118.52/124.42 U23(mark(X:S)) -> U23(X:S) 118.52/124.42 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.42 U32(active(X:S)) -> U32(X:S) 118.52/124.42 U32(mark(X:S)) -> U32(X:S) 118.52/124.42 U41(active(X:S)) -> U41(X:S) 118.52/124.42 U41(mark(X:S)) -> U41(X:S) 118.52/124.42 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.42 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.42 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.42 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.42 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.42 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.42 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.42 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.42 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.42 active(U16(tt)) -> mark(tt) 118.52/124.42 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.42 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.42 active(U23(tt)) -> mark(tt) 118.52/124.42 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.42 active(U32(tt)) -> mark(tt) 118.52/124.42 active(U41(tt)) -> mark(tt) 118.52/124.42 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.42 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.42 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.42 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.42 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.42 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.42 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.42 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.42 active(isNat(0)) -> mark(tt) 118.52/124.42 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.42 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.42 active(isNatKind(0)) -> mark(tt) 118.52/124.42 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.42 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.42 isNat(active(X:S)) -> isNat(X:S) 118.52/124.42 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.42 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.42 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.42 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.42 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.42 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.42 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.42 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.42 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.42 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.42 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.42 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.42 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.42 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.42 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.42 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.42 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.42 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.42 mark(0) -> active(0) 118.52/124.42 mark(tt) -> active(tt) 118.52/124.42 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 118.52/124.43 Problem 1.23: 118.52/124.43 118.52/124.43 Reduction Pairs Processor: 118.52/124.43 -> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U52(tt,N:S)) -> MARK(N:S) 118.52/124.43 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 -> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 -> Usable rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 ->Interpretation type: 118.52/124.43 Linear 118.52/124.43 ->Coefficients: 118.52/124.43 Natural Numbers 118.52/124.43 ->Dimension: 118.52/124.43 1 118.52/124.43 ->Bound: 118.52/124.43 2 118.52/124.43 ->Interpretation: 118.52/124.43 118.52/124.43 [U11](X1,X2,X3) = X1 118.52/124.43 [U12](X1,X2,X3) = X1 118.52/124.43 [U13](X1,X2,X3) = X1 118.52/124.43 [U14](X1,X2,X3) = X1 118.52/124.43 [U15](X1,X2) = X1 118.52/124.43 [U16](X) = X 118.52/124.43 [U21](X1,X2) = X1 118.52/124.43 [U22](X1,X2) = X1 118.52/124.43 [U23](X) = X 118.52/124.43 [U31](X1,X2) = X1 118.52/124.43 [U32](X) = X 118.52/124.43 [U41](X) = X 118.52/124.43 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.43 [U52](X1,X2) = 2.X1 + X2 + 1 118.52/124.43 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [active](X) = X 118.52/124.43 [isNat](X) = 2 118.52/124.43 [isNatKind](X) = 2 118.52/124.43 [mark](X) = X 118.52/124.43 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.43 [s](X) = X + 2 118.52/124.43 [0] = 2 118.52/124.43 [fSNonEmpty] = 0 118.52/124.43 [tt] = 2 118.52/124.43 [U11#](X1,X2,X3) = 0 118.52/124.43 [U12#](X1,X2,X3) = 0 118.52/124.43 [U13#](X1,X2,X3) = 0 118.52/124.43 [U14#](X1,X2,X3) = 0 118.52/124.43 [U15#](X1,X2) = 0 118.52/124.43 [U16#](X) = 0 118.52/124.43 [U21#](X1,X2) = 0 118.52/124.43 [U22#](X1,X2) = 0 118.52/124.43 [U23#](X) = 0 118.52/124.43 [U31#](X1,X2) = 0 118.52/124.43 [U32#](X) = 0 118.52/124.43 [U41#](X) = 0 118.52/124.43 [U51#](X1,X2) = 0 118.52/124.43 [U52#](X1,X2) = 0 118.52/124.43 [U61#](X1,X2,X3) = 0 118.52/124.43 [U62#](X1,X2,X3) = 0 118.52/124.43 [U63#](X1,X2,X3) = 0 118.52/124.43 [U64#](X1,X2,X3) = 0 118.52/124.43 [ACTIVE](X) = 2.X + 2 118.52/124.43 [ISNAT](X) = 0 118.52/124.43 [ISNATKIND](X) = 0 118.52/124.43 [MARK](X) = 2.X + 2 118.52/124.43 [PLUS](X1,X2) = 0 118.52/124.43 [S](X) = 0 118.52/124.43 118.52/124.43 Problem 1.23: 118.52/124.43 118.52/124.43 SCC Processor: 118.52/124.43 -> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 -> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 ->Strongly Connected Components: 118.52/124.43 ->->Cycle: 118.52/124.43 ->->-> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 ->->-> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 118.52/124.43 Problem 1.23: 118.52/124.43 118.52/124.43 Reduction Pairs Processor: 118.52/124.43 -> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U61(tt,M:S,N:S)) -> MARK(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 -> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 -> Usable rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 ->Interpretation type: 118.52/124.43 Linear 118.52/124.43 ->Coefficients: 118.52/124.43 Natural Numbers 118.52/124.43 ->Dimension: 118.52/124.43 1 118.52/124.43 ->Bound: 118.52/124.43 2 118.52/124.43 ->Interpretation: 118.52/124.43 118.52/124.43 [U11](X1,X2,X3) = X1 118.52/124.43 [U12](X1,X2,X3) = X1 118.52/124.43 [U13](X1,X2,X3) = X1 118.52/124.43 [U14](X1,X2,X3) = X1 118.52/124.43 [U15](X1,X2) = X1 118.52/124.43 [U16](X) = X 118.52/124.43 [U21](X1,X2) = X1 118.52/124.43 [U22](X1,X2) = X1 118.52/124.43 [U23](X) = X 118.52/124.43 [U31](X1,X2) = X1 118.52/124.43 [U32](X) = X 118.52/124.43 [U41](X) = X 118.52/124.43 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.43 [U52](X1,X2) = X1 + X2 + 2 118.52/124.43 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.43 [active](X) = X 118.52/124.43 [isNat](X) = 2 118.52/124.43 [isNatKind](X) = 2 118.52/124.43 [mark](X) = X 118.52/124.43 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.43 [s](X) = X + 2 118.52/124.43 [0] = 2 118.52/124.43 [fSNonEmpty] = 0 118.52/124.43 [tt] = 2 118.52/124.43 [U11#](X1,X2,X3) = 0 118.52/124.43 [U12#](X1,X2,X3) = 0 118.52/124.43 [U13#](X1,X2,X3) = 0 118.52/124.43 [U14#](X1,X2,X3) = 0 118.52/124.43 [U15#](X1,X2) = 0 118.52/124.43 [U16#](X) = 0 118.52/124.43 [U21#](X1,X2) = 0 118.52/124.43 [U22#](X1,X2) = 0 118.52/124.43 [U23#](X) = 0 118.52/124.43 [U31#](X1,X2) = 0 118.52/124.43 [U32#](X) = 0 118.52/124.43 [U41#](X) = 0 118.52/124.43 [U51#](X1,X2) = 0 118.52/124.43 [U52#](X1,X2) = 0 118.52/124.43 [U61#](X1,X2,X3) = 0 118.52/124.43 [U62#](X1,X2,X3) = 0 118.52/124.43 [U63#](X1,X2,X3) = 0 118.52/124.43 [U64#](X1,X2,X3) = 0 118.52/124.43 [ACTIVE](X) = X + 2 118.52/124.43 [ISNAT](X) = 0 118.52/124.43 [ISNATKIND](X) = 0 118.52/124.43 [MARK](X) = X + 2 118.52/124.43 [PLUS](X1,X2) = 0 118.52/124.43 [S](X) = 0 118.52/124.43 118.52/124.43 Problem 1.23: 118.52/124.43 118.52/124.43 SCC Processor: 118.52/124.43 -> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 -> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 ->Strongly Connected Components: 118.52/124.43 ->->Cycle: 118.52/124.43 ->->-> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 ->->-> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 118.52/124.43 Problem 1.23: 118.52/124.43 118.52/124.43 Reduction Pairs Processor: 118.52/124.43 -> Pairs: 118.52/124.43 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.43 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.43 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.43 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.43 ACTIVE(U62(tt,M:S,N:S)) -> MARK(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.43 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.43 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.43 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.43 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.43 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.43 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.43 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.43 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.43 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.43 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.43 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.43 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.43 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.43 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.43 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.43 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.43 MARK(s(X:S)) -> MARK(X:S) 118.52/124.43 -> Rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 -> Usable rules: 118.52/124.43 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.43 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.43 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.43 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.43 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.43 U16(active(X:S)) -> U16(X:S) 118.52/124.43 U16(mark(X:S)) -> U16(X:S) 118.52/124.43 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.43 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.43 U23(active(X:S)) -> U23(X:S) 118.52/124.43 U23(mark(X:S)) -> U23(X:S) 118.52/124.43 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.43 U32(active(X:S)) -> U32(X:S) 118.52/124.43 U32(mark(X:S)) -> U32(X:S) 118.52/124.43 U41(active(X:S)) -> U41(X:S) 118.52/124.43 U41(mark(X:S)) -> U41(X:S) 118.52/124.43 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.43 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.43 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.43 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.43 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.43 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.43 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.43 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.43 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.43 active(U16(tt)) -> mark(tt) 118.52/124.43 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.43 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.43 active(U23(tt)) -> mark(tt) 118.52/124.43 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.43 active(U32(tt)) -> mark(tt) 118.52/124.43 active(U41(tt)) -> mark(tt) 118.52/124.43 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.43 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.43 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.43 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.43 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.43 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.43 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.43 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.43 active(isNat(0)) -> mark(tt) 118.52/124.43 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.43 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.43 active(isNatKind(0)) -> mark(tt) 118.52/124.43 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.43 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.43 isNat(active(X:S)) -> isNat(X:S) 118.52/124.43 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.43 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.43 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.43 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.43 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.43 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.43 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.43 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.43 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.43 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.43 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.43 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.43 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.43 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.43 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.43 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.43 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.43 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.43 mark(0) -> active(0) 118.52/124.43 mark(tt) -> active(tt) 118.52/124.43 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.43 s(active(X:S)) -> s(X:S) 118.52/124.43 s(mark(X:S)) -> s(X:S) 118.52/124.43 ->Interpretation type: 118.52/124.43 Linear 118.52/124.43 ->Coefficients: 118.52/124.43 Natural Numbers 118.52/124.43 ->Dimension: 118.52/124.43 1 118.52/124.43 ->Bound: 118.52/124.43 2 118.52/124.43 ->Interpretation: 118.52/124.43 118.52/124.43 [U11](X1,X2,X3) = X1 118.52/124.43 [U12](X1,X2,X3) = X1 118.52/124.44 [U13](X1,X2,X3) = X1 118.52/124.44 [U14](X1,X2,X3) = X1 118.52/124.44 [U15](X1,X2) = X1 118.52/124.44 [U16](X) = X 118.52/124.44 [U21](X1,X2) = X1 118.52/124.44 [U22](X1,X2) = X1 118.52/124.44 [U23](X) = X 118.52/124.44 [U31](X1,X2) = X1 118.52/124.44 [U32](X) = X 118.52/124.44 [U41](X) = X 118.52/124.44 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.44 [U52](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.44 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 118.52/124.44 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.52/124.44 [active](X) = X 118.52/124.44 [isNat](X) = 2 118.52/124.44 [isNatKind](X) = 2 118.52/124.44 [mark](X) = X 118.52/124.44 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.44 [s](X) = X + 2 118.52/124.44 [0] = 2 118.52/124.44 [fSNonEmpty] = 0 118.52/124.44 [tt] = 2 118.52/124.44 [U11#](X1,X2,X3) = 0 118.52/124.44 [U12#](X1,X2,X3) = 0 118.52/124.44 [U13#](X1,X2,X3) = 0 118.52/124.44 [U14#](X1,X2,X3) = 0 118.52/124.44 [U15#](X1,X2) = 0 118.52/124.44 [U16#](X) = 0 118.52/124.44 [U21#](X1,X2) = 0 118.52/124.44 [U22#](X1,X2) = 0 118.52/124.44 [U23#](X) = 0 118.52/124.44 [U31#](X1,X2) = 0 118.52/124.44 [U32#](X) = 0 118.52/124.44 [U41#](X) = 0 118.52/124.44 [U51#](X1,X2) = 0 118.52/124.44 [U52#](X1,X2) = 0 118.52/124.44 [U61#](X1,X2,X3) = 0 118.52/124.44 [U62#](X1,X2,X3) = 0 118.52/124.44 [U63#](X1,X2,X3) = 0 118.52/124.44 [U64#](X1,X2,X3) = 0 118.52/124.44 [ACTIVE](X) = 2.X + 2 118.52/124.44 [ISNAT](X) = 0 118.52/124.44 [ISNATKIND](X) = 0 118.52/124.44 [MARK](X) = 2.X + 2 118.52/124.44 [PLUS](X1,X2) = 0 118.52/124.44 [S](X) = 0 118.52/124.44 118.52/124.44 Problem 1.23: 118.52/124.44 118.52/124.44 SCC Processor: 118.52/124.44 -> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 -> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 ->Strongly Connected Components: 118.52/124.44 ->->Cycle: 118.52/124.44 ->->-> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 ->->-> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 118.52/124.44 Problem 1.23: 118.52/124.44 118.52/124.44 Reduction Pairs Processor: 118.52/124.44 -> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(U63(tt,M:S,N:S)) -> MARK(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 -> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 -> Usable rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 ->Interpretation type: 118.52/124.44 Linear 118.52/124.44 ->Coefficients: 118.52/124.44 Natural Numbers 118.52/124.44 ->Dimension: 118.52/124.44 1 118.52/124.44 ->Bound: 118.52/124.44 2 118.52/124.44 ->Interpretation: 118.52/124.44 118.52/124.44 [U11](X1,X2,X3) = X1 118.52/124.44 [U12](X1,X2,X3) = X1 118.52/124.44 [U13](X1,X2,X3) = X1 118.52/124.44 [U14](X1,X2,X3) = X1 118.52/124.44 [U15](X1,X2) = X1 118.52/124.44 [U16](X) = X 118.52/124.44 [U21](X1,X2) = X1 118.52/124.44 [U22](X1,X2) = X1 118.52/124.44 [U23](X) = X 118.52/124.44 [U31](X1,X2) = X1 118.52/124.44 [U32](X) = X 118.52/124.44 [U41](X) = X 118.52/124.44 [U51](X1,X2) = X1 + 2.X2 + 2 118.52/124.44 [U52](X1,X2) = X1 + 2.X2 + 2 118.52/124.44 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 118.52/124.44 [active](X) = X 118.52/124.44 [isNat](X) = 2 118.52/124.44 [isNatKind](X) = 2 118.52/124.44 [mark](X) = X 118.52/124.44 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.44 [s](X) = X + 2 118.52/124.44 [0] = 2 118.52/124.44 [fSNonEmpty] = 0 118.52/124.44 [tt] = 2 118.52/124.44 [U11#](X1,X2,X3) = 0 118.52/124.44 [U12#](X1,X2,X3) = 0 118.52/124.44 [U13#](X1,X2,X3) = 0 118.52/124.44 [U14#](X1,X2,X3) = 0 118.52/124.44 [U15#](X1,X2) = 0 118.52/124.44 [U16#](X) = 0 118.52/124.44 [U21#](X1,X2) = 0 118.52/124.44 [U22#](X1,X2) = 0 118.52/124.44 [U23#](X) = 0 118.52/124.44 [U31#](X1,X2) = 0 118.52/124.44 [U32#](X) = 0 118.52/124.44 [U41#](X) = 0 118.52/124.44 [U51#](X1,X2) = 0 118.52/124.44 [U52#](X1,X2) = 0 118.52/124.44 [U61#](X1,X2,X3) = 0 118.52/124.44 [U62#](X1,X2,X3) = 0 118.52/124.44 [U63#](X1,X2,X3) = 0 118.52/124.44 [U64#](X1,X2,X3) = 0 118.52/124.44 [ACTIVE](X) = 2.X + 2 118.52/124.44 [ISNAT](X) = 0 118.52/124.44 [ISNATKIND](X) = 0 118.52/124.44 [MARK](X) = 2.X + 2 118.52/124.44 [PLUS](X1,X2) = 0 118.52/124.44 [S](X) = 0 118.52/124.44 118.52/124.44 Problem 1.23: 118.52/124.44 118.52/124.44 SCC Processor: 118.52/124.44 -> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 -> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 ->Strongly Connected Components: 118.52/124.44 ->->Cycle: 118.52/124.44 ->->-> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 ->->-> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 118.52/124.44 Problem 1.23: 118.52/124.44 118.52/124.44 Reduction Pairs Processor: 118.52/124.44 -> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(U64(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 -> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 -> Usable rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 ->Interpretation type: 118.52/124.44 Linear 118.52/124.44 ->Coefficients: 118.52/124.44 Natural Numbers 118.52/124.44 ->Dimension: 118.52/124.44 1 118.52/124.44 ->Bound: 118.52/124.44 2 118.52/124.44 ->Interpretation: 118.52/124.44 118.52/124.44 [U11](X1,X2,X3) = X1 118.52/124.44 [U12](X1,X2,X3) = X1 118.52/124.44 [U13](X1,X2,X3) = X1 118.52/124.44 [U14](X1,X2,X3) = X1 118.52/124.44 [U15](X1,X2) = X1 118.52/124.44 [U16](X) = X 118.52/124.44 [U21](X1,X2) = X1 118.52/124.44 [U22](X1,X2) = X1 118.52/124.44 [U23](X) = X 118.52/124.44 [U31](X1,X2) = X1 118.52/124.44 [U32](X) = X 118.52/124.44 [U41](X) = X 118.52/124.44 [U51](X1,X2) = 2.X1 + 2.X2 + 1 118.52/124.44 [U52](X1,X2) = X1 + 2.X2 + 2 118.52/124.44 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.52/124.44 [active](X) = X 118.52/124.44 [isNat](X) = 2 118.52/124.44 [isNatKind](X) = 2 118.52/124.44 [mark](X) = X 118.52/124.44 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.44 [s](X) = X + 2 118.52/124.44 [0] = 2 118.52/124.44 [fSNonEmpty] = 0 118.52/124.44 [tt] = 2 118.52/124.44 [U11#](X1,X2,X3) = 0 118.52/124.44 [U12#](X1,X2,X3) = 0 118.52/124.44 [U13#](X1,X2,X3) = 0 118.52/124.44 [U14#](X1,X2,X3) = 0 118.52/124.44 [U15#](X1,X2) = 0 118.52/124.44 [U16#](X) = 0 118.52/124.44 [U21#](X1,X2) = 0 118.52/124.44 [U22#](X1,X2) = 0 118.52/124.44 [U23#](X) = 0 118.52/124.44 [U31#](X1,X2) = 0 118.52/124.44 [U32#](X) = 0 118.52/124.44 [U41#](X) = 0 118.52/124.44 [U51#](X1,X2) = 0 118.52/124.44 [U52#](X1,X2) = 0 118.52/124.44 [U61#](X1,X2,X3) = 0 118.52/124.44 [U62#](X1,X2,X3) = 0 118.52/124.44 [U63#](X1,X2,X3) = 0 118.52/124.44 [U64#](X1,X2,X3) = 0 118.52/124.44 [ACTIVE](X) = 2.X + 2 118.52/124.44 [ISNAT](X) = 0 118.52/124.44 [ISNATKIND](X) = 0 118.52/124.44 [MARK](X) = 2.X + 2 118.52/124.44 [PLUS](X1,X2) = 0 118.52/124.44 [S](X) = 0 118.52/124.44 118.52/124.44 Problem 1.23: 118.52/124.44 118.52/124.44 SCC Processor: 118.52/124.44 -> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 -> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.44 U41(mark(X:S)) -> U41(X:S) 118.52/124.44 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.44 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.44 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.44 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.44 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.44 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.44 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.44 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.44 active(U16(tt)) -> mark(tt) 118.52/124.44 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.44 active(U23(tt)) -> mark(tt) 118.52/124.44 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.44 active(U32(tt)) -> mark(tt) 118.52/124.44 active(U41(tt)) -> mark(tt) 118.52/124.44 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.44 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.44 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.44 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.44 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.44 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.44 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 active(isNat(0)) -> mark(tt) 118.52/124.44 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.44 active(isNatKind(0)) -> mark(tt) 118.52/124.44 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.44 isNat(active(X:S)) -> isNat(X:S) 118.52/124.44 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.44 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.44 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.44 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.44 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.44 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.44 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.44 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.44 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.44 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.44 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.44 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.44 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.44 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.44 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.44 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.44 mark(0) -> active(0) 118.52/124.44 mark(tt) -> active(tt) 118.52/124.44 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.44 s(active(X:S)) -> s(X:S) 118.52/124.44 s(mark(X:S)) -> s(X:S) 118.52/124.44 ->Strongly Connected Components: 118.52/124.44 ->->Cycle: 118.52/124.44 ->->-> Pairs: 118.52/124.44 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.44 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.44 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.44 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.44 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.44 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.44 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.44 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.44 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.44 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.44 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.44 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.44 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.44 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.44 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.44 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.44 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.44 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.44 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.44 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.44 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.44 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.44 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.44 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.44 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.44 MARK(s(X:S)) -> MARK(X:S) 118.52/124.44 ->->-> Rules: 118.52/124.44 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.44 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.44 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.44 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.44 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.44 U16(active(X:S)) -> U16(X:S) 118.52/124.44 U16(mark(X:S)) -> U16(X:S) 118.52/124.44 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.44 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.44 U23(active(X:S)) -> U23(X:S) 118.52/124.44 U23(mark(X:S)) -> U23(X:S) 118.52/124.44 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.44 U32(active(X:S)) -> U32(X:S) 118.52/124.44 U32(mark(X:S)) -> U32(X:S) 118.52/124.44 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 118.52/124.45 Problem 1.23: 118.52/124.45 118.52/124.45 Reduction Pairs Processor: 118.52/124.45 -> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 ACTIVE(plus(N:S,s(M:S))) -> MARK(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 -> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 -> Usable rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 ->Interpretation type: 118.52/124.45 Linear 118.52/124.45 ->Coefficients: 118.52/124.45 Natural Numbers 118.52/124.45 ->Dimension: 118.52/124.45 1 118.52/124.45 ->Bound: 118.52/124.45 2 118.52/124.45 ->Interpretation: 118.52/124.45 118.52/124.45 [U11](X1,X2,X3) = X1 118.52/124.45 [U12](X1,X2,X3) = X1 118.52/124.45 [U13](X1,X2,X3) = X1 118.52/124.45 [U14](X1,X2,X3) = X1 118.52/124.45 [U15](X1,X2) = X1 118.52/124.45 [U16](X) = X 118.52/124.45 [U21](X1,X2) = X1 118.52/124.45 [U22](X1,X2) = X1 118.52/124.45 [U23](X) = X 118.52/124.45 [U31](X1,X2) = X1 118.52/124.45 [U32](X) = X 118.52/124.45 [U41](X) = X 118.52/124.45 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.45 [U52](X1,X2) = X1 + 2.X2 + 1 118.52/124.45 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 118.52/124.45 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 118.52/124.45 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.45 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.45 [active](X) = X 118.52/124.45 [isNat](X) = 2 118.52/124.45 [isNatKind](X) = 2 118.52/124.45 [mark](X) = X 118.52/124.45 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.52/124.45 [s](X) = X + 2 118.52/124.45 [0] = 2 118.52/124.45 [fSNonEmpty] = 0 118.52/124.45 [tt] = 2 118.52/124.45 [U11#](X1,X2,X3) = 0 118.52/124.45 [U12#](X1,X2,X3) = 0 118.52/124.45 [U13#](X1,X2,X3) = 0 118.52/124.45 [U14#](X1,X2,X3) = 0 118.52/124.45 [U15#](X1,X2) = 0 118.52/124.45 [U16#](X) = 0 118.52/124.45 [U21#](X1,X2) = 0 118.52/124.45 [U22#](X1,X2) = 0 118.52/124.45 [U23#](X) = 0 118.52/124.45 [U31#](X1,X2) = 0 118.52/124.45 [U32#](X) = 0 118.52/124.45 [U41#](X) = 0 118.52/124.45 [U51#](X1,X2) = 0 118.52/124.45 [U52#](X1,X2) = 0 118.52/124.45 [U61#](X1,X2,X3) = 0 118.52/124.45 [U62#](X1,X2,X3) = 0 118.52/124.45 [U63#](X1,X2,X3) = 0 118.52/124.45 [U64#](X1,X2,X3) = 0 118.52/124.45 [ACTIVE](X) = 2.X + 2 118.52/124.45 [ISNAT](X) = 0 118.52/124.45 [ISNATKIND](X) = 0 118.52/124.45 [MARK](X) = 2.X + 2 118.52/124.45 [PLUS](X1,X2) = 0 118.52/124.45 [S](X) = 0 118.52/124.45 118.52/124.45 Problem 1.23: 118.52/124.45 118.52/124.45 SCC Processor: 118.52/124.45 -> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 -> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 ->Strongly Connected Components: 118.52/124.45 ->->Cycle: 118.52/124.45 ->->-> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 ->->-> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 118.52/124.45 Problem 1.23: 118.52/124.45 118.52/124.45 Reduction Pairs Processor: 118.52/124.45 -> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 ACTIVE(plus(N:S,0)) -> MARK(U51(isNat(N:S),N:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 -> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 -> Usable rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 ->Interpretation type: 118.52/124.45 Linear 118.52/124.45 ->Coefficients: 118.52/124.45 Natural Numbers 118.52/124.45 ->Dimension: 118.52/124.45 1 118.52/124.45 ->Bound: 118.52/124.45 2 118.52/124.45 ->Interpretation: 118.52/124.45 118.52/124.45 [U11](X1,X2,X3) = X1 118.52/124.45 [U12](X1,X2,X3) = X1 118.52/124.45 [U13](X1,X2,X3) = X1 118.52/124.45 [U14](X1,X2,X3) = X1 118.52/124.45 [U15](X1,X2) = X1 118.52/124.45 [U16](X) = X 118.52/124.45 [U21](X1,X2) = X1 118.52/124.45 [U22](X1,X2) = X1 118.52/124.45 [U23](X) = X 118.52/124.45 [U31](X1,X2) = X1 118.52/124.45 [U32](X) = X 118.52/124.45 [U41](X) = X 118.52/124.45 [U51](X1,X2) = X1 + 2.X2 + 1 118.52/124.45 [U52](X1,X2) = X1 + 2.X2 118.52/124.45 [U61](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.45 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.52/124.45 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.52/124.45 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.52/124.45 [active](X) = X 118.52/124.45 [isNat](X) = 2 118.52/124.45 [isNatKind](X) = 2 118.52/124.45 [mark](X) = X 118.52/124.45 [plus](X1,X2) = 2.X1 + 2.X2 118.52/124.45 [s](X) = X + 2 118.52/124.45 [0] = 2 118.52/124.45 [fSNonEmpty] = 0 118.52/124.45 [tt] = 2 118.52/124.45 [U11#](X1,X2,X3) = 0 118.52/124.45 [U12#](X1,X2,X3) = 0 118.52/124.45 [U13#](X1,X2,X3) = 0 118.52/124.45 [U14#](X1,X2,X3) = 0 118.52/124.45 [U15#](X1,X2) = 0 118.52/124.45 [U16#](X) = 0 118.52/124.45 [U21#](X1,X2) = 0 118.52/124.45 [U22#](X1,X2) = 0 118.52/124.45 [U23#](X) = 0 118.52/124.45 [U31#](X1,X2) = 0 118.52/124.45 [U32#](X) = 0 118.52/124.45 [U41#](X) = 0 118.52/124.45 [U51#](X1,X2) = 0 118.52/124.45 [U52#](X1,X2) = 0 118.52/124.45 [U61#](X1,X2,X3) = 0 118.52/124.45 [U62#](X1,X2,X3) = 0 118.52/124.45 [U63#](X1,X2,X3) = 0 118.52/124.45 [U64#](X1,X2,X3) = 0 118.52/124.45 [ACTIVE](X) = 2.X + 2 118.52/124.45 [ISNAT](X) = 0 118.52/124.45 [ISNATKIND](X) = 0 118.52/124.45 [MARK](X) = 2.X + 2 118.52/124.45 [PLUS](X1,X2) = 0 118.52/124.45 [S](X) = 0 118.52/124.45 118.52/124.45 Problem 1.23: 118.52/124.45 118.52/124.45 SCC Processor: 118.52/124.45 -> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 -> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 ->Strongly Connected Components: 118.52/124.45 ->->Cycle: 118.52/124.45 ->->-> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 ->->-> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 118.52/124.45 Problem 1.23: 118.52/124.45 118.52/124.45 Reduction Pairs Processor: 118.52/124.45 -> Pairs: 118.52/124.45 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.45 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.45 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.45 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.45 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.45 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U16(X:S)) -> ACTIVE(U16(mark(X:S))) 118.52/124.45 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.45 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.45 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.45 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.45 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.45 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.45 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.45 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.45 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.45 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.45 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.45 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.45 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.45 MARK(s(X:S)) -> MARK(X:S) 118.52/124.45 -> Rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.45 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.45 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.45 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.45 active(isNat(0)) -> mark(tt) 118.52/124.45 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.45 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.45 active(isNatKind(0)) -> mark(tt) 118.52/124.45 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.45 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.45 isNat(active(X:S)) -> isNat(X:S) 118.52/124.45 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.45 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.45 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.45 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.45 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.45 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.45 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.45 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.45 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.45 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.45 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.45 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.45 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.45 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.45 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.45 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.45 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.45 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.45 mark(0) -> active(0) 118.52/124.45 mark(tt) -> active(tt) 118.52/124.45 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.45 s(active(X:S)) -> s(X:S) 118.52/124.45 s(mark(X:S)) -> s(X:S) 118.52/124.45 -> Usable rules: 118.52/124.45 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.45 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.45 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.45 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.45 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.45 U16(active(X:S)) -> U16(X:S) 118.52/124.45 U16(mark(X:S)) -> U16(X:S) 118.52/124.45 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.45 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.45 U23(active(X:S)) -> U23(X:S) 118.52/124.45 U23(mark(X:S)) -> U23(X:S) 118.52/124.45 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.45 U32(active(X:S)) -> U32(X:S) 118.52/124.45 U32(mark(X:S)) -> U32(X:S) 118.52/124.45 U41(active(X:S)) -> U41(X:S) 118.52/124.45 U41(mark(X:S)) -> U41(X:S) 118.52/124.45 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.45 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.45 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.45 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.45 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.45 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.45 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.45 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.45 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.45 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.45 active(U16(tt)) -> mark(tt) 118.52/124.45 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.45 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.45 active(U23(tt)) -> mark(tt) 118.52/124.45 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.45 active(U32(tt)) -> mark(tt) 118.52/124.45 active(U41(tt)) -> mark(tt) 118.52/124.45 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.45 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.45 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.45 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 ->Interpretation type: 118.52/124.46 Linear 118.52/124.46 ->Coefficients: 118.52/124.46 Natural Numbers 118.52/124.46 ->Dimension: 118.52/124.46 1 118.52/124.46 ->Bound: 118.52/124.46 2 118.52/124.46 ->Interpretation: 118.52/124.46 118.52/124.46 [U11](X1,X2,X3) = 1 118.52/124.46 [U12](X1,X2,X3) = 1 118.52/124.46 [U13](X1,X2,X3) = 1 118.52/124.46 [U14](X1,X2,X3) = 1 118.52/124.46 [U15](X1,X2) = 1 118.52/124.46 [U16](X) = 0 118.52/124.46 [U21](X1,X2) = 1 118.52/124.46 [U22](X1,X2) = 1 118.52/124.46 [U23](X) = 1 118.52/124.46 [U31](X1,X2) = 1 118.52/124.46 [U32](X) = 1 118.52/124.46 [U41](X) = 0 118.52/124.46 [U51](X1,X2) = 1 118.52/124.46 [U52](X1,X2) = 1 118.52/124.46 [U61](X1,X2,X3) = 1 118.52/124.46 [U62](X1,X2,X3) = 1 118.52/124.46 [U63](X1,X2,X3) = 1 118.52/124.46 [U64](X1,X2,X3) = 1 118.52/124.46 [active](X) = 2 118.52/124.46 [isNat](X) = 1 118.52/124.46 [isNatKind](X) = 1 118.52/124.46 [mark](X) = 2 118.52/124.46 [plus](X1,X2) = 1 118.52/124.46 [s](X) = 1 118.52/124.46 [0] = 2 118.52/124.46 [fSNonEmpty] = 0 118.52/124.46 [tt] = 2 118.52/124.46 [U11#](X1,X2,X3) = 0 118.52/124.46 [U12#](X1,X2,X3) = 0 118.52/124.46 [U13#](X1,X2,X3) = 0 118.52/124.46 [U14#](X1,X2,X3) = 0 118.52/124.46 [U15#](X1,X2) = 0 118.52/124.46 [U16#](X) = 0 118.52/124.46 [U21#](X1,X2) = 0 118.52/124.46 [U22#](X1,X2) = 0 118.52/124.46 [U23#](X) = 0 118.52/124.46 [U31#](X1,X2) = 0 118.52/124.46 [U32#](X) = 0 118.52/124.46 [U41#](X) = 0 118.52/124.46 [U51#](X1,X2) = 0 118.52/124.46 [U52#](X1,X2) = 0 118.52/124.46 [U61#](X1,X2,X3) = 0 118.52/124.46 [U62#](X1,X2,X3) = 0 118.52/124.46 [U63#](X1,X2,X3) = 0 118.52/124.46 [U64#](X1,X2,X3) = 0 118.52/124.46 [ACTIVE](X) = 2.X 118.52/124.46 [ISNAT](X) = 0 118.52/124.46 [ISNATKIND](X) = 0 118.52/124.46 [MARK](X) = 2 118.52/124.46 [PLUS](X1,X2) = 0 118.52/124.46 [S](X) = 0 118.52/124.46 118.52/124.46 Problem 1.23: 118.52/124.46 118.52/124.46 SCC Processor: 118.52/124.46 -> Pairs: 118.52/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.46 MARK(s(X:S)) -> MARK(X:S) 118.52/124.46 -> Rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 ->Strongly Connected Components: 118.52/124.46 ->->Cycle: 118.52/124.46 ->->-> Pairs: 118.52/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.46 MARK(s(X:S)) -> MARK(X:S) 118.52/124.46 ->->-> Rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 118.52/124.46 Problem 1.23: 118.52/124.46 118.52/124.46 Reduction Pairs Processor: 118.52/124.46 -> Pairs: 118.52/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U23(X:S)) -> ACTIVE(U23(mark(X:S))) 118.52/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.46 MARK(s(X:S)) -> MARK(X:S) 118.52/124.46 -> Rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 -> Usable rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 ->Interpretation type: 118.52/124.46 Linear 118.52/124.46 ->Coefficients: 118.52/124.46 Natural Numbers 118.52/124.46 ->Dimension: 118.52/124.46 1 118.52/124.46 ->Bound: 118.52/124.46 2 118.52/124.46 ->Interpretation: 118.52/124.46 118.52/124.46 [U11](X1,X2,X3) = 1 118.52/124.46 [U12](X1,X2,X3) = 1 118.52/124.46 [U13](X1,X2,X3) = 1 118.52/124.46 [U14](X1,X2,X3) = 1 118.52/124.46 [U15](X1,X2) = 1 118.52/124.46 [U16](X) = 0 118.52/124.46 [U21](X1,X2) = 1 118.52/124.46 [U22](X1,X2) = 1 118.52/124.46 [U23](X) = 0 118.52/124.46 [U31](X1,X2) = 1 118.52/124.46 [U32](X) = 0 118.52/124.46 [U41](X) = 0 118.52/124.46 [U51](X1,X2) = 1 118.52/124.46 [U52](X1,X2) = 1 118.52/124.46 [U61](X1,X2,X3) = 0 118.52/124.46 [U62](X1,X2,X3) = 0 118.52/124.46 [U63](X1,X2,X3) = 1 118.52/124.46 [U64](X1,X2,X3) = 0 118.52/124.46 [active](X) = 2 118.52/124.46 [isNat](X) = 1 118.52/124.46 [isNatKind](X) = 1 118.52/124.46 [mark](X) = 2 118.52/124.46 [plus](X1,X2) = 1 118.52/124.46 [s](X) = 1 118.52/124.46 [0] = 1 118.52/124.46 [fSNonEmpty] = 0 118.52/124.46 [tt] = 0 118.52/124.46 [U11#](X1,X2,X3) = 0 118.52/124.46 [U12#](X1,X2,X3) = 0 118.52/124.46 [U13#](X1,X2,X3) = 0 118.52/124.46 [U14#](X1,X2,X3) = 0 118.52/124.46 [U15#](X1,X2) = 0 118.52/124.46 [U16#](X) = 0 118.52/124.46 [U21#](X1,X2) = 0 118.52/124.46 [U22#](X1,X2) = 0 118.52/124.46 [U23#](X) = 0 118.52/124.46 [U31#](X1,X2) = 0 118.52/124.46 [U32#](X) = 0 118.52/124.46 [U41#](X) = 0 118.52/124.46 [U51#](X1,X2) = 0 118.52/124.46 [U52#](X1,X2) = 0 118.52/124.46 [U61#](X1,X2,X3) = 0 118.52/124.46 [U62#](X1,X2,X3) = 0 118.52/124.46 [U63#](X1,X2,X3) = 0 118.52/124.46 [U64#](X1,X2,X3) = 0 118.52/124.46 [ACTIVE](X) = 2.X 118.52/124.46 [ISNAT](X) = 0 118.52/124.46 [ISNATKIND](X) = 0 118.52/124.46 [MARK](X) = 2 118.52/124.46 [PLUS](X1,X2) = 0 118.52/124.46 [S](X) = 0 118.52/124.46 118.52/124.46 Problem 1.23: 118.52/124.46 118.52/124.46 SCC Processor: 118.52/124.46 -> Pairs: 118.52/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.46 MARK(s(X:S)) -> MARK(X:S) 118.52/124.46 -> Rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 ->Strongly Connected Components: 118.52/124.46 ->->Cycle: 118.52/124.46 ->->-> Pairs: 118.52/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.46 MARK(s(X:S)) -> MARK(X:S) 118.52/124.46 ->->-> Rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 118.52/124.46 Problem 1.23: 118.52/124.46 118.52/124.46 Reduction Pairs Processor: 118.52/124.46 -> Pairs: 118.52/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.52/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.52/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.52/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.52/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.52/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.52/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.52/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.52/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U32(X:S)) -> ACTIVE(U32(mark(X:S))) 118.52/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.52/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.52/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.52/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.52/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.52/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.52/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.52/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.52/124.46 MARK(s(X:S)) -> MARK(X:S) 118.52/124.46 -> Rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.52/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.52/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.52/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.52/124.46 active(U16(tt)) -> mark(tt) 118.52/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.52/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.52/124.46 active(U23(tt)) -> mark(tt) 118.52/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.52/124.46 active(U32(tt)) -> mark(tt) 118.52/124.46 active(U41(tt)) -> mark(tt) 118.52/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.52/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.52/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.52/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.52/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.52/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.52/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.52/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.52/124.46 active(isNat(0)) -> mark(tt) 118.52/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.52/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.52/124.46 active(isNatKind(0)) -> mark(tt) 118.52/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.52/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.52/124.46 isNat(active(X:S)) -> isNat(X:S) 118.52/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.52/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.52/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.52/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.52/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.52/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.52/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.52/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.52/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.52/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.52/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.52/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.52/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.52/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.52/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.52/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.52/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.52/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.52/124.46 mark(0) -> active(0) 118.52/124.46 mark(tt) -> active(tt) 118.52/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.52/124.46 s(active(X:S)) -> s(X:S) 118.52/124.46 s(mark(X:S)) -> s(X:S) 118.52/124.46 -> Usable rules: 118.52/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.52/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.52/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.52/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.52/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.52/124.46 U16(active(X:S)) -> U16(X:S) 118.52/124.46 U16(mark(X:S)) -> U16(X:S) 118.52/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.52/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.52/124.46 U23(active(X:S)) -> U23(X:S) 118.52/124.46 U23(mark(X:S)) -> U23(X:S) 118.52/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.52/124.46 U32(active(X:S)) -> U32(X:S) 118.52/124.46 U32(mark(X:S)) -> U32(X:S) 118.52/124.46 U41(active(X:S)) -> U41(X:S) 118.52/124.46 U41(mark(X:S)) -> U41(X:S) 118.52/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.52/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.52/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.52/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.52/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.52/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.46 active(U16(tt)) -> mark(tt) 118.55/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.46 active(U23(tt)) -> mark(tt) 118.55/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.46 active(U32(tt)) -> mark(tt) 118.55/124.46 active(U41(tt)) -> mark(tt) 118.55/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.46 active(isNat(0)) -> mark(tt) 118.55/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.46 active(isNatKind(0)) -> mark(tt) 118.55/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.46 isNat(active(X:S)) -> isNat(X:S) 118.55/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.46 mark(0) -> active(0) 118.55/124.46 mark(tt) -> active(tt) 118.55/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.46 s(active(X:S)) -> s(X:S) 118.55/124.46 s(mark(X:S)) -> s(X:S) 118.55/124.46 ->Interpretation type: 118.55/124.46 Linear 118.55/124.46 ->Coefficients: 118.55/124.46 Natural Numbers 118.55/124.46 ->Dimension: 118.55/124.46 1 118.55/124.46 ->Bound: 118.55/124.46 2 118.55/124.46 ->Interpretation: 118.55/124.46 118.55/124.46 [U11](X1,X2,X3) = 1 118.55/124.46 [U12](X1,X2,X3) = 1 118.55/124.46 [U13](X1,X2,X3) = 1 118.55/124.46 [U14](X1,X2,X3) = 1 118.55/124.46 [U15](X1,X2) = 1 118.55/124.46 [U16](X) = 2 118.55/124.46 [U21](X1,X2) = 1 118.55/124.46 [U22](X1,X2) = 1 118.55/124.46 [U23](X) = 2 118.55/124.46 [U31](X1,X2) = 1 118.55/124.46 [U32](X) = 0 118.55/124.46 [U41](X) = 0 118.55/124.46 [U51](X1,X2) = 1 118.55/124.46 [U52](X1,X2) = 1 118.55/124.46 [U61](X1,X2,X3) = 1 118.55/124.46 [U62](X1,X2,X3) = 1 118.55/124.46 [U63](X1,X2,X3) = 1 118.55/124.46 [U64](X1,X2,X3) = 0 118.55/124.46 [active](X) = 2 118.55/124.46 [isNat](X) = 1 118.55/124.46 [isNatKind](X) = 1 118.55/124.46 [mark](X) = 2 118.55/124.46 [plus](X1,X2) = 0 118.55/124.46 [s](X) = 0 118.55/124.46 [0] = 2 118.55/124.46 [fSNonEmpty] = 0 118.55/124.46 [tt] = 1 118.55/124.46 [U11#](X1,X2,X3) = 0 118.55/124.46 [U12#](X1,X2,X3) = 0 118.55/124.46 [U13#](X1,X2,X3) = 0 118.55/124.46 [U14#](X1,X2,X3) = 0 118.55/124.46 [U15#](X1,X2) = 0 118.55/124.46 [U16#](X) = 0 118.55/124.46 [U21#](X1,X2) = 0 118.55/124.46 [U22#](X1,X2) = 0 118.55/124.46 [U23#](X) = 0 118.55/124.46 [U31#](X1,X2) = 0 118.55/124.46 [U32#](X) = 0 118.55/124.46 [U41#](X) = 0 118.55/124.46 [U51#](X1,X2) = 0 118.55/124.46 [U52#](X1,X2) = 0 118.55/124.46 [U61#](X1,X2,X3) = 0 118.55/124.46 [U62#](X1,X2,X3) = 0 118.55/124.46 [U63#](X1,X2,X3) = 0 118.55/124.46 [U64#](X1,X2,X3) = 0 118.55/124.46 [ACTIVE](X) = 2.X 118.55/124.46 [ISNAT](X) = 0 118.55/124.46 [ISNATKIND](X) = 0 118.55/124.46 [MARK](X) = 2 118.55/124.46 [PLUS](X1,X2) = 0 118.55/124.46 [S](X) = 0 118.55/124.46 118.55/124.46 Problem 1.23: 118.55/124.46 118.55/124.46 SCC Processor: 118.55/124.46 -> Pairs: 118.55/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.55/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.55/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.46 MARK(s(X:S)) -> MARK(X:S) 118.55/124.46 -> Rules: 118.55/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.46 U16(active(X:S)) -> U16(X:S) 118.55/124.46 U16(mark(X:S)) -> U16(X:S) 118.55/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.46 U23(active(X:S)) -> U23(X:S) 118.55/124.46 U23(mark(X:S)) -> U23(X:S) 118.55/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.46 U32(active(X:S)) -> U32(X:S) 118.55/124.46 U32(mark(X:S)) -> U32(X:S) 118.55/124.46 U41(active(X:S)) -> U41(X:S) 118.55/124.46 U41(mark(X:S)) -> U41(X:S) 118.55/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.46 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.46 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.46 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.46 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.46 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.46 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.46 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.46 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.46 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.46 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.46 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.46 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.46 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.46 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.46 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.46 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.46 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.46 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.46 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.46 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.46 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.46 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.46 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.46 active(U16(tt)) -> mark(tt) 118.55/124.46 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.46 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.46 active(U23(tt)) -> mark(tt) 118.55/124.46 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.46 active(U32(tt)) -> mark(tt) 118.55/124.46 active(U41(tt)) -> mark(tt) 118.55/124.46 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.46 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.46 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.46 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.46 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.46 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.46 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.46 active(isNat(0)) -> mark(tt) 118.55/124.46 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.46 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.46 active(isNatKind(0)) -> mark(tt) 118.55/124.46 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.46 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.46 isNat(active(X:S)) -> isNat(X:S) 118.55/124.46 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.46 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.46 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.46 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.46 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.46 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.46 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.46 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.46 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.46 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.46 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.46 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.46 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.46 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.46 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.46 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.46 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.46 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.46 mark(0) -> active(0) 118.55/124.46 mark(tt) -> active(tt) 118.55/124.46 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.46 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.46 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.46 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.46 s(active(X:S)) -> s(X:S) 118.55/124.46 s(mark(X:S)) -> s(X:S) 118.55/124.46 ->Strongly Connected Components: 118.55/124.46 ->->Cycle: 118.55/124.46 ->->-> Pairs: 118.55/124.46 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.46 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.46 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.46 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.46 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.46 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.46 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.46 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.46 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.46 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.46 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.46 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.46 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.55/124.46 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.46 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.55/124.46 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.46 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.46 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.46 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.46 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.46 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.46 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.46 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.46 MARK(s(X:S)) -> MARK(X:S) 118.55/124.46 ->->-> Rules: 118.55/124.46 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.46 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.46 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.46 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.46 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.46 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.46 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.46 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.46 U16(active(X:S)) -> U16(X:S) 118.55/124.46 U16(mark(X:S)) -> U16(X:S) 118.55/124.46 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.46 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.46 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.46 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.46 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.46 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.46 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.46 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.46 U23(active(X:S)) -> U23(X:S) 118.55/124.46 U23(mark(X:S)) -> U23(X:S) 118.55/124.46 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.46 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.46 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.46 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.46 U32(active(X:S)) -> U32(X:S) 118.55/124.46 U32(mark(X:S)) -> U32(X:S) 118.55/124.46 U41(active(X:S)) -> U41(X:S) 118.55/124.46 U41(mark(X:S)) -> U41(X:S) 118.55/124.46 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 118.55/124.47 Problem 1.23: 118.55/124.47 118.55/124.47 Reduction Pairs Processor: 118.55/124.47 -> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> ACTIVE(U41(mark(X:S))) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 -> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 -> Usable rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 ->Interpretation type: 118.55/124.47 Linear 118.55/124.47 ->Coefficients: 118.55/124.47 Natural Numbers 118.55/124.47 ->Dimension: 118.55/124.47 1 118.55/124.47 ->Bound: 118.55/124.47 2 118.55/124.47 ->Interpretation: 118.55/124.47 118.55/124.47 [U11](X1,X2,X3) = 2 118.55/124.47 [U12](X1,X2,X3) = 2 118.55/124.47 [U13](X1,X2,X3) = 2 118.55/124.47 [U14](X1,X2,X3) = 2 118.55/124.47 [U15](X1,X2) = 2 118.55/124.47 [U16](X) = 0 118.55/124.47 [U21](X1,X2) = 2 118.55/124.47 [U22](X1,X2) = 2 118.55/124.47 [U23](X) = 0 118.55/124.47 [U31](X1,X2) = 2 118.55/124.47 [U32](X) = 0 118.55/124.47 [U41](X) = 1 118.55/124.47 [U51](X1,X2) = 1 118.55/124.47 [U52](X1,X2) = 0 118.55/124.47 [U61](X1,X2,X3) = 2 118.55/124.47 [U62](X1,X2,X3) = 0 118.55/124.47 [U63](X1,X2,X3) = 2 118.55/124.47 [U64](X1,X2,X3) = 0 118.55/124.47 [active](X) = 2 118.55/124.47 [isNat](X) = 2 118.55/124.47 [isNatKind](X) = 2 118.55/124.47 [mark](X) = 2 118.55/124.47 [plus](X1,X2) = 2 118.55/124.47 [s](X) = 1 118.55/124.47 [0] = 2 118.55/124.47 [fSNonEmpty] = 0 118.55/124.47 [tt] = 0 118.55/124.47 [U11#](X1,X2,X3) = 0 118.55/124.47 [U12#](X1,X2,X3) = 0 118.55/124.47 [U13#](X1,X2,X3) = 0 118.55/124.47 [U14#](X1,X2,X3) = 0 118.55/124.47 [U15#](X1,X2) = 0 118.55/124.47 [U16#](X) = 0 118.55/124.47 [U21#](X1,X2) = 0 118.55/124.47 [U22#](X1,X2) = 0 118.55/124.47 [U23#](X) = 0 118.55/124.47 [U31#](X1,X2) = 0 118.55/124.47 [U32#](X) = 0 118.55/124.47 [U41#](X) = 0 118.55/124.47 [U51#](X1,X2) = 0 118.55/124.47 [U52#](X1,X2) = 0 118.55/124.47 [U61#](X1,X2,X3) = 0 118.55/124.47 [U62#](X1,X2,X3) = 0 118.55/124.47 [U63#](X1,X2,X3) = 0 118.55/124.47 [U64#](X1,X2,X3) = 0 118.55/124.47 [ACTIVE](X) = X 118.55/124.47 [ISNAT](X) = 0 118.55/124.47 [ISNATKIND](X) = 0 118.55/124.47 [MARK](X) = 2 118.55/124.47 [PLUS](X1,X2) = 0 118.55/124.47 [S](X) = 0 118.55/124.47 118.55/124.47 Problem 1.23: 118.55/124.47 118.55/124.47 SCC Processor: 118.55/124.47 -> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 -> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 ->Strongly Connected Components: 118.55/124.47 ->->Cycle: 118.55/124.47 ->->-> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 ->->-> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 118.55/124.47 Problem 1.23: 118.55/124.47 118.55/124.47 Reduction Pairs Processor: 118.55/124.47 -> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> ACTIVE(U51(mark(X1:S),X2:S)) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 -> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 -> Usable rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 ->Interpretation type: 118.55/124.47 Linear 118.55/124.47 ->Coefficients: 118.55/124.47 Natural Numbers 118.55/124.47 ->Dimension: 118.55/124.47 1 118.55/124.47 ->Bound: 118.55/124.47 2 118.55/124.47 ->Interpretation: 118.55/124.47 118.55/124.47 [U11](X1,X2,X3) = 1 118.55/124.47 [U12](X1,X2,X3) = 1 118.55/124.47 [U13](X1,X2,X3) = 1 118.55/124.47 [U14](X1,X2,X3) = 1 118.55/124.47 [U15](X1,X2) = 1 118.55/124.47 [U16](X) = 0 118.55/124.47 [U21](X1,X2) = 1 118.55/124.47 [U22](X1,X2) = 1 118.55/124.47 [U23](X) = 0 118.55/124.47 [U31](X1,X2) = 1 118.55/124.47 [U32](X) = 2 118.55/124.47 [U41](X) = 0 118.55/124.47 [U51](X1,X2) = 0 118.55/124.47 [U52](X1,X2) = 1 118.55/124.47 [U61](X1,X2,X3) = 1 118.55/124.47 [U62](X1,X2,X3) = 1 118.55/124.47 [U63](X1,X2,X3) = 1 118.55/124.47 [U64](X1,X2,X3) = 0 118.55/124.47 [active](X) = 2 118.55/124.47 [isNat](X) = 1 118.55/124.47 [isNatKind](X) = 1 118.55/124.47 [mark](X) = 2 118.55/124.47 [plus](X1,X2) = 1 118.55/124.47 [s](X) = 1 118.55/124.47 [0] = 1 118.55/124.47 [fSNonEmpty] = 0 118.55/124.47 [tt] = 2 118.55/124.47 [U11#](X1,X2,X3) = 0 118.55/124.47 [U12#](X1,X2,X3) = 0 118.55/124.47 [U13#](X1,X2,X3) = 0 118.55/124.47 [U14#](X1,X2,X3) = 0 118.55/124.47 [U15#](X1,X2) = 0 118.55/124.47 [U16#](X) = 0 118.55/124.47 [U21#](X1,X2) = 0 118.55/124.47 [U22#](X1,X2) = 0 118.55/124.47 [U23#](X) = 0 118.55/124.47 [U31#](X1,X2) = 0 118.55/124.47 [U32#](X) = 0 118.55/124.47 [U41#](X) = 0 118.55/124.47 [U51#](X1,X2) = 0 118.55/124.47 [U52#](X1,X2) = 0 118.55/124.47 [U61#](X1,X2,X3) = 0 118.55/124.47 [U62#](X1,X2,X3) = 0 118.55/124.47 [U63#](X1,X2,X3) = 0 118.55/124.47 [U64#](X1,X2,X3) = 0 118.55/124.47 [ACTIVE](X) = X + 1 118.55/124.47 [ISNAT](X) = 0 118.55/124.47 [ISNATKIND](X) = 0 118.55/124.47 [MARK](X) = 2 118.55/124.47 [PLUS](X1,X2) = 0 118.55/124.47 [S](X) = 0 118.55/124.47 118.55/124.47 Problem 1.23: 118.55/124.47 118.55/124.47 SCC Processor: 118.55/124.47 -> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 -> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 ->Strongly Connected Components: 118.55/124.47 ->->Cycle: 118.55/124.47 ->->-> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 ->->-> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 118.55/124.47 Problem 1.23: 118.55/124.47 118.55/124.47 Reduction Pairs Processor: 118.55/124.47 -> Pairs: 118.55/124.47 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.47 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.47 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.47 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.47 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.47 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.47 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.47 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.47 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.47 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.47 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.47 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.47 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.47 MARK(s(X:S)) -> MARK(X:S) 118.55/124.47 -> Rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.47 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.47 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.47 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.47 U16(active(X:S)) -> U16(X:S) 118.55/124.47 U16(mark(X:S)) -> U16(X:S) 118.55/124.47 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.47 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.47 U23(active(X:S)) -> U23(X:S) 118.55/124.47 U23(mark(X:S)) -> U23(X:S) 118.55/124.47 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.47 U32(active(X:S)) -> U32(X:S) 118.55/124.47 U32(mark(X:S)) -> U32(X:S) 118.55/124.47 U41(active(X:S)) -> U41(X:S) 118.55/124.47 U41(mark(X:S)) -> U41(X:S) 118.55/124.47 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.47 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.47 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.47 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.47 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.47 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.47 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.47 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.47 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.47 active(U16(tt)) -> mark(tt) 118.55/124.47 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.47 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.47 active(U23(tt)) -> mark(tt) 118.55/124.47 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.47 active(U32(tt)) -> mark(tt) 118.55/124.47 active(U41(tt)) -> mark(tt) 118.55/124.47 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.47 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.47 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.47 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.47 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.47 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.47 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.47 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.47 active(isNat(0)) -> mark(tt) 118.55/124.47 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.47 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.47 active(isNatKind(0)) -> mark(tt) 118.55/124.47 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.47 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.47 isNat(active(X:S)) -> isNat(X:S) 118.55/124.47 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.47 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.47 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.47 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.47 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.47 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.47 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.47 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.47 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.47 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.47 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.47 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.47 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.47 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.47 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.47 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.47 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.47 mark(0) -> active(0) 118.55/124.47 mark(tt) -> active(tt) 118.55/124.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.47 s(active(X:S)) -> s(X:S) 118.55/124.47 s(mark(X:S)) -> s(X:S) 118.55/124.47 -> Usable rules: 118.55/124.47 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.47 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 ->Interpretation type: 118.55/124.48 Linear 118.55/124.48 ->Coefficients: 118.55/124.48 Natural Numbers 118.55/124.48 ->Dimension: 118.55/124.48 1 118.55/124.48 ->Bound: 118.55/124.48 2 118.55/124.48 ->Interpretation: 118.55/124.48 118.55/124.48 [U11](X1,X2,X3) = X1 118.55/124.48 [U12](X1,X2,X3) = X1 118.55/124.48 [U13](X1,X2,X3) = X1 118.55/124.48 [U14](X1,X2,X3) = X1 118.55/124.48 [U15](X1,X2) = X1 118.55/124.48 [U16](X) = X 118.55/124.48 [U21](X1,X2) = X1 118.55/124.48 [U22](X1,X2) = X1 118.55/124.48 [U23](X) = X 118.55/124.48 [U31](X1,X2) = X1 118.55/124.48 [U32](X) = X 118.55/124.48 [U41](X) = X 118.55/124.48 [U51](X1,X2) = X1 + 2.X2 + 2 118.55/124.48 [U52](X1,X2) = 2.X1 + X2 118.55/124.48 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [active](X) = X 118.55/124.48 [isNat](X) = 2 118.55/124.48 [isNatKind](X) = 2 118.55/124.48 [mark](X) = X 118.55/124.48 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.48 [s](X) = X + 2 118.55/124.48 [0] = 1 118.55/124.48 [fSNonEmpty] = 0 118.55/124.48 [tt] = 2 118.55/124.48 [U11#](X1,X2,X3) = 0 118.55/124.48 [U12#](X1,X2,X3) = 0 118.55/124.48 [U13#](X1,X2,X3) = 0 118.55/124.48 [U14#](X1,X2,X3) = 0 118.55/124.48 [U15#](X1,X2) = 0 118.55/124.48 [U16#](X) = 0 118.55/124.48 [U21#](X1,X2) = 0 118.55/124.48 [U22#](X1,X2) = 0 118.55/124.48 [U23#](X) = 0 118.55/124.48 [U31#](X1,X2) = 0 118.55/124.48 [U32#](X) = 0 118.55/124.48 [U41#](X) = 0 118.55/124.48 [U51#](X1,X2) = 0 118.55/124.48 [U52#](X1,X2) = 0 118.55/124.48 [U61#](X1,X2,X3) = 0 118.55/124.48 [U62#](X1,X2,X3) = 0 118.55/124.48 [U63#](X1,X2,X3) = 0 118.55/124.48 [U64#](X1,X2,X3) = 0 118.55/124.48 [ACTIVE](X) = X + 2 118.55/124.48 [ISNAT](X) = 0 118.55/124.48 [ISNATKIND](X) = 0 118.55/124.48 [MARK](X) = X + 2 118.55/124.48 [PLUS](X1,X2) = 0 118.55/124.48 [S](X) = 0 118.55/124.48 118.55/124.48 Problem 1.23: 118.55/124.48 118.55/124.48 SCC Processor: 118.55/124.48 -> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 -> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 ->Strongly Connected Components: 118.55/124.48 ->->Cycle: 118.55/124.48 ->->-> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 ->->-> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 118.55/124.48 Problem 1.23: 118.55/124.48 118.55/124.48 Reduction Pairs Processor: 118.55/124.48 -> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> ACTIVE(U52(mark(X1:S),X2:S)) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 -> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 -> Usable rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 ->Interpretation type: 118.55/124.48 Linear 118.55/124.48 ->Coefficients: 118.55/124.48 Natural Numbers 118.55/124.48 ->Dimension: 118.55/124.48 1 118.55/124.48 ->Bound: 118.55/124.48 2 118.55/124.48 ->Interpretation: 118.55/124.48 118.55/124.48 [U11](X1,X2,X3) = 2.X1 118.55/124.48 [U12](X1,X2,X3) = 2.X1 118.55/124.48 [U13](X1,X2,X3) = 2.X1 118.55/124.48 [U14](X1,X2,X3) = 2.X1 118.55/124.48 [U15](X1,X2) = 2.X1 118.55/124.48 [U16](X) = 2.X 118.55/124.48 [U21](X1,X2) = 2.X1 118.55/124.48 [U22](X1,X2) = 2.X1 118.55/124.48 [U23](X) = 2.X 118.55/124.48 [U31](X1,X2) = 2.X1 118.55/124.48 [U32](X) = 2.X 118.55/124.48 [U41](X) = 2.X 118.55/124.48 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.48 [U52](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.48 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [active](X) = X 118.55/124.48 [isNat](X) = 0 118.55/124.48 [isNatKind](X) = 0 118.55/124.48 [mark](X) = X 118.55/124.48 [plus](X1,X2) = 2.X1 + 2.X2 118.55/124.48 [s](X) = X + 2 118.55/124.48 [0] = 2 118.55/124.48 [fSNonEmpty] = 0 118.55/124.48 [tt] = 0 118.55/124.48 [U11#](X1,X2,X3) = 0 118.55/124.48 [U12#](X1,X2,X3) = 0 118.55/124.48 [U13#](X1,X2,X3) = 0 118.55/124.48 [U14#](X1,X2,X3) = 0 118.55/124.48 [U15#](X1,X2) = 0 118.55/124.48 [U16#](X) = 0 118.55/124.48 [U21#](X1,X2) = 0 118.55/124.48 [U22#](X1,X2) = 0 118.55/124.48 [U23#](X) = 0 118.55/124.48 [U31#](X1,X2) = 0 118.55/124.48 [U32#](X) = 0 118.55/124.48 [U41#](X) = 0 118.55/124.48 [U51#](X1,X2) = 0 118.55/124.48 [U52#](X1,X2) = 0 118.55/124.48 [U61#](X1,X2,X3) = 0 118.55/124.48 [U62#](X1,X2,X3) = 0 118.55/124.48 [U63#](X1,X2,X3) = 0 118.55/124.48 [U64#](X1,X2,X3) = 0 118.55/124.48 [ACTIVE](X) = 2 118.55/124.48 [ISNAT](X) = 0 118.55/124.48 [ISNATKIND](X) = 0 118.55/124.48 [MARK](X) = 2.X + 2 118.55/124.48 [PLUS](X1,X2) = 0 118.55/124.48 [S](X) = 0 118.55/124.48 118.55/124.48 Problem 1.23: 118.55/124.48 118.55/124.48 SCC Processor: 118.55/124.48 -> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 -> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 ->Strongly Connected Components: 118.55/124.48 ->->Cycle: 118.55/124.48 ->->-> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 ->->-> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 118.55/124.48 Problem 1.23: 118.55/124.48 118.55/124.48 Reduction Pairs Processor: 118.55/124.48 -> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U52(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 -> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 -> Usable rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 ->Interpretation type: 118.55/124.48 Linear 118.55/124.48 ->Coefficients: 118.55/124.48 Natural Numbers 118.55/124.48 ->Dimension: 118.55/124.48 1 118.55/124.48 ->Bound: 118.55/124.48 2 118.55/124.48 ->Interpretation: 118.55/124.48 118.55/124.48 [U11](X1,X2,X3) = X1 118.55/124.48 [U12](X1,X2,X3) = X1 118.55/124.48 [U13](X1,X2,X3) = X1 118.55/124.48 [U14](X1,X2,X3) = X1 118.55/124.48 [U15](X1,X2) = X1 118.55/124.48 [U16](X) = X 118.55/124.48 [U21](X1,X2) = X1 118.55/124.48 [U22](X1,X2) = X1 118.55/124.48 [U23](X) = X 118.55/124.48 [U31](X1,X2) = X1 118.55/124.48 [U32](X) = X 118.55/124.48 [U41](X) = X 118.55/124.48 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.48 [U52](X1,X2) = X1 + 2.X2 + 2 118.55/124.48 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.48 [active](X) = X 118.55/124.48 [isNat](X) = 2 118.55/124.48 [isNatKind](X) = 2 118.55/124.48 [mark](X) = X 118.55/124.48 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.48 [s](X) = X + 2 118.55/124.48 [0] = 2 118.55/124.48 [fSNonEmpty] = 0 118.55/124.48 [tt] = 2 118.55/124.48 [U11#](X1,X2,X3) = 0 118.55/124.48 [U12#](X1,X2,X3) = 0 118.55/124.48 [U13#](X1,X2,X3) = 0 118.55/124.48 [U14#](X1,X2,X3) = 0 118.55/124.48 [U15#](X1,X2) = 0 118.55/124.48 [U16#](X) = 0 118.55/124.48 [U21#](X1,X2) = 0 118.55/124.48 [U22#](X1,X2) = 0 118.55/124.48 [U23#](X) = 0 118.55/124.48 [U31#](X1,X2) = 0 118.55/124.48 [U32#](X) = 0 118.55/124.48 [U41#](X) = 0 118.55/124.48 [U51#](X1,X2) = 0 118.55/124.48 [U52#](X1,X2) = 0 118.55/124.48 [U61#](X1,X2,X3) = 0 118.55/124.48 [U62#](X1,X2,X3) = 0 118.55/124.48 [U63#](X1,X2,X3) = 0 118.55/124.48 [U64#](X1,X2,X3) = 0 118.55/124.48 [ACTIVE](X) = 2.X + 2 118.55/124.48 [ISNAT](X) = 0 118.55/124.48 [ISNATKIND](X) = 0 118.55/124.48 [MARK](X) = 2.X + 2 118.55/124.48 [PLUS](X1,X2) = 0 118.55/124.48 [S](X) = 0 118.55/124.48 118.55/124.48 Problem 1.23: 118.55/124.48 118.55/124.48 SCC Processor: 118.55/124.48 -> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 -> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.48 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.48 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.48 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.48 U16(active(X:S)) -> U16(X:S) 118.55/124.48 U16(mark(X:S)) -> U16(X:S) 118.55/124.48 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.48 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.48 U23(active(X:S)) -> U23(X:S) 118.55/124.48 U23(mark(X:S)) -> U23(X:S) 118.55/124.48 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.48 U32(active(X:S)) -> U32(X:S) 118.55/124.48 U32(mark(X:S)) -> U32(X:S) 118.55/124.48 U41(active(X:S)) -> U41(X:S) 118.55/124.48 U41(mark(X:S)) -> U41(X:S) 118.55/124.48 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.48 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.48 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.48 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.48 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.48 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.48 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.48 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.48 active(U16(tt)) -> mark(tt) 118.55/124.48 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.48 active(U23(tt)) -> mark(tt) 118.55/124.48 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.48 active(U32(tt)) -> mark(tt) 118.55/124.48 active(U41(tt)) -> mark(tt) 118.55/124.48 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.48 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.48 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.48 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.48 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.48 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.48 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 active(isNat(0)) -> mark(tt) 118.55/124.48 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.48 active(isNatKind(0)) -> mark(tt) 118.55/124.48 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.48 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.48 isNat(active(X:S)) -> isNat(X:S) 118.55/124.48 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.48 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.48 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.48 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.48 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.48 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.48 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.48 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.48 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.48 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.48 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.48 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.48 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.48 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.48 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.48 mark(0) -> active(0) 118.55/124.48 mark(tt) -> active(tt) 118.55/124.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.48 s(active(X:S)) -> s(X:S) 118.55/124.48 s(mark(X:S)) -> s(X:S) 118.55/124.48 ->Strongly Connected Components: 118.55/124.48 ->->Cycle: 118.55/124.48 ->->-> Pairs: 118.55/124.48 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.48 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.48 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.48 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.48 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.48 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.48 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.48 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.48 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.48 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.48 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.48 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.48 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.48 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.48 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.48 MARK(s(X:S)) -> MARK(X:S) 118.55/124.48 ->->-> Rules: 118.55/124.48 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.48 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 118.55/124.49 Problem 1.23: 118.55/124.49 118.55/124.49 Reduction Pairs Processor: 118.55/124.49 -> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U61(X1:S,X2:S,X3:S)) -> ACTIVE(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 -> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 -> Usable rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 ->Interpretation type: 118.55/124.49 Linear 118.55/124.49 ->Coefficients: 118.55/124.49 Natural Numbers 118.55/124.49 ->Dimension: 118.55/124.49 1 118.55/124.49 ->Bound: 118.55/124.49 2 118.55/124.49 ->Interpretation: 118.55/124.49 118.55/124.49 [U11](X1,X2,X3) = 2.X1 118.55/124.49 [U12](X1,X2,X3) = 2.X1 118.55/124.49 [U13](X1,X2,X3) = 2.X1 118.55/124.49 [U14](X1,X2,X3) = 2.X1 118.55/124.49 [U15](X1,X2) = 2.X1 118.55/124.49 [U16](X) = 2.X 118.55/124.49 [U21](X1,X2) = 2.X1 118.55/124.49 [U22](X1,X2) = 2.X1 118.55/124.49 [U23](X) = 2.X 118.55/124.49 [U31](X1,X2) = 2.X1 118.55/124.49 [U32](X) = 2.X 118.55/124.49 [U41](X) = 2.X 118.55/124.49 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.49 [U52](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.49 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.49 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.49 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.49 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.49 [active](X) = X 118.55/124.49 [isNat](X) = 0 118.55/124.49 [isNatKind](X) = 0 118.55/124.49 [mark](X) = X 118.55/124.49 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.49 [s](X) = X 118.55/124.49 [0] = 2 118.55/124.49 [fSNonEmpty] = 0 118.55/124.49 [tt] = 0 118.55/124.49 [U11#](X1,X2,X3) = 0 118.55/124.49 [U12#](X1,X2,X3) = 0 118.55/124.49 [U13#](X1,X2,X3) = 0 118.55/124.49 [U14#](X1,X2,X3) = 0 118.55/124.49 [U15#](X1,X2) = 0 118.55/124.49 [U16#](X) = 0 118.55/124.49 [U21#](X1,X2) = 0 118.55/124.49 [U22#](X1,X2) = 0 118.55/124.49 [U23#](X) = 0 118.55/124.49 [U31#](X1,X2) = 0 118.55/124.49 [U32#](X) = 0 118.55/124.49 [U41#](X) = 0 118.55/124.49 [U51#](X1,X2) = 0 118.55/124.49 [U52#](X1,X2) = 0 118.55/124.49 [U61#](X1,X2,X3) = 0 118.55/124.49 [U62#](X1,X2,X3) = 0 118.55/124.49 [U63#](X1,X2,X3) = 0 118.55/124.49 [U64#](X1,X2,X3) = 0 118.55/124.49 [ACTIVE](X) = 2 118.55/124.49 [ISNAT](X) = 0 118.55/124.49 [ISNATKIND](X) = 0 118.55/124.49 [MARK](X) = 2.X + 2 118.55/124.49 [PLUS](X1,X2) = 0 118.55/124.49 [S](X) = 0 118.55/124.49 118.55/124.49 Problem 1.23: 118.55/124.49 118.55/124.49 SCC Processor: 118.55/124.49 -> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 -> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 ->Strongly Connected Components: 118.55/124.49 ->->Cycle: 118.55/124.49 ->->-> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 ->->-> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 118.55/124.49 Problem 1.23: 118.55/124.49 118.55/124.49 Reduction Pairs Processor: 118.55/124.49 -> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U61(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 -> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 -> Usable rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 ->Interpretation type: 118.55/124.49 Linear 118.55/124.49 ->Coefficients: 118.55/124.49 Natural Numbers 118.55/124.49 ->Dimension: 118.55/124.49 1 118.55/124.49 ->Bound: 118.55/124.49 2 118.55/124.49 ->Interpretation: 118.55/124.49 118.55/124.49 [U11](X1,X2,X3) = X1 118.55/124.49 [U12](X1,X2,X3) = X1 118.55/124.49 [U13](X1,X2,X3) = X1 118.55/124.49 [U14](X1,X2,X3) = X1 118.55/124.49 [U15](X1,X2) = X1 118.55/124.49 [U16](X) = X 118.55/124.49 [U21](X1,X2) = X1 118.55/124.49 [U22](X1,X2) = X1 118.55/124.49 [U23](X) = X 118.55/124.49 [U31](X1,X2) = X1 118.55/124.49 [U32](X) = X 118.55/124.49 [U41](X) = X 118.55/124.49 [U51](X1,X2) = 2.X2 + 2 118.55/124.49 [U52](X1,X2) = X1 + 2.X2 118.55/124.49 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 118.55/124.49 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.49 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.55/124.49 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 118.55/124.49 [active](X) = X 118.55/124.49 [isNat](X) = 2 118.55/124.49 [isNatKind](X) = 2 118.55/124.49 [mark](X) = X 118.55/124.49 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.55/124.49 [s](X) = X + 2 118.55/124.49 [0] = 2 118.55/124.49 [fSNonEmpty] = 0 118.55/124.49 [tt] = 2 118.55/124.49 [U11#](X1,X2,X3) = 0 118.55/124.49 [U12#](X1,X2,X3) = 0 118.55/124.49 [U13#](X1,X2,X3) = 0 118.55/124.49 [U14#](X1,X2,X3) = 0 118.55/124.49 [U15#](X1,X2) = 0 118.55/124.49 [U16#](X) = 0 118.55/124.49 [U21#](X1,X2) = 0 118.55/124.49 [U22#](X1,X2) = 0 118.55/124.49 [U23#](X) = 0 118.55/124.49 [U31#](X1,X2) = 0 118.55/124.49 [U32#](X) = 0 118.55/124.49 [U41#](X) = 0 118.55/124.49 [U51#](X1,X2) = 0 118.55/124.49 [U52#](X1,X2) = 0 118.55/124.49 [U61#](X1,X2,X3) = 0 118.55/124.49 [U62#](X1,X2,X3) = 0 118.55/124.49 [U63#](X1,X2,X3) = 0 118.55/124.49 [U64#](X1,X2,X3) = 0 118.55/124.49 [ACTIVE](X) = 2.X + 2 118.55/124.49 [ISNAT](X) = 0 118.55/124.49 [ISNATKIND](X) = 0 118.55/124.49 [MARK](X) = 2.X + 2 118.55/124.49 [PLUS](X1,X2) = 0 118.55/124.49 [S](X) = 0 118.55/124.49 118.55/124.49 Problem 1.23: 118.55/124.49 118.55/124.49 SCC Processor: 118.55/124.49 -> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 -> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 ->Strongly Connected Components: 118.55/124.49 ->->Cycle: 118.55/124.49 ->->-> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 ->->-> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 118.55/124.49 Problem 1.23: 118.55/124.49 118.55/124.49 Reduction Pairs Processor: 118.55/124.49 -> Pairs: 118.55/124.49 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.49 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.49 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.49 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.49 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.49 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.49 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.49 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.49 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> ACTIVE(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.49 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.49 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.49 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.49 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.49 MARK(s(X:S)) -> MARK(X:S) 118.55/124.49 -> Rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.49 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.49 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.49 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.49 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.49 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.49 mark(0) -> active(0) 118.55/124.49 mark(tt) -> active(tt) 118.55/124.49 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.49 s(active(X:S)) -> s(X:S) 118.55/124.49 s(mark(X:S)) -> s(X:S) 118.55/124.49 -> Usable rules: 118.55/124.49 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.49 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.49 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.49 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.49 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.49 U16(active(X:S)) -> U16(X:S) 118.55/124.49 U16(mark(X:S)) -> U16(X:S) 118.55/124.49 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.49 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.49 U23(active(X:S)) -> U23(X:S) 118.55/124.49 U23(mark(X:S)) -> U23(X:S) 118.55/124.49 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.49 U32(active(X:S)) -> U32(X:S) 118.55/124.49 U32(mark(X:S)) -> U32(X:S) 118.55/124.49 U41(active(X:S)) -> U41(X:S) 118.55/124.49 U41(mark(X:S)) -> U41(X:S) 118.55/124.49 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.49 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.49 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.49 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.49 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.49 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.49 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.49 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.49 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.49 active(U16(tt)) -> mark(tt) 118.55/124.49 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.49 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.49 active(U23(tt)) -> mark(tt) 118.55/124.49 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.49 active(U32(tt)) -> mark(tt) 118.55/124.49 active(U41(tt)) -> mark(tt) 118.55/124.49 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.49 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.49 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.49 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.49 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.49 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.49 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.49 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.49 active(isNat(0)) -> mark(tt) 118.55/124.49 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.49 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.49 active(isNatKind(0)) -> mark(tt) 118.55/124.49 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.49 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.49 isNat(active(X:S)) -> isNat(X:S) 118.55/124.49 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.49 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.49 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.49 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.49 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.49 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.49 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.49 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.49 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.49 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.49 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.49 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.49 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 ->Interpretation type: 118.55/124.50 Linear 118.55/124.50 ->Coefficients: 118.55/124.50 Natural Numbers 118.55/124.50 ->Dimension: 118.55/124.50 1 118.55/124.50 ->Bound: 118.55/124.50 2 118.55/124.50 ->Interpretation: 118.55/124.50 118.55/124.50 [U11](X1,X2,X3) = 2.X1 118.55/124.50 [U12](X1,X2,X3) = 2.X1 118.55/124.50 [U13](X1,X2,X3) = 2.X1 118.55/124.50 [U14](X1,X2,X3) = 2.X1 118.55/124.50 [U15](X1,X2) = 2.X1 118.55/124.50 [U16](X) = 2.X 118.55/124.50 [U21](X1,X2) = 2.X1 118.55/124.50 [U22](X1,X2) = 2.X1 118.55/124.50 [U23](X) = 2.X 118.55/124.50 [U31](X1,X2) = 2.X1 118.55/124.50 [U32](X) = 2.X 118.55/124.50 [U41](X) = 2.X 118.55/124.50 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.50 [U52](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.50 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [active](X) = X 118.55/124.50 [isNat](X) = 0 118.55/124.50 [isNatKind](X) = 0 118.55/124.50 [mark](X) = X 118.55/124.50 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.50 [s](X) = X 118.55/124.50 [0] = 0 118.55/124.50 [fSNonEmpty] = 0 118.55/124.50 [tt] = 0 118.55/124.50 [U11#](X1,X2,X3) = 0 118.55/124.50 [U12#](X1,X2,X3) = 0 118.55/124.50 [U13#](X1,X2,X3) = 0 118.55/124.50 [U14#](X1,X2,X3) = 0 118.55/124.50 [U15#](X1,X2) = 0 118.55/124.50 [U16#](X) = 0 118.55/124.50 [U21#](X1,X2) = 0 118.55/124.50 [U22#](X1,X2) = 0 118.55/124.50 [U23#](X) = 0 118.55/124.50 [U31#](X1,X2) = 0 118.55/124.50 [U32#](X) = 0 118.55/124.50 [U41#](X) = 0 118.55/124.50 [U51#](X1,X2) = 0 118.55/124.50 [U52#](X1,X2) = 0 118.55/124.50 [U61#](X1,X2,X3) = 0 118.55/124.50 [U62#](X1,X2,X3) = 0 118.55/124.50 [U63#](X1,X2,X3) = 0 118.55/124.50 [U64#](X1,X2,X3) = 0 118.55/124.50 [ACTIVE](X) = X + 2 118.55/124.50 [ISNAT](X) = 0 118.55/124.50 [ISNATKIND](X) = 0 118.55/124.50 [MARK](X) = 2.X + 2 118.55/124.50 [PLUS](X1,X2) = 0 118.55/124.50 [S](X) = 0 118.55/124.50 118.55/124.50 Problem 1.23: 118.55/124.50 118.55/124.50 SCC Processor: 118.55/124.50 -> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 -> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 ->Strongly Connected Components: 118.55/124.50 ->->Cycle: 118.55/124.50 ->->-> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 ->->-> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 118.55/124.50 Problem 1.23: 118.55/124.50 118.55/124.50 Reduction Pairs Processor: 118.55/124.50 -> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U62(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 -> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 -> Usable rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 ->Interpretation type: 118.55/124.50 Linear 118.55/124.50 ->Coefficients: 118.55/124.50 Natural Numbers 118.55/124.50 ->Dimension: 118.55/124.50 1 118.55/124.50 ->Bound: 118.55/124.50 2 118.55/124.50 ->Interpretation: 118.55/124.50 118.55/124.50 [U11](X1,X2,X3) = 2.X1 118.55/124.50 [U12](X1,X2,X3) = 2.X1 118.55/124.50 [U13](X1,X2,X3) = 2.X1 118.55/124.50 [U14](X1,X2,X3) = 2.X1 118.55/124.50 [U15](X1,X2) = 2.X1 118.55/124.50 [U16](X) = 2.X 118.55/124.50 [U21](X1,X2) = 2.X1 118.55/124.50 [U22](X1,X2) = 2.X1 118.55/124.50 [U23](X) = 2.X 118.55/124.50 [U31](X1,X2) = 2.X1 118.55/124.50 [U32](X) = X 118.55/124.50 [U41](X) = 2.X 118.55/124.50 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.50 [U52](X1,X2) = X2 + 2 118.55/124.50 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [active](X) = X 118.55/124.50 [isNat](X) = 0 118.55/124.50 [isNatKind](X) = 0 118.55/124.50 [mark](X) = X 118.55/124.50 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.50 [s](X) = X 118.55/124.50 [0] = 1 118.55/124.50 [fSNonEmpty] = 0 118.55/124.50 [tt] = 0 118.55/124.50 [U11#](X1,X2,X3) = 0 118.55/124.50 [U12#](X1,X2,X3) = 0 118.55/124.50 [U13#](X1,X2,X3) = 0 118.55/124.50 [U14#](X1,X2,X3) = 0 118.55/124.50 [U15#](X1,X2) = 0 118.55/124.50 [U16#](X) = 0 118.55/124.50 [U21#](X1,X2) = 0 118.55/124.50 [U22#](X1,X2) = 0 118.55/124.50 [U23#](X) = 0 118.55/124.50 [U31#](X1,X2) = 0 118.55/124.50 [U32#](X) = 0 118.55/124.50 [U41#](X) = 0 118.55/124.50 [U51#](X1,X2) = 0 118.55/124.50 [U52#](X1,X2) = 0 118.55/124.50 [U61#](X1,X2,X3) = 0 118.55/124.50 [U62#](X1,X2,X3) = 0 118.55/124.50 [U63#](X1,X2,X3) = 0 118.55/124.50 [U64#](X1,X2,X3) = 0 118.55/124.50 [ACTIVE](X) = 2 118.55/124.50 [ISNAT](X) = 0 118.55/124.50 [ISNATKIND](X) = 0 118.55/124.50 [MARK](X) = 2.X + 2 118.55/124.50 [PLUS](X1,X2) = 0 118.55/124.50 [S](X) = 0 118.55/124.50 118.55/124.50 Problem 1.23: 118.55/124.50 118.55/124.50 SCC Processor: 118.55/124.50 -> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 -> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 ->Strongly Connected Components: 118.55/124.50 ->->Cycle: 118.55/124.50 ->->-> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 ->->-> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 118.55/124.50 Problem 1.23: 118.55/124.50 118.55/124.50 Reduction Pairs Processor: 118.55/124.50 -> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> ACTIVE(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 -> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 -> Usable rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 ->Interpretation type: 118.55/124.50 Linear 118.55/124.50 ->Coefficients: 118.55/124.50 Natural Numbers 118.55/124.50 ->Dimension: 118.55/124.50 1 118.55/124.50 ->Bound: 118.55/124.50 2 118.55/124.50 ->Interpretation: 118.55/124.50 118.55/124.50 [U11](X1,X2,X3) = X1 118.55/124.50 [U12](X1,X2,X3) = 2.X1 118.55/124.50 [U13](X1,X2,X3) = 2.X1 118.55/124.50 [U14](X1,X2,X3) = 2.X1 118.55/124.50 [U15](X1,X2) = 2.X1 118.55/124.50 [U16](X) = 2.X 118.55/124.50 [U21](X1,X2) = 2.X1 118.55/124.50 [U22](X1,X2) = 2.X1 118.55/124.50 [U23](X) = 2.X 118.55/124.50 [U31](X1,X2) = X1 118.55/124.50 [U32](X) = 2.X 118.55/124.50 [U41](X) = 2.X 118.55/124.50 [U51](X1,X2) = 2.X1 + 2.X2 + 1 118.55/124.50 [U52](X1,X2) = 2.X1 + 2.X2 + 1 118.55/124.50 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.50 [active](X) = X 118.55/124.50 [isNat](X) = 0 118.55/124.50 [isNatKind](X) = 0 118.55/124.50 [mark](X) = X 118.55/124.50 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.50 [s](X) = X 118.55/124.50 [0] = 0 118.55/124.50 [fSNonEmpty] = 0 118.55/124.50 [tt] = 0 118.55/124.50 [U11#](X1,X2,X3) = 0 118.55/124.50 [U12#](X1,X2,X3) = 0 118.55/124.50 [U13#](X1,X2,X3) = 0 118.55/124.50 [U14#](X1,X2,X3) = 0 118.55/124.50 [U15#](X1,X2) = 0 118.55/124.50 [U16#](X) = 0 118.55/124.50 [U21#](X1,X2) = 0 118.55/124.50 [U22#](X1,X2) = 0 118.55/124.50 [U23#](X) = 0 118.55/124.50 [U31#](X1,X2) = 0 118.55/124.50 [U32#](X) = 0 118.55/124.50 [U41#](X) = 0 118.55/124.50 [U51#](X1,X2) = 0 118.55/124.50 [U52#](X1,X2) = 0 118.55/124.50 [U61#](X1,X2,X3) = 0 118.55/124.50 [U62#](X1,X2,X3) = 0 118.55/124.50 [U63#](X1,X2,X3) = 0 118.55/124.50 [U64#](X1,X2,X3) = 0 118.55/124.50 [ACTIVE](X) = X + 2 118.55/124.50 [ISNAT](X) = 0 118.55/124.50 [ISNATKIND](X) = 0 118.55/124.50 [MARK](X) = 2.X + 2 118.55/124.50 [PLUS](X1,X2) = 0 118.55/124.50 [S](X) = 0 118.55/124.50 118.55/124.50 Problem 1.23: 118.55/124.50 118.55/124.50 SCC Processor: 118.55/124.50 -> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 -> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 ->Strongly Connected Components: 118.55/124.50 ->->Cycle: 118.55/124.50 ->->-> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.50 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.50 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.50 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.50 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.50 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.50 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.50 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.50 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.50 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.50 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.50 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.50 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.50 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.50 MARK(s(X:S)) -> MARK(X:S) 118.55/124.50 ->->-> Rules: 118.55/124.50 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.50 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.50 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.50 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.50 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.50 U16(active(X:S)) -> U16(X:S) 118.55/124.50 U16(mark(X:S)) -> U16(X:S) 118.55/124.50 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.50 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.50 U23(active(X:S)) -> U23(X:S) 118.55/124.50 U23(mark(X:S)) -> U23(X:S) 118.55/124.50 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.50 U32(active(X:S)) -> U32(X:S) 118.55/124.50 U32(mark(X:S)) -> U32(X:S) 118.55/124.50 U41(active(X:S)) -> U41(X:S) 118.55/124.50 U41(mark(X:S)) -> U41(X:S) 118.55/124.50 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.50 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.50 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.50 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.50 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.50 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.50 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.50 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.50 active(U16(tt)) -> mark(tt) 118.55/124.50 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.50 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.50 active(U23(tt)) -> mark(tt) 118.55/124.50 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.50 active(U32(tt)) -> mark(tt) 118.55/124.50 active(U41(tt)) -> mark(tt) 118.55/124.50 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.50 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.50 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.50 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.50 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.50 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.50 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.50 active(isNat(0)) -> mark(tt) 118.55/124.50 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.50 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.50 active(isNatKind(0)) -> mark(tt) 118.55/124.50 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.50 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.50 isNat(active(X:S)) -> isNat(X:S) 118.55/124.50 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.50 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.50 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.50 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.50 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.50 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.50 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.50 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.50 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.50 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.50 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.50 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.50 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.50 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.50 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.50 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.50 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.50 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.50 mark(0) -> active(0) 118.55/124.50 mark(tt) -> active(tt) 118.55/124.50 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.50 s(active(X:S)) -> s(X:S) 118.55/124.50 s(mark(X:S)) -> s(X:S) 118.55/124.50 118.55/124.50 Problem 1.23: 118.55/124.50 118.55/124.50 Reduction Pairs Processor: 118.55/124.50 -> Pairs: 118.55/124.50 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.50 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U63(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.51 MARK(s(X:S)) -> MARK(X:S) 118.55/124.51 -> Rules: 118.55/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.51 U16(active(X:S)) -> U16(X:S) 118.55/124.51 U16(mark(X:S)) -> U16(X:S) 118.55/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.51 U23(active(X:S)) -> U23(X:S) 118.55/124.51 U23(mark(X:S)) -> U23(X:S) 118.55/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.51 U32(active(X:S)) -> U32(X:S) 118.55/124.51 U32(mark(X:S)) -> U32(X:S) 118.55/124.51 U41(active(X:S)) -> U41(X:S) 118.55/124.51 U41(mark(X:S)) -> U41(X:S) 118.55/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.51 active(U16(tt)) -> mark(tt) 118.55/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.51 active(U23(tt)) -> mark(tt) 118.55/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.51 active(U32(tt)) -> mark(tt) 118.55/124.51 active(U41(tt)) -> mark(tt) 118.55/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.51 active(isNat(0)) -> mark(tt) 118.55/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.51 active(isNatKind(0)) -> mark(tt) 118.55/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.51 isNat(active(X:S)) -> isNat(X:S) 118.55/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.51 mark(0) -> active(0) 118.55/124.51 mark(tt) -> active(tt) 118.55/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.51 s(active(X:S)) -> s(X:S) 118.55/124.51 s(mark(X:S)) -> s(X:S) 118.55/124.51 -> Usable rules: 118.55/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.51 U16(active(X:S)) -> U16(X:S) 118.55/124.51 U16(mark(X:S)) -> U16(X:S) 118.55/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.51 U23(active(X:S)) -> U23(X:S) 118.55/124.51 U23(mark(X:S)) -> U23(X:S) 118.55/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.51 U32(active(X:S)) -> U32(X:S) 118.55/124.51 U32(mark(X:S)) -> U32(X:S) 118.55/124.51 U41(active(X:S)) -> U41(X:S) 118.55/124.51 U41(mark(X:S)) -> U41(X:S) 118.55/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.51 active(U16(tt)) -> mark(tt) 118.55/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.51 active(U23(tt)) -> mark(tt) 118.55/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.51 active(U32(tt)) -> mark(tt) 118.55/124.51 active(U41(tt)) -> mark(tt) 118.55/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.51 active(isNat(0)) -> mark(tt) 118.55/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.51 active(isNatKind(0)) -> mark(tt) 118.55/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.51 isNat(active(X:S)) -> isNat(X:S) 118.55/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.55/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.55/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.55/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.55/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.55/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.55/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.55/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.55/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.55/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.55/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.55/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.55/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.55/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.55/124.51 mark(0) -> active(0) 118.55/124.51 mark(tt) -> active(tt) 118.55/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.55/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.55/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.55/124.51 s(active(X:S)) -> s(X:S) 118.55/124.51 s(mark(X:S)) -> s(X:S) 118.55/124.51 ->Interpretation type: 118.55/124.51 Linear 118.55/124.51 ->Coefficients: 118.55/124.51 Natural Numbers 118.55/124.51 ->Dimension: 118.55/124.51 1 118.55/124.51 ->Bound: 118.55/124.51 2 118.55/124.51 ->Interpretation: 118.55/124.51 118.55/124.51 [U11](X1,X2,X3) = X1 118.55/124.51 [U12](X1,X2,X3) = X1 118.55/124.51 [U13](X1,X2,X3) = X1 118.55/124.51 [U14](X1,X2,X3) = X1 118.55/124.51 [U15](X1,X2) = X1 118.55/124.51 [U16](X) = X 118.55/124.51 [U21](X1,X2) = X1 118.55/124.51 [U22](X1,X2) = X1 118.55/124.51 [U23](X) = X 118.55/124.51 [U31](X1,X2) = X1 118.55/124.51 [U32](X) = X 118.55/124.51 [U41](X) = X 118.55/124.51 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.51 [U52](X1,X2) = 2.X1 + 2.X2 + 1 118.55/124.51 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.51 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.55/124.51 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.51 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.55/124.51 [active](X) = X 118.55/124.51 [isNat](X) = 2 118.55/124.51 [isNatKind](X) = 2 118.55/124.51 [mark](X) = X 118.55/124.51 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.55/124.51 [s](X) = X + 2 118.55/124.51 [0] = 2 118.55/124.51 [fSNonEmpty] = 0 118.55/124.51 [tt] = 2 118.55/124.51 [U11#](X1,X2,X3) = 0 118.55/124.51 [U12#](X1,X2,X3) = 0 118.55/124.51 [U13#](X1,X2,X3) = 0 118.55/124.51 [U14#](X1,X2,X3) = 0 118.55/124.51 [U15#](X1,X2) = 0 118.55/124.51 [U16#](X) = 0 118.55/124.51 [U21#](X1,X2) = 0 118.55/124.51 [U22#](X1,X2) = 0 118.55/124.51 [U23#](X) = 0 118.55/124.51 [U31#](X1,X2) = 0 118.55/124.51 [U32#](X) = 0 118.55/124.51 [U41#](X) = 0 118.55/124.51 [U51#](X1,X2) = 0 118.55/124.51 [U52#](X1,X2) = 0 118.55/124.51 [U61#](X1,X2,X3) = 0 118.55/124.51 [U62#](X1,X2,X3) = 0 118.55/124.51 [U63#](X1,X2,X3) = 0 118.55/124.51 [U64#](X1,X2,X3) = 0 118.55/124.51 [ACTIVE](X) = 2.X + 2 118.55/124.51 [ISNAT](X) = 0 118.55/124.51 [ISNATKIND](X) = 0 118.55/124.51 [MARK](X) = 2.X + 2 118.55/124.51 [PLUS](X1,X2) = 0 118.55/124.51 [S](X) = 0 118.55/124.51 118.55/124.51 Problem 1.23: 118.55/124.51 118.55/124.51 SCC Processor: 118.55/124.51 -> Pairs: 118.55/124.51 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.55/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.55/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.55/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.55/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.55/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.55/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.55/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.55/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.55/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.55/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.55/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.55/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.55/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.55/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.55/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.55/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.55/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.55/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.55/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.55/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.55/124.51 MARK(s(X:S)) -> MARK(X:S) 118.55/124.51 -> Rules: 118.55/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.55/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.55/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.55/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.55/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.55/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.55/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.55/124.51 U16(active(X:S)) -> U16(X:S) 118.55/124.51 U16(mark(X:S)) -> U16(X:S) 118.55/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.55/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.55/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.55/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.55/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.55/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.55/124.51 U23(active(X:S)) -> U23(X:S) 118.55/124.51 U23(mark(X:S)) -> U23(X:S) 118.55/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.55/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.55/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.55/124.51 U32(active(X:S)) -> U32(X:S) 118.55/124.51 U32(mark(X:S)) -> U32(X:S) 118.55/124.51 U41(active(X:S)) -> U41(X:S) 118.55/124.51 U41(mark(X:S)) -> U41(X:S) 118.55/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.55/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.55/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.55/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.55/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.55/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.55/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.55/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.55/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.55/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.55/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.55/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.55/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.55/124.51 active(U16(tt)) -> mark(tt) 118.55/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.55/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.55/124.51 active(U23(tt)) -> mark(tt) 118.55/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.55/124.51 active(U32(tt)) -> mark(tt) 118.55/124.51 active(U41(tt)) -> mark(tt) 118.55/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.55/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.55/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.55/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.55/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.55/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.55/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.55/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.55/124.51 active(isNat(0)) -> mark(tt) 118.55/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.55/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.55/124.51 active(isNatKind(0)) -> mark(tt) 118.55/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.55/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.55/124.51 isNat(active(X:S)) -> isNat(X:S) 118.55/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.55/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.55/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.55/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.55/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 ->Strongly Connected Components: 118.56/124.51 ->->Cycle: 118.56/124.51 ->->-> Pairs: 118.56/124.51 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.51 MARK(s(X:S)) -> MARK(X:S) 118.56/124.51 ->->-> Rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 118.56/124.51 Problem 1.23: 118.56/124.51 118.56/124.51 Reduction Pairs Processor: 118.56/124.51 -> Pairs: 118.56/124.51 ACTIVE(U11(tt,V1:S,V2:S)) -> MARK(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.51 MARK(s(X:S)) -> MARK(X:S) 118.56/124.51 -> Rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 -> Usable rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 ->Interpretation type: 118.56/124.51 Linear 118.56/124.51 ->Coefficients: 118.56/124.51 Natural Numbers 118.56/124.51 ->Dimension: 118.56/124.51 1 118.56/124.51 ->Bound: 118.56/124.51 2 118.56/124.51 ->Interpretation: 118.56/124.51 118.56/124.51 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.51 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 118.56/124.51 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.51 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.51 [U15](X1,X2) = X1 + 2.X2 + 2 118.56/124.51 [U16](X) = X + 2 118.56/124.51 [U21](X1,X2) = X1 + 2.X2 118.56/124.51 [U22](X1,X2) = X1 + 2.X2 118.56/124.51 [U23](X) = X 118.56/124.51 [U31](X1,X2) = X1 118.56/124.51 [U32](X) = X 118.56/124.51 [U41](X) = X 118.56/124.51 [U51](X1,X2) = 2.X2 + 2 118.56/124.51 [U52](X1,X2) = X2 + 2 118.56/124.51 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.51 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.51 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.51 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.51 [active](X) = X 118.56/124.51 [isNat](X) = 2.X + 2 118.56/124.51 [isNatKind](X) = 2 118.56/124.51 [mark](X) = X 118.56/124.51 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.56/124.51 [s](X) = X 118.56/124.51 [0] = 2 118.56/124.51 [fSNonEmpty] = 0 118.56/124.51 [tt] = 2 118.56/124.51 [U11#](X1,X2,X3) = 0 118.56/124.51 [U12#](X1,X2,X3) = 0 118.56/124.51 [U13#](X1,X2,X3) = 0 118.56/124.51 [U14#](X1,X2,X3) = 0 118.56/124.51 [U15#](X1,X2) = 0 118.56/124.51 [U16#](X) = 0 118.56/124.51 [U21#](X1,X2) = 0 118.56/124.51 [U22#](X1,X2) = 0 118.56/124.51 [U23#](X) = 0 118.56/124.51 [U31#](X1,X2) = 0 118.56/124.51 [U32#](X) = 0 118.56/124.51 [U41#](X) = 0 118.56/124.51 [U51#](X1,X2) = 0 118.56/124.51 [U52#](X1,X2) = 0 118.56/124.51 [U61#](X1,X2,X3) = 0 118.56/124.51 [U62#](X1,X2,X3) = 0 118.56/124.51 [U63#](X1,X2,X3) = 0 118.56/124.51 [U64#](X1,X2,X3) = 0 118.56/124.51 [ACTIVE](X) = 2.X + 1 118.56/124.51 [ISNAT](X) = 0 118.56/124.51 [ISNATKIND](X) = 0 118.56/124.51 [MARK](X) = 2.X + 1 118.56/124.51 [PLUS](X1,X2) = 0 118.56/124.51 [S](X) = 0 118.56/124.51 118.56/124.51 Problem 1.23: 118.56/124.51 118.56/124.51 SCC Processor: 118.56/124.51 -> Pairs: 118.56/124.51 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.51 MARK(s(X:S)) -> MARK(X:S) 118.56/124.51 -> Rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 ->Strongly Connected Components: 118.56/124.51 ->->Cycle: 118.56/124.51 ->->-> Pairs: 118.56/124.51 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.51 MARK(s(X:S)) -> MARK(X:S) 118.56/124.51 ->->-> Rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 118.56/124.51 Problem 1.23: 118.56/124.51 118.56/124.51 Reduction Pairs Processor: 118.56/124.51 -> Pairs: 118.56/124.51 ACTIVE(U12(tt,V1:S,V2:S)) -> MARK(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.51 MARK(s(X:S)) -> MARK(X:S) 118.56/124.51 -> Rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 -> Usable rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.51 U16(mark(X:S)) -> U16(X:S) 118.56/124.51 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.51 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.51 U23(active(X:S)) -> U23(X:S) 118.56/124.51 U23(mark(X:S)) -> U23(X:S) 118.56/124.51 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.51 U32(active(X:S)) -> U32(X:S) 118.56/124.51 U32(mark(X:S)) -> U32(X:S) 118.56/124.51 U41(active(X:S)) -> U41(X:S) 118.56/124.51 U41(mark(X:S)) -> U41(X:S) 118.56/124.51 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.51 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.51 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.51 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.51 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.51 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.51 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.51 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.51 active(U16(tt)) -> mark(tt) 118.56/124.51 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.51 active(U23(tt)) -> mark(tt) 118.56/124.51 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.51 active(U32(tt)) -> mark(tt) 118.56/124.51 active(U41(tt)) -> mark(tt) 118.56/124.51 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.51 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.51 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.51 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.51 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.51 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.51 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 active(isNat(0)) -> mark(tt) 118.56/124.51 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.51 active(isNatKind(0)) -> mark(tt) 118.56/124.51 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.51 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.51 isNat(active(X:S)) -> isNat(X:S) 118.56/124.51 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.51 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.51 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.51 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.51 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.51 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.51 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.51 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.51 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.51 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.51 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.51 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.51 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.51 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.51 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.51 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.51 mark(0) -> active(0) 118.56/124.51 mark(tt) -> active(tt) 118.56/124.51 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.51 s(active(X:S)) -> s(X:S) 118.56/124.51 s(mark(X:S)) -> s(X:S) 118.56/124.51 ->Interpretation type: 118.56/124.51 Linear 118.56/124.51 ->Coefficients: 118.56/124.51 Natural Numbers 118.56/124.51 ->Dimension: 118.56/124.51 1 118.56/124.51 ->Bound: 118.56/124.51 2 118.56/124.51 ->Interpretation: 118.56/124.51 118.56/124.51 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.51 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.51 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.51 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.56/124.51 [U15](X1,X2) = X1 + 2.X2 + 2 118.56/124.51 [U16](X) = X + 2 118.56/124.51 [U21](X1,X2) = X1 + 2.X2 118.56/124.51 [U22](X1,X2) = X1 + 2.X2 118.56/124.51 [U23](X) = X 118.56/124.51 [U31](X1,X2) = X1 118.56/124.51 [U32](X) = X 118.56/124.51 [U41](X) = X 118.56/124.51 [U51](X1,X2) = 2.X2 + 2 118.56/124.51 [U52](X1,X2) = 2.X2 + 2 118.56/124.51 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.51 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.51 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.51 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.51 [active](X) = X 118.56/124.51 [isNat](X) = 2.X + 2 118.56/124.51 [isNatKind](X) = 2 118.56/124.51 [mark](X) = X 118.56/124.51 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.56/124.51 [s](X) = X 118.56/124.51 [0] = 1 118.56/124.51 [fSNonEmpty] = 0 118.56/124.51 [tt] = 2 118.56/124.51 [U11#](X1,X2,X3) = 0 118.56/124.51 [U12#](X1,X2,X3) = 0 118.56/124.51 [U13#](X1,X2,X3) = 0 118.56/124.51 [U14#](X1,X2,X3) = 0 118.56/124.51 [U15#](X1,X2) = 0 118.56/124.51 [U16#](X) = 0 118.56/124.51 [U21#](X1,X2) = 0 118.56/124.51 [U22#](X1,X2) = 0 118.56/124.51 [U23#](X) = 0 118.56/124.51 [U31#](X1,X2) = 0 118.56/124.51 [U32#](X) = 0 118.56/124.51 [U41#](X) = 0 118.56/124.51 [U51#](X1,X2) = 0 118.56/124.51 [U52#](X1,X2) = 0 118.56/124.51 [U61#](X1,X2,X3) = 0 118.56/124.51 [U62#](X1,X2,X3) = 0 118.56/124.51 [U63#](X1,X2,X3) = 0 118.56/124.51 [U64#](X1,X2,X3) = 0 118.56/124.51 [ACTIVE](X) = 2.X 118.56/124.51 [ISNAT](X) = 0 118.56/124.51 [ISNATKIND](X) = 0 118.56/124.51 [MARK](X) = 2.X 118.56/124.51 [PLUS](X1,X2) = 0 118.56/124.51 [S](X) = 0 118.56/124.51 118.56/124.51 Problem 1.23: 118.56/124.51 118.56/124.51 SCC Processor: 118.56/124.51 -> Pairs: 118.56/124.51 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.51 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.51 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.51 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.51 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.51 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.51 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.51 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.51 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.51 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.51 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.51 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.51 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.51 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.51 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.51 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.51 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.51 MARK(s(X:S)) -> MARK(X:S) 118.56/124.51 -> Rules: 118.56/124.51 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.51 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.51 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.51 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.51 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.51 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 ->Strongly Connected Components: 118.56/124.52 ->->Cycle: 118.56/124.52 ->->-> Pairs: 118.56/124.52 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 ->->-> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 118.56/124.52 Problem 1.23: 118.56/124.52 118.56/124.52 Reduction Pairs Processor: 118.56/124.52 -> Pairs: 118.56/124.52 ACTIVE(U13(tt,V1:S,V2:S)) -> MARK(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 -> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 -> Usable rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 ->Interpretation type: 118.56/124.52 Linear 118.56/124.52 ->Coefficients: 118.56/124.52 Natural Numbers 118.56/124.52 ->Dimension: 118.56/124.52 1 118.56/124.52 ->Bound: 118.56/124.52 2 118.56/124.52 ->Interpretation: 118.56/124.52 118.56/124.52 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1 118.56/124.52 [U15](X1,X2) = X1 + 2.X2 + 1 118.56/124.52 [U16](X) = X + 1 118.56/124.52 [U21](X1,X2) = X1 + 2.X2 118.56/124.52 [U22](X1,X2) = X1 + 2.X2 118.56/124.52 [U23](X) = X 118.56/124.52 [U31](X1,X2) = X1 118.56/124.52 [U32](X) = X 118.56/124.52 [U41](X) = X 118.56/124.52 [U51](X1,X2) = 2.X2 + 2 118.56/124.52 [U52](X1,X2) = 2.X2 + 2 118.56/124.52 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.52 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.52 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.52 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.52 [active](X) = X 118.56/124.52 [isNat](X) = 2.X + 2 118.56/124.52 [isNatKind](X) = 2 118.56/124.52 [mark](X) = X 118.56/124.52 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.56/124.52 [s](X) = X 118.56/124.52 [0] = 0 118.56/124.52 [fSNonEmpty] = 0 118.56/124.52 [tt] = 2 118.56/124.52 [U11#](X1,X2,X3) = 0 118.56/124.52 [U12#](X1,X2,X3) = 0 118.56/124.52 [U13#](X1,X2,X3) = 0 118.56/124.52 [U14#](X1,X2,X3) = 0 118.56/124.52 [U15#](X1,X2) = 0 118.56/124.52 [U16#](X) = 0 118.56/124.52 [U21#](X1,X2) = 0 118.56/124.52 [U22#](X1,X2) = 0 118.56/124.52 [U23#](X) = 0 118.56/124.52 [U31#](X1,X2) = 0 118.56/124.52 [U32#](X) = 0 118.56/124.52 [U41#](X) = 0 118.56/124.52 [U51#](X1,X2) = 0 118.56/124.52 [U52#](X1,X2) = 0 118.56/124.52 [U61#](X1,X2,X3) = 0 118.56/124.52 [U62#](X1,X2,X3) = 0 118.56/124.52 [U63#](X1,X2,X3) = 0 118.56/124.52 [U64#](X1,X2,X3) = 0 118.56/124.52 [ACTIVE](X) = 2.X + 2 118.56/124.52 [ISNAT](X) = 0 118.56/124.52 [ISNATKIND](X) = 0 118.56/124.52 [MARK](X) = 2.X + 2 118.56/124.52 [PLUS](X1,X2) = 0 118.56/124.52 [S](X) = 0 118.56/124.52 118.56/124.52 Problem 1.23: 118.56/124.52 118.56/124.52 SCC Processor: 118.56/124.52 -> Pairs: 118.56/124.52 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 -> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 ->Strongly Connected Components: 118.56/124.52 ->->Cycle: 118.56/124.52 ->->-> Pairs: 118.56/124.52 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 ->->-> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 118.56/124.52 Problem 1.23: 118.56/124.52 118.56/124.52 Reduction Pairs Processor: 118.56/124.52 -> Pairs: 118.56/124.52 ACTIVE(U14(tt,V1:S,V2:S)) -> MARK(U15(isNat(V1:S),V2:S)) 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 -> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 -> Usable rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 ->Interpretation type: 118.56/124.52 Linear 118.56/124.52 ->Coefficients: 118.56/124.52 Natural Numbers 118.56/124.52 ->Dimension: 118.56/124.52 1 118.56/124.52 ->Bound: 118.56/124.52 2 118.56/124.52 ->Interpretation: 118.56/124.52 118.56/124.52 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U13](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.52 [U15](X1,X2) = X1 + 2.X2 + 2 118.56/124.52 [U16](X) = X + 2 118.56/124.52 [U21](X1,X2) = X1 + 2.X2 118.56/124.52 [U22](X1,X2) = X1 + 2.X2 118.56/124.52 [U23](X) = X 118.56/124.52 [U31](X1,X2) = X1 118.56/124.52 [U32](X) = X 118.56/124.52 [U41](X) = X 118.56/124.52 [U51](X1,X2) = 2.X2 + 2 118.56/124.52 [U52](X1,X2) = 2.X2 + 2 118.56/124.52 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.52 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.52 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.52 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.52 [active](X) = X 118.56/124.52 [isNat](X) = 2.X + 2 118.56/124.52 [isNatKind](X) = 2 118.56/124.52 [mark](X) = X 118.56/124.52 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.56/124.52 [s](X) = X 118.56/124.52 [0] = 2 118.56/124.52 [fSNonEmpty] = 0 118.56/124.52 [tt] = 2 118.56/124.52 [U11#](X1,X2,X3) = 0 118.56/124.52 [U12#](X1,X2,X3) = 0 118.56/124.52 [U13#](X1,X2,X3) = 0 118.56/124.52 [U14#](X1,X2,X3) = 0 118.56/124.52 [U15#](X1,X2) = 0 118.56/124.52 [U16#](X) = 0 118.56/124.52 [U21#](X1,X2) = 0 118.56/124.52 [U22#](X1,X2) = 0 118.56/124.52 [U23#](X) = 0 118.56/124.52 [U31#](X1,X2) = 0 118.56/124.52 [U32#](X) = 0 118.56/124.52 [U41#](X) = 0 118.56/124.52 [U51#](X1,X2) = 0 118.56/124.52 [U52#](X1,X2) = 0 118.56/124.52 [U61#](X1,X2,X3) = 0 118.56/124.52 [U62#](X1,X2,X3) = 0 118.56/124.52 [U63#](X1,X2,X3) = 0 118.56/124.52 [U64#](X1,X2,X3) = 0 118.56/124.52 [ACTIVE](X) = 2.X + 2 118.56/124.52 [ISNAT](X) = 0 118.56/124.52 [ISNATKIND](X) = 0 118.56/124.52 [MARK](X) = 2.X + 2 118.56/124.52 [PLUS](X1,X2) = 0 118.56/124.52 [S](X) = 0 118.56/124.52 118.56/124.52 Problem 1.23: 118.56/124.52 118.56/124.52 SCC Processor: 118.56/124.52 -> Pairs: 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 -> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 ->Strongly Connected Components: 118.56/124.52 ->->Cycle: 118.56/124.52 ->->-> Pairs: 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 ->->-> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 118.56/124.52 Problem 1.23: 118.56/124.52 118.56/124.52 Reduction Pairs Processor: 118.56/124.52 -> Pairs: 118.56/124.52 ACTIVE(U15(tt,V2:S)) -> MARK(U16(isNat(V2:S))) 118.56/124.52 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.52 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.52 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.52 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.52 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.52 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.52 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.52 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.52 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.52 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.52 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.52 MARK(s(X:S)) -> MARK(X:S) 118.56/124.52 -> Rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.52 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.52 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.52 U16(active(X:S)) -> U16(X:S) 118.56/124.52 U16(mark(X:S)) -> U16(X:S) 118.56/124.52 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.52 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.52 U23(active(X:S)) -> U23(X:S) 118.56/124.52 U23(mark(X:S)) -> U23(X:S) 118.56/124.52 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.52 U32(active(X:S)) -> U32(X:S) 118.56/124.52 U32(mark(X:S)) -> U32(X:S) 118.56/124.52 U41(active(X:S)) -> U41(X:S) 118.56/124.52 U41(mark(X:S)) -> U41(X:S) 118.56/124.52 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.52 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.52 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.52 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.52 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.52 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.52 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.52 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.52 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.52 active(U16(tt)) -> mark(tt) 118.56/124.52 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.52 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.52 active(U23(tt)) -> mark(tt) 118.56/124.52 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.52 active(U32(tt)) -> mark(tt) 118.56/124.52 active(U41(tt)) -> mark(tt) 118.56/124.52 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.52 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.52 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.52 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.52 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.52 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.52 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.52 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.52 active(isNat(0)) -> mark(tt) 118.56/124.52 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.52 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.52 active(isNatKind(0)) -> mark(tt) 118.56/124.52 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.52 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.52 isNat(active(X:S)) -> isNat(X:S) 118.56/124.52 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.52 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.52 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.52 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.52 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.52 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.52 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.52 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.52 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.52 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.52 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.52 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.52 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.52 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.52 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.52 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.52 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.52 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.52 mark(0) -> active(0) 118.56/124.52 mark(tt) -> active(tt) 118.56/124.52 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.52 s(active(X:S)) -> s(X:S) 118.56/124.52 s(mark(X:S)) -> s(X:S) 118.56/124.52 -> Usable rules: 118.56/124.52 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.52 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.52 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 ->Interpretation type: 118.56/124.53 Linear 118.56/124.53 ->Coefficients: 118.56/124.53 Natural Numbers 118.56/124.53 ->Dimension: 118.56/124.53 1 118.56/124.53 ->Bound: 118.56/124.53 2 118.56/124.53 ->Interpretation: 118.56/124.53 118.56/124.53 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.56/124.53 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.56/124.53 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.53 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.53 [U15](X1,X2) = X1 + 2.X2 + 2 118.56/124.53 [U16](X) = X + 1 118.56/124.53 [U21](X1,X2) = X1 + 2.X2 118.56/124.53 [U22](X1,X2) = X1 + 2.X2 118.56/124.53 [U23](X) = X 118.56/124.53 [U31](X1,X2) = X1 118.56/124.53 [U32](X) = X 118.56/124.53 [U41](X) = X 118.56/124.53 [U51](X1,X2) = X2 + 2 118.56/124.53 [U52](X1,X2) = X1 + X2 118.56/124.53 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [active](X) = X 118.56/124.53 [isNat](X) = 2.X + 2 118.56/124.53 [isNatKind](X) = 2 118.56/124.53 [mark](X) = X 118.56/124.53 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.56/124.53 [s](X) = X 118.56/124.53 [0] = 1 118.56/124.53 [fSNonEmpty] = 0 118.56/124.53 [tt] = 2 118.56/124.53 [U11#](X1,X2,X3) = 0 118.56/124.53 [U12#](X1,X2,X3) = 0 118.56/124.53 [U13#](X1,X2,X3) = 0 118.56/124.53 [U14#](X1,X2,X3) = 0 118.56/124.53 [U15#](X1,X2) = 0 118.56/124.53 [U16#](X) = 0 118.56/124.53 [U21#](X1,X2) = 0 118.56/124.53 [U22#](X1,X2) = 0 118.56/124.53 [U23#](X) = 0 118.56/124.53 [U31#](X1,X2) = 0 118.56/124.53 [U32#](X) = 0 118.56/124.53 [U41#](X) = 0 118.56/124.53 [U51#](X1,X2) = 0 118.56/124.53 [U52#](X1,X2) = 0 118.56/124.53 [U61#](X1,X2,X3) = 0 118.56/124.53 [U62#](X1,X2,X3) = 0 118.56/124.53 [U63#](X1,X2,X3) = 0 118.56/124.53 [U64#](X1,X2,X3) = 0 118.56/124.53 [ACTIVE](X) = 2.X + 2 118.56/124.53 [ISNAT](X) = 0 118.56/124.53 [ISNATKIND](X) = 0 118.56/124.53 [MARK](X) = 2.X + 2 118.56/124.53 [PLUS](X1,X2) = 0 118.56/124.53 [S](X) = 0 118.56/124.53 118.56/124.53 Problem 1.23: 118.56/124.53 118.56/124.53 SCC Processor: 118.56/124.53 -> Pairs: 118.56/124.53 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 -> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 ->Strongly Connected Components: 118.56/124.53 ->->Cycle: 118.56/124.53 ->->-> Pairs: 118.56/124.53 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 ->->-> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 118.56/124.53 Problem 1.23: 118.56/124.53 118.56/124.53 Reduction Pairs Processor: 118.56/124.53 -> Pairs: 118.56/124.53 ACTIVE(U21(tt,V1:S)) -> MARK(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 -> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 -> Usable rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 ->Interpretation type: 118.56/124.53 Linear 118.56/124.53 ->Coefficients: 118.56/124.53 Natural Numbers 118.56/124.53 ->Dimension: 118.56/124.53 1 118.56/124.53 ->Bound: 118.56/124.53 2 118.56/124.53 ->Interpretation: 118.56/124.53 118.56/124.53 [U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [U12](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [U15](X1,X2) = X1 + 2.X2 118.56/124.53 [U16](X) = X 118.56/124.53 [U21](X1,X2) = 2.X1 + 2.X2 + 1 118.56/124.53 [U22](X1,X2) = X1 + 2.X2 + 2 118.56/124.53 [U23](X) = X + 2 118.56/124.53 [U31](X1,X2) = X1 118.56/124.53 [U32](X) = X 118.56/124.53 [U41](X) = X 118.56/124.53 [U51](X1,X2) = 2.X2 + 2 118.56/124.53 [U52](X1,X2) = X1 + 2.X2 118.56/124.53 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [active](X) = X 118.56/124.53 [isNat](X) = 2.X + 2 118.56/124.53 [isNatKind](X) = 2 118.56/124.53 [mark](X) = X 118.56/124.53 [plus](X1,X2) = 2.X1 + 2.X2 118.56/124.53 [s](X) = X + 2 118.56/124.53 [0] = 2 118.56/124.53 [fSNonEmpty] = 0 118.56/124.53 [tt] = 2 118.56/124.53 [U11#](X1,X2,X3) = 0 118.56/124.53 [U12#](X1,X2,X3) = 0 118.56/124.53 [U13#](X1,X2,X3) = 0 118.56/124.53 [U14#](X1,X2,X3) = 0 118.56/124.53 [U15#](X1,X2) = 0 118.56/124.53 [U16#](X) = 0 118.56/124.53 [U21#](X1,X2) = 0 118.56/124.53 [U22#](X1,X2) = 0 118.56/124.53 [U23#](X) = 0 118.56/124.53 [U31#](X1,X2) = 0 118.56/124.53 [U32#](X) = 0 118.56/124.53 [U41#](X) = 0 118.56/124.53 [U51#](X1,X2) = 0 118.56/124.53 [U52#](X1,X2) = 0 118.56/124.53 [U61#](X1,X2,X3) = 0 118.56/124.53 [U62#](X1,X2,X3) = 0 118.56/124.53 [U63#](X1,X2,X3) = 0 118.56/124.53 [U64#](X1,X2,X3) = 0 118.56/124.53 [ACTIVE](X) = 2.X + 2 118.56/124.53 [ISNAT](X) = 0 118.56/124.53 [ISNATKIND](X) = 0 118.56/124.53 [MARK](X) = 2.X + 2 118.56/124.53 [PLUS](X1,X2) = 0 118.56/124.53 [S](X) = 0 118.56/124.53 118.56/124.53 Problem 1.23: 118.56/124.53 118.56/124.53 SCC Processor: 118.56/124.53 -> Pairs: 118.56/124.53 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 -> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 ->Strongly Connected Components: 118.56/124.53 ->->Cycle: 118.56/124.53 ->->-> Pairs: 118.56/124.53 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 ->->-> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 118.56/124.53 Problem 1.23: 118.56/124.53 118.56/124.53 Reduction Pairs Processor: 118.56/124.53 -> Pairs: 118.56/124.53 ACTIVE(U22(tt,V1:S)) -> MARK(U23(isNat(V1:S))) 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 -> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 -> Usable rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 ->Interpretation type: 118.56/124.53 Linear 118.56/124.53 ->Coefficients: 118.56/124.53 Natural Numbers 118.56/124.53 ->Dimension: 118.56/124.53 1 118.56/124.53 ->Bound: 118.56/124.53 2 118.56/124.53 ->Interpretation: 118.56/124.53 118.56/124.53 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.56/124.53 [U12](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.53 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.53 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.53 [U15](X1,X2) = X1 + 2.X2 + 2 118.56/124.53 [U16](X) = X + 2 118.56/124.53 [U21](X1,X2) = X1 + 2.X2 + 2 118.56/124.53 [U22](X1,X2) = 2.X1 + 2.X2 118.56/124.53 [U23](X) = X + 1 118.56/124.53 [U31](X1,X2) = X1 118.56/124.53 [U32](X) = X 118.56/124.53 [U41](X) = X 118.56/124.53 [U51](X1,X2) = 2.X2 + 2 118.56/124.53 [U52](X1,X2) = X1 + 2.X2 118.56/124.53 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.53 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.53 [active](X) = X 118.56/124.53 [isNat](X) = 2.X + 2 118.56/124.53 [isNatKind](X) = 2 118.56/124.53 [mark](X) = X 118.56/124.53 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.56/124.53 [s](X) = X + 1 118.56/124.53 [0] = 2 118.56/124.53 [fSNonEmpty] = 0 118.56/124.53 [tt] = 2 118.56/124.53 [U11#](X1,X2,X3) = 0 118.56/124.53 [U12#](X1,X2,X3) = 0 118.56/124.53 [U13#](X1,X2,X3) = 0 118.56/124.53 [U14#](X1,X2,X3) = 0 118.56/124.53 [U15#](X1,X2) = 0 118.56/124.53 [U16#](X) = 0 118.56/124.53 [U21#](X1,X2) = 0 118.56/124.53 [U22#](X1,X2) = 0 118.56/124.53 [U23#](X) = 0 118.56/124.53 [U31#](X1,X2) = 0 118.56/124.53 [U32#](X) = 0 118.56/124.53 [U41#](X) = 0 118.56/124.53 [U51#](X1,X2) = 0 118.56/124.53 [U52#](X1,X2) = 0 118.56/124.53 [U61#](X1,X2,X3) = 0 118.56/124.53 [U62#](X1,X2,X3) = 0 118.56/124.53 [U63#](X1,X2,X3) = 0 118.56/124.53 [U64#](X1,X2,X3) = 0 118.56/124.53 [ACTIVE](X) = 2.X + 2 118.56/124.53 [ISNAT](X) = 0 118.56/124.53 [ISNATKIND](X) = 0 118.56/124.53 [MARK](X) = 2.X + 2 118.56/124.53 [PLUS](X1,X2) = 0 118.56/124.53 [S](X) = 0 118.56/124.53 118.56/124.53 Problem 1.23: 118.56/124.53 118.56/124.53 SCC Processor: 118.56/124.53 -> Pairs: 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 -> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.53 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.53 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.53 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.53 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.53 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.53 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.53 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.53 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.53 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.53 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.53 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.53 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.53 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.53 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.53 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.53 mark(0) -> active(0) 118.56/124.53 mark(tt) -> active(tt) 118.56/124.53 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.53 s(active(X:S)) -> s(X:S) 118.56/124.53 s(mark(X:S)) -> s(X:S) 118.56/124.53 ->Strongly Connected Components: 118.56/124.53 ->->Cycle: 118.56/124.53 ->->-> Pairs: 118.56/124.53 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.53 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.53 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.53 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.53 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.53 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.53 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.53 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.53 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.53 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.53 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.53 MARK(s(X:S)) -> MARK(X:S) 118.56/124.53 ->->-> Rules: 118.56/124.53 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.53 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.53 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.53 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.53 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.53 U16(active(X:S)) -> U16(X:S) 118.56/124.53 U16(mark(X:S)) -> U16(X:S) 118.56/124.53 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.53 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.53 U23(active(X:S)) -> U23(X:S) 118.56/124.53 U23(mark(X:S)) -> U23(X:S) 118.56/124.53 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.53 U32(active(X:S)) -> U32(X:S) 118.56/124.53 U32(mark(X:S)) -> U32(X:S) 118.56/124.53 U41(active(X:S)) -> U41(X:S) 118.56/124.53 U41(mark(X:S)) -> U41(X:S) 118.56/124.53 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.53 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.53 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.53 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.53 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.53 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.53 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.53 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.53 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.53 active(U16(tt)) -> mark(tt) 118.56/124.53 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.53 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.53 active(U23(tt)) -> mark(tt) 118.56/124.53 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.53 active(U32(tt)) -> mark(tt) 118.56/124.53 active(U41(tt)) -> mark(tt) 118.56/124.53 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.53 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.53 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.53 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.53 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.53 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.53 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.53 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.53 active(isNat(0)) -> mark(tt) 118.56/124.53 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.53 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.53 active(isNatKind(0)) -> mark(tt) 118.56/124.53 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.53 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.53 isNat(active(X:S)) -> isNat(X:S) 118.56/124.53 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.54 mark(0) -> active(0) 118.56/124.54 mark(tt) -> active(tt) 118.56/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 s(active(X:S)) -> s(X:S) 118.56/124.54 s(mark(X:S)) -> s(X:S) 118.56/124.54 118.56/124.54 Problem 1.23: 118.56/124.54 118.56/124.54 Reduction Pairs Processor: 118.56/124.54 -> Pairs: 118.56/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.54 ACTIVE(isNat(plus(V1:S,V2:S))) -> MARK(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.54 MARK(s(X:S)) -> MARK(X:S) 118.56/124.54 -> Rules: 118.56/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U16(active(X:S)) -> U16(X:S) 118.56/124.54 U16(mark(X:S)) -> U16(X:S) 118.56/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U23(active(X:S)) -> U23(X:S) 118.56/124.54 U23(mark(X:S)) -> U23(X:S) 118.56/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U32(active(X:S)) -> U32(X:S) 118.56/124.54 U32(mark(X:S)) -> U32(X:S) 118.56/124.54 U41(active(X:S)) -> U41(X:S) 118.56/124.54 U41(mark(X:S)) -> U41(X:S) 118.56/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.54 active(U16(tt)) -> mark(tt) 118.56/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.54 active(U23(tt)) -> mark(tt) 118.56/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.54 active(U32(tt)) -> mark(tt) 118.56/124.54 active(U41(tt)) -> mark(tt) 118.56/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 active(isNat(0)) -> mark(tt) 118.56/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.54 active(isNatKind(0)) -> mark(tt) 118.56/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.54 isNat(active(X:S)) -> isNat(X:S) 118.56/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.54 mark(0) -> active(0) 118.56/124.54 mark(tt) -> active(tt) 118.56/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 s(active(X:S)) -> s(X:S) 118.56/124.54 s(mark(X:S)) -> s(X:S) 118.56/124.54 -> Usable rules: 118.56/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U16(active(X:S)) -> U16(X:S) 118.56/124.54 U16(mark(X:S)) -> U16(X:S) 118.56/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U23(active(X:S)) -> U23(X:S) 118.56/124.54 U23(mark(X:S)) -> U23(X:S) 118.56/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U32(active(X:S)) -> U32(X:S) 118.56/124.54 U32(mark(X:S)) -> U32(X:S) 118.56/124.54 U41(active(X:S)) -> U41(X:S) 118.56/124.54 U41(mark(X:S)) -> U41(X:S) 118.56/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.54 active(U16(tt)) -> mark(tt) 118.56/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.54 active(U23(tt)) -> mark(tt) 118.56/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.54 active(U32(tt)) -> mark(tt) 118.56/124.54 active(U41(tt)) -> mark(tt) 118.56/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 active(isNat(0)) -> mark(tt) 118.56/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.54 active(isNatKind(0)) -> mark(tt) 118.56/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.54 isNat(active(X:S)) -> isNat(X:S) 118.56/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.54 mark(0) -> active(0) 118.56/124.54 mark(tt) -> active(tt) 118.56/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 s(active(X:S)) -> s(X:S) 118.56/124.54 s(mark(X:S)) -> s(X:S) 118.56/124.54 ->Interpretation type: 118.56/124.54 Linear 118.56/124.54 ->Coefficients: 118.56/124.54 Natural Numbers 118.56/124.54 ->Dimension: 118.56/124.54 1 118.56/124.54 ->Bound: 118.56/124.54 2 118.56/124.54 ->Interpretation: 118.56/124.54 118.56/124.54 [U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.54 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.56/124.54 [U13](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.56/124.54 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.56/124.54 [U15](X1,X2) = X1 + 2.X2 + 2 118.56/124.54 [U16](X) = X 118.56/124.54 [U21](X1,X2) = X1 + 2.X2 118.56/124.54 [U22](X1,X2) = X1 + 2.X2 118.56/124.54 [U23](X) = X 118.56/124.54 [U31](X1,X2) = X1 118.56/124.54 [U32](X) = X 118.56/124.54 [U41](X) = X 118.56/124.54 [U51](X1,X2) = 2.X2 + 2 118.56/124.54 [U52](X1,X2) = X1 + 2.X2 118.56/124.54 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.54 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.54 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.56/124.54 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.56/124.54 [active](X) = X 118.56/124.54 [isNat](X) = 2.X + 2 118.56/124.54 [isNatKind](X) = 2 118.56/124.54 [mark](X) = X 118.56/124.54 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.56/124.54 [s](X) = X 118.56/124.54 [0] = 2 118.56/124.54 [fSNonEmpty] = 0 118.56/124.54 [tt] = 2 118.56/124.54 [U11#](X1,X2,X3) = 0 118.56/124.54 [U12#](X1,X2,X3) = 0 118.56/124.54 [U13#](X1,X2,X3) = 0 118.56/124.54 [U14#](X1,X2,X3) = 0 118.56/124.54 [U15#](X1,X2) = 0 118.56/124.54 [U16#](X) = 0 118.56/124.54 [U21#](X1,X2) = 0 118.56/124.54 [U22#](X1,X2) = 0 118.56/124.54 [U23#](X) = 0 118.56/124.54 [U31#](X1,X2) = 0 118.56/124.54 [U32#](X) = 0 118.56/124.54 [U41#](X) = 0 118.56/124.54 [U51#](X1,X2) = 0 118.56/124.54 [U52#](X1,X2) = 0 118.56/124.54 [U61#](X1,X2,X3) = 0 118.56/124.54 [U62#](X1,X2,X3) = 0 118.56/124.54 [U63#](X1,X2,X3) = 0 118.56/124.54 [U64#](X1,X2,X3) = 0 118.56/124.54 [ACTIVE](X) = 2.X + 2 118.56/124.54 [ISNAT](X) = 0 118.56/124.54 [ISNATKIND](X) = 0 118.56/124.54 [MARK](X) = 2.X + 2 118.56/124.54 [PLUS](X1,X2) = 0 118.56/124.54 [S](X) = 0 118.56/124.54 118.56/124.54 Problem 1.23: 118.56/124.54 118.56/124.54 SCC Processor: 118.56/124.54 -> Pairs: 118.56/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.54 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.54 MARK(s(X:S)) -> MARK(X:S) 118.56/124.54 -> Rules: 118.56/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U16(active(X:S)) -> U16(X:S) 118.56/124.54 U16(mark(X:S)) -> U16(X:S) 118.56/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U23(active(X:S)) -> U23(X:S) 118.56/124.54 U23(mark(X:S)) -> U23(X:S) 118.56/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U32(active(X:S)) -> U32(X:S) 118.56/124.54 U32(mark(X:S)) -> U32(X:S) 118.56/124.54 U41(active(X:S)) -> U41(X:S) 118.56/124.54 U41(mark(X:S)) -> U41(X:S) 118.56/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.54 active(U16(tt)) -> mark(tt) 118.56/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.54 active(U23(tt)) -> mark(tt) 118.56/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.54 active(U32(tt)) -> mark(tt) 118.56/124.54 active(U41(tt)) -> mark(tt) 118.56/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 active(isNat(0)) -> mark(tt) 118.56/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.54 active(isNatKind(0)) -> mark(tt) 118.56/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.54 isNat(active(X:S)) -> isNat(X:S) 118.56/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.54 mark(0) -> active(0) 118.56/124.54 mark(tt) -> active(tt) 118.56/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 s(active(X:S)) -> s(X:S) 118.56/124.54 s(mark(X:S)) -> s(X:S) 118.56/124.54 ->Strongly Connected Components: 118.56/124.54 ->->Cycle: 118.56/124.54 ->->-> Pairs: 118.56/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.54 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.54 MARK(s(X:S)) -> MARK(X:S) 118.56/124.54 ->->-> Rules: 118.56/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.56/124.54 U16(active(X:S)) -> U16(X:S) 118.56/124.54 U16(mark(X:S)) -> U16(X:S) 118.56/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.56/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.56/124.54 U23(active(X:S)) -> U23(X:S) 118.56/124.54 U23(mark(X:S)) -> U23(X:S) 118.56/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.56/124.54 U32(active(X:S)) -> U32(X:S) 118.56/124.54 U32(mark(X:S)) -> U32(X:S) 118.56/124.54 U41(active(X:S)) -> U41(X:S) 118.56/124.54 U41(mark(X:S)) -> U41(X:S) 118.56/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.56/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.56/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.56/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.56/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.56/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.56/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.56/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.56/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.56/124.54 active(U16(tt)) -> mark(tt) 118.56/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.56/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.56/124.54 active(U23(tt)) -> mark(tt) 118.56/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.56/124.54 active(U32(tt)) -> mark(tt) 118.56/124.54 active(U41(tt)) -> mark(tt) 118.56/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.56/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.56/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.56/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.56/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.56/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.56/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.56/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 active(isNat(0)) -> mark(tt) 118.56/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.56/124.54 active(isNatKind(0)) -> mark(tt) 118.56/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.56/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.56/124.54 isNat(active(X:S)) -> isNat(X:S) 118.56/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.56/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.56/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.56/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.56/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.56/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.56/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.56/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.56/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.56/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.56/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.56/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.56/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.56/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.56/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.56/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.56/124.54 mark(0) -> active(0) 118.56/124.54 mark(tt) -> active(tt) 118.56/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.56/124.54 s(active(X:S)) -> s(X:S) 118.56/124.54 s(mark(X:S)) -> s(X:S) 118.56/124.54 118.56/124.54 Problem 1.23: 118.56/124.54 118.56/124.54 Reduction Pairs Processor: 118.56/124.54 -> Pairs: 118.56/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.56/124.54 ACTIVE(isNat(s(V1:S))) -> MARK(U21(isNatKind(V1:S),V1:S)) 118.56/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.56/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.56/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.56/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.56/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.56/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.56/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.56/124.54 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.56/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.56/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.56/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.56/124.54 MARK(s(X:S)) -> MARK(X:S) 118.56/124.54 -> Rules: 118.56/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.56/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.56/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.56/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.56/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.54 active(U16(tt)) -> mark(tt) 118.58/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.54 active(U23(tt)) -> mark(tt) 118.58/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.54 active(U32(tt)) -> mark(tt) 118.58/124.54 active(U41(tt)) -> mark(tt) 118.58/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.54 active(isNat(0)) -> mark(tt) 118.58/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.54 active(isNatKind(0)) -> mark(tt) 118.58/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.54 isNat(active(X:S)) -> isNat(X:S) 118.58/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.54 mark(0) -> active(0) 118.58/124.54 mark(tt) -> active(tt) 118.58/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 s(active(X:S)) -> s(X:S) 118.58/124.54 s(mark(X:S)) -> s(X:S) 118.58/124.54 -> Usable rules: 118.58/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.54 active(U16(tt)) -> mark(tt) 118.58/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.54 active(U23(tt)) -> mark(tt) 118.58/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.54 active(U32(tt)) -> mark(tt) 118.58/124.54 active(U41(tt)) -> mark(tt) 118.58/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.54 active(isNat(0)) -> mark(tt) 118.58/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.54 active(isNatKind(0)) -> mark(tt) 118.58/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.54 isNat(active(X:S)) -> isNat(X:S) 118.58/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.54 mark(0) -> active(0) 118.58/124.54 mark(tt) -> active(tt) 118.58/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 s(active(X:S)) -> s(X:S) 118.58/124.54 s(mark(X:S)) -> s(X:S) 118.58/124.54 ->Interpretation type: 118.58/124.54 Linear 118.58/124.54 ->Coefficients: 118.58/124.54 Natural Numbers 118.58/124.54 ->Dimension: 118.58/124.54 1 118.58/124.54 ->Bound: 118.58/124.54 2 118.58/124.54 ->Interpretation: 118.58/124.54 118.58/124.54 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.54 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.54 [U13](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.54 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.54 [U15](X1,X2) = X1 + 2.X2 + 1 118.58/124.54 [U16](X) = X 118.58/124.54 [U21](X1,X2) = X1 + 2.X2 + 1 118.58/124.54 [U22](X1,X2) = X1 + 2.X2 + 1 118.58/124.54 [U23](X) = X 118.58/124.54 [U31](X1,X2) = X1 118.58/124.54 [U32](X) = X 118.58/124.54 [U41](X) = X 118.58/124.54 [U51](X1,X2) = 2.X2 + 2 118.58/124.54 [U52](X1,X2) = 2.X2 + 1 118.58/124.54 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.54 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.54 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.54 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.54 [active](X) = X 118.58/124.54 [isNat](X) = 2.X + 2 118.58/124.54 [isNatKind](X) = 2 118.58/124.54 [mark](X) = X 118.58/124.54 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.54 [s](X) = X + 1 118.58/124.54 [0] = 2 118.58/124.54 [fSNonEmpty] = 0 118.58/124.54 [tt] = 2 118.58/124.54 [U11#](X1,X2,X3) = 0 118.58/124.54 [U12#](X1,X2,X3) = 0 118.58/124.54 [U13#](X1,X2,X3) = 0 118.58/124.54 [U14#](X1,X2,X3) = 0 118.58/124.54 [U15#](X1,X2) = 0 118.58/124.54 [U16#](X) = 0 118.58/124.54 [U21#](X1,X2) = 0 118.58/124.54 [U22#](X1,X2) = 0 118.58/124.54 [U23#](X) = 0 118.58/124.54 [U31#](X1,X2) = 0 118.58/124.54 [U32#](X) = 0 118.58/124.54 [U41#](X) = 0 118.58/124.54 [U51#](X1,X2) = 0 118.58/124.54 [U52#](X1,X2) = 0 118.58/124.54 [U61#](X1,X2,X3) = 0 118.58/124.54 [U62#](X1,X2,X3) = 0 118.58/124.54 [U63#](X1,X2,X3) = 0 118.58/124.54 [U64#](X1,X2,X3) = 0 118.58/124.54 [ACTIVE](X) = 2.X + 1 118.58/124.54 [ISNAT](X) = 0 118.58/124.54 [ISNATKIND](X) = 0 118.58/124.54 [MARK](X) = 2.X + 1 118.58/124.54 [PLUS](X1,X2) = 0 118.58/124.54 [S](X) = 0 118.58/124.54 118.58/124.54 Problem 1.23: 118.58/124.54 118.58/124.54 SCC Processor: 118.58/124.54 -> Pairs: 118.58/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(isNat(X:S)) -> ACTIVE(isNat(X:S)) 118.58/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.54 MARK(s(X:S)) -> MARK(X:S) 118.58/124.54 -> Rules: 118.58/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.54 active(U16(tt)) -> mark(tt) 118.58/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.54 active(U23(tt)) -> mark(tt) 118.58/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.54 active(U32(tt)) -> mark(tt) 118.58/124.54 active(U41(tt)) -> mark(tt) 118.58/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.54 active(isNat(0)) -> mark(tt) 118.58/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.54 active(isNatKind(0)) -> mark(tt) 118.58/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.54 isNat(active(X:S)) -> isNat(X:S) 118.58/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.54 mark(0) -> active(0) 118.58/124.54 mark(tt) -> active(tt) 118.58/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 s(active(X:S)) -> s(X:S) 118.58/124.54 s(mark(X:S)) -> s(X:S) 118.58/124.54 ->Strongly Connected Components: 118.58/124.54 ->->Cycle: 118.58/124.54 ->->-> Pairs: 118.58/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.54 MARK(s(X:S)) -> MARK(X:S) 118.58/124.54 ->->-> Rules: 118.58/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.54 active(U16(tt)) -> mark(tt) 118.58/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.54 active(U23(tt)) -> mark(tt) 118.58/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.54 active(U32(tt)) -> mark(tt) 118.58/124.54 active(U41(tt)) -> mark(tt) 118.58/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.54 active(isNat(0)) -> mark(tt) 118.58/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.54 active(isNatKind(0)) -> mark(tt) 118.58/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.54 isNat(active(X:S)) -> isNat(X:S) 118.58/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.54 mark(0) -> active(0) 118.58/124.54 mark(tt) -> active(tt) 118.58/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 s(active(X:S)) -> s(X:S) 118.58/124.54 s(mark(X:S)) -> s(X:S) 118.58/124.54 118.58/124.54 Problem 1.23: 118.58/124.54 118.58/124.54 Reduction Pairs Processor: 118.58/124.54 -> Pairs: 118.58/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.54 MARK(s(X:S)) -> MARK(X:S) 118.58/124.54 -> Rules: 118.58/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.54 active(U16(tt)) -> mark(tt) 118.58/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.54 active(U23(tt)) -> mark(tt) 118.58/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.54 active(U32(tt)) -> mark(tt) 118.58/124.54 active(U41(tt)) -> mark(tt) 118.58/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.54 active(isNat(0)) -> mark(tt) 118.58/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.54 active(isNatKind(0)) -> mark(tt) 118.58/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.54 isNat(active(X:S)) -> isNat(X:S) 118.58/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.54 mark(0) -> active(0) 118.58/124.54 mark(tt) -> active(tt) 118.58/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 s(active(X:S)) -> s(X:S) 118.58/124.54 s(mark(X:S)) -> s(X:S) 118.58/124.54 -> Usable rules: 118.58/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.54 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.54 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.54 active(U16(tt)) -> mark(tt) 118.58/124.54 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.54 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.54 active(U23(tt)) -> mark(tt) 118.58/124.54 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.54 active(U32(tt)) -> mark(tt) 118.58/124.54 active(U41(tt)) -> mark(tt) 118.58/124.54 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.54 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.54 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.54 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.54 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.54 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.54 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.54 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.54 active(isNat(0)) -> mark(tt) 118.58/124.54 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.54 active(isNatKind(0)) -> mark(tt) 118.58/124.54 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.54 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.54 isNat(active(X:S)) -> isNat(X:S) 118.58/124.54 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.54 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.54 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.54 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.54 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.54 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.54 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.54 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.54 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.54 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.54 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.54 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.54 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.54 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.54 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.54 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.54 mark(0) -> active(0) 118.58/124.54 mark(tt) -> active(tt) 118.58/124.54 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.54 s(active(X:S)) -> s(X:S) 118.58/124.54 s(mark(X:S)) -> s(X:S) 118.58/124.54 ->Interpretation type: 118.58/124.54 Linear 118.58/124.54 ->Coefficients: 118.58/124.54 Natural Numbers 118.58/124.54 ->Dimension: 118.58/124.54 1 118.58/124.54 ->Bound: 118.58/124.54 2 118.58/124.54 ->Interpretation: 118.58/124.54 118.58/124.54 [U11](X1,X2,X3) = 0 118.58/124.54 [U12](X1,X2,X3) = 1 118.58/124.54 [U13](X1,X2,X3) = 1 118.58/124.54 [U14](X1,X2,X3) = 1 118.58/124.54 [U15](X1,X2) = 1 118.58/124.54 [U16](X) = 1 118.58/124.54 [U21](X1,X2) = 1 118.58/124.54 [U22](X1,X2) = 1 118.58/124.54 [U23](X) = 1 118.58/124.54 [U31](X1,X2) = 1 118.58/124.54 [U32](X) = 1 118.58/124.54 [U41](X) = 2 118.58/124.54 [U51](X1,X2) = 1 118.58/124.54 [U52](X1,X2) = 2 118.58/124.54 [U61](X1,X2,X3) = 0 118.58/124.54 [U62](X1,X2,X3) = 2 118.58/124.54 [U63](X1,X2,X3) = 0 118.58/124.54 [U64](X1,X2,X3) = 0 118.58/124.54 [active](X) = 0 118.58/124.54 [isNat](X) = 0 118.58/124.54 [isNatKind](X) = 1 118.58/124.54 [mark](X) = 0 118.58/124.54 [plus](X1,X2) = 1 118.58/124.54 [s](X) = 0 118.58/124.54 [0] = 2 118.58/124.54 [fSNonEmpty] = 0 118.58/124.54 [tt] = 1 118.58/124.54 [U11#](X1,X2,X3) = 0 118.58/124.54 [U12#](X1,X2,X3) = 0 118.58/124.54 [U13#](X1,X2,X3) = 0 118.58/124.54 [U14#](X1,X2,X3) = 0 118.58/124.54 [U15#](X1,X2) = 0 118.58/124.54 [U16#](X) = 0 118.58/124.54 [U21#](X1,X2) = 0 118.58/124.54 [U22#](X1,X2) = 0 118.58/124.54 [U23#](X) = 0 118.58/124.54 [U31#](X1,X2) = 0 118.58/124.54 [U32#](X) = 0 118.58/124.54 [U41#](X) = 0 118.58/124.54 [U51#](X1,X2) = 0 118.58/124.54 [U52#](X1,X2) = 0 118.58/124.54 [U61#](X1,X2,X3) = 0 118.58/124.54 [U62#](X1,X2,X3) = 0 118.58/124.54 [U63#](X1,X2,X3) = 0 118.58/124.54 [U64#](X1,X2,X3) = 0 118.58/124.54 [ACTIVE](X) = 2.X 118.58/124.54 [ISNAT](X) = 0 118.58/124.54 [ISNATKIND](X) = 0 118.58/124.54 [MARK](X) = 2 118.58/124.54 [PLUS](X1,X2) = 0 118.58/124.54 [S](X) = 0 118.58/124.54 118.58/124.54 Problem 1.23: 118.58/124.54 118.58/124.54 SCC Processor: 118.58/124.54 -> Pairs: 118.58/124.54 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.54 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.54 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.54 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.54 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.54 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.54 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.54 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.54 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.54 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.54 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.54 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.54 MARK(s(X:S)) -> MARK(X:S) 118.58/124.54 -> Rules: 118.58/124.54 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.54 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.54 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.54 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.54 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.54 U16(active(X:S)) -> U16(X:S) 118.58/124.54 U16(mark(X:S)) -> U16(X:S) 118.58/124.54 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.54 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.54 U23(active(X:S)) -> U23(X:S) 118.58/124.54 U23(mark(X:S)) -> U23(X:S) 118.58/124.54 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.54 U32(active(X:S)) -> U32(X:S) 118.58/124.54 U32(mark(X:S)) -> U32(X:S) 118.58/124.54 U41(active(X:S)) -> U41(X:S) 118.58/124.54 U41(mark(X:S)) -> U41(X:S) 118.58/124.54 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.54 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.54 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.54 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.54 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.54 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.54 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 ->Strongly Connected Components: 118.58/124.55 ->->Cycle: 118.58/124.55 ->->-> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 ->->-> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 118.58/124.55 Problem 1.23: 118.58/124.55 118.58/124.55 Reduction Pairs Processor: 118.58/124.55 -> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 -> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 -> Usable rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 ->Interpretation type: 118.58/124.55 Linear 118.58/124.55 ->Coefficients: 118.58/124.55 Natural Numbers 118.58/124.55 ->Dimension: 118.58/124.55 1 118.58/124.55 ->Bound: 118.58/124.55 2 118.58/124.55 ->Interpretation: 118.58/124.55 118.58/124.55 [U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U12](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U13](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.55 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U15](X1,X2) = X1 + 2.X2 + 1 118.58/124.55 [U16](X) = X + 1 118.58/124.55 [U21](X1,X2) = 2.X1 + 2.X2 118.58/124.55 [U22](X1,X2) = X1 + 2.X2 + 2 118.58/124.55 [U23](X) = X + 1 118.58/124.55 [U31](X1,X2) = X1 118.58/124.55 [U32](X) = X 118.58/124.55 [U41](X) = X 118.58/124.55 [U51](X1,X2) = 2.X2 + 2 118.58/124.55 [U52](X1,X2) = 2.X2 + 1 118.58/124.55 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.55 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.55 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.55 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.55 [active](X) = X 118.58/124.55 [isNat](X) = 2.X + 2 118.58/124.55 [isNatKind](X) = 2 118.58/124.55 [mark](X) = X 118.58/124.55 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.55 [s](X) = X + 1 118.58/124.55 [0] = 2 118.58/124.55 [fSNonEmpty] = 0 118.58/124.55 [tt] = 2 118.58/124.55 [U11#](X1,X2,X3) = 0 118.58/124.55 [U12#](X1,X2,X3) = 0 118.58/124.55 [U13#](X1,X2,X3) = 0 118.58/124.55 [U14#](X1,X2,X3) = 0 118.58/124.55 [U15#](X1,X2) = 0 118.58/124.55 [U16#](X) = 0 118.58/124.55 [U21#](X1,X2) = 0 118.58/124.55 [U22#](X1,X2) = 0 118.58/124.55 [U23#](X) = 0 118.58/124.55 [U31#](X1,X2) = 0 118.58/124.55 [U32#](X) = 0 118.58/124.55 [U41#](X) = 0 118.58/124.55 [U51#](X1,X2) = 0 118.58/124.55 [U52#](X1,X2) = 0 118.58/124.55 [U61#](X1,X2,X3) = 0 118.58/124.55 [U62#](X1,X2,X3) = 0 118.58/124.55 [U63#](X1,X2,X3) = 0 118.58/124.55 [U64#](X1,X2,X3) = 0 118.58/124.55 [ACTIVE](X) = 2.X + 2 118.58/124.55 [ISNAT](X) = 0 118.58/124.55 [ISNATKIND](X) = 0 118.58/124.55 [MARK](X) = 2.X + 2 118.58/124.55 [PLUS](X1,X2) = 0 118.58/124.55 [S](X) = 0 118.58/124.55 118.58/124.55 Problem 1.23: 118.58/124.55 118.58/124.55 SCC Processor: 118.58/124.55 -> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 -> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 ->Strongly Connected Components: 118.58/124.55 ->->Cycle: 118.58/124.55 ->->-> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 ->->-> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 118.58/124.55 Problem 1.23: 118.58/124.55 118.58/124.55 Reduction Pairs Processor: 118.58/124.55 -> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 -> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 -> Usable rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 ->Interpretation type: 118.58/124.55 Linear 118.58/124.55 ->Coefficients: 118.58/124.55 Natural Numbers 118.58/124.55 ->Dimension: 118.58/124.55 1 118.58/124.55 ->Bound: 118.58/124.55 2 118.58/124.55 ->Interpretation: 118.58/124.55 118.58/124.55 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U13](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.55 [U16](X) = X + 2 118.58/124.55 [U21](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.55 [U22](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.55 [U23](X) = X + 2 118.58/124.55 [U31](X1,X2) = 2.X1 118.58/124.55 [U32](X) = 2.X 118.58/124.55 [U41](X) = 2.X 118.58/124.55 [U51](X1,X2) = 2.X2 + 2 118.58/124.55 [U52](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.55 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.55 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.55 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.55 [active](X) = X 118.58/124.55 [isNat](X) = 2.X 118.58/124.55 [isNatKind](X) = 0 118.58/124.55 [mark](X) = X 118.58/124.55 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.55 [s](X) = X + 1 118.58/124.55 [0] = 2 118.58/124.55 [fSNonEmpty] = 0 118.58/124.55 [tt] = 0 118.58/124.55 [U11#](X1,X2,X3) = 0 118.58/124.55 [U12#](X1,X2,X3) = 0 118.58/124.55 [U13#](X1,X2,X3) = 0 118.58/124.55 [U14#](X1,X2,X3) = 0 118.58/124.55 [U15#](X1,X2) = 0 118.58/124.55 [U16#](X) = 0 118.58/124.55 [U21#](X1,X2) = 0 118.58/124.55 [U22#](X1,X2) = 0 118.58/124.55 [U23#](X) = 0 118.58/124.55 [U31#](X1,X2) = 0 118.58/124.55 [U32#](X) = 0 118.58/124.55 [U41#](X) = 0 118.58/124.55 [U51#](X1,X2) = 0 118.58/124.55 [U52#](X1,X2) = 0 118.58/124.55 [U61#](X1,X2,X3) = 0 118.58/124.55 [U62#](X1,X2,X3) = 0 118.58/124.55 [U63#](X1,X2,X3) = 0 118.58/124.55 [U64#](X1,X2,X3) = 0 118.58/124.55 [ACTIVE](X) = X + 2 118.58/124.55 [ISNAT](X) = 0 118.58/124.55 [ISNATKIND](X) = 0 118.58/124.55 [MARK](X) = 2.X + 2 118.58/124.55 [PLUS](X1,X2) = 0 118.58/124.55 [S](X) = 0 118.58/124.55 118.58/124.55 Problem 1.23: 118.58/124.55 118.58/124.55 SCC Processor: 118.58/124.55 -> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 -> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 ->Strongly Connected Components: 118.58/124.55 ->->Cycle: 118.58/124.55 ->->-> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 ->->-> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 118.58/124.55 Problem 1.23: 118.58/124.55 118.58/124.55 Reduction Pairs Processor: 118.58/124.55 -> Pairs: 118.58/124.55 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.55 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.55 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.55 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.55 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.55 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.55 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.55 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.55 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.55 MARK(s(X:S)) -> MARK(X:S) 118.58/124.55 -> Rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 s(active(X:S)) -> s(X:S) 118.58/124.55 s(mark(X:S)) -> s(X:S) 118.58/124.55 -> Usable rules: 118.58/124.55 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.55 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.55 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.55 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.55 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.55 U16(active(X:S)) -> U16(X:S) 118.58/124.55 U16(mark(X:S)) -> U16(X:S) 118.58/124.55 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.55 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.55 U23(active(X:S)) -> U23(X:S) 118.58/124.55 U23(mark(X:S)) -> U23(X:S) 118.58/124.55 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.55 U32(active(X:S)) -> U32(X:S) 118.58/124.55 U32(mark(X:S)) -> U32(X:S) 118.58/124.55 U41(active(X:S)) -> U41(X:S) 118.58/124.55 U41(mark(X:S)) -> U41(X:S) 118.58/124.55 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.55 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.55 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.55 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.55 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.55 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.55 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.55 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.55 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.55 active(U16(tt)) -> mark(tt) 118.58/124.55 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.55 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.55 active(U23(tt)) -> mark(tt) 118.58/124.55 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.55 active(U32(tt)) -> mark(tt) 118.58/124.55 active(U41(tt)) -> mark(tt) 118.58/124.55 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.55 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.55 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.55 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.55 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.55 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.55 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.55 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.55 active(isNat(0)) -> mark(tt) 118.58/124.55 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.55 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.55 active(isNatKind(0)) -> mark(tt) 118.58/124.55 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.55 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.55 isNat(active(X:S)) -> isNat(X:S) 118.58/124.55 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.55 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.55 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.55 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.55 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.55 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.55 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.55 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.55 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.55 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.55 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.55 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.55 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.55 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.55 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.55 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.55 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.55 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.55 mark(0) -> active(0) 118.58/124.55 mark(tt) -> active(tt) 118.58/124.55 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.55 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 ->Interpretation type: 118.58/124.56 Linear 118.58/124.56 ->Coefficients: 118.58/124.56 Natural Numbers 118.58/124.56 ->Dimension: 118.58/124.56 1 118.58/124.56 ->Bound: 118.58/124.56 2 118.58/124.56 ->Interpretation: 118.58/124.56 118.58/124.56 [U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.56 [U12](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.56 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.56 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.56 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.56 [U16](X) = X 118.58/124.56 [U21](X1,X2) = 2.X1 + 2.X2 118.58/124.56 [U22](X1,X2) = 2.X1 + 2.X2 118.58/124.56 [U23](X) = X + 2 118.58/124.56 [U31](X1,X2) = X1 118.58/124.56 [U32](X) = X 118.58/124.56 [U41](X) = X 118.58/124.56 [U51](X1,X2) = X2 + 2 118.58/124.56 [U52](X1,X2) = X2 118.58/124.56 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.56 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.56 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.56 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.56 [active](X) = X 118.58/124.56 [isNat](X) = 2.X + 2 118.58/124.56 [isNatKind](X) = 2 118.58/124.56 [mark](X) = X 118.58/124.56 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.56 [s](X) = X + 1 118.58/124.56 [0] = 2 118.58/124.56 [fSNonEmpty] = 0 118.58/124.56 [tt] = 2 118.58/124.56 [U11#](X1,X2,X3) = 0 118.58/124.56 [U12#](X1,X2,X3) = 0 118.58/124.56 [U13#](X1,X2,X3) = 0 118.58/124.56 [U14#](X1,X2,X3) = 0 118.58/124.56 [U15#](X1,X2) = 0 118.58/124.56 [U16#](X) = 0 118.58/124.56 [U21#](X1,X2) = 0 118.58/124.56 [U22#](X1,X2) = 0 118.58/124.56 [U23#](X) = 0 118.58/124.56 [U31#](X1,X2) = 0 118.58/124.56 [U32#](X) = 0 118.58/124.56 [U41#](X) = 0 118.58/124.56 [U51#](X1,X2) = 0 118.58/124.56 [U52#](X1,X2) = 0 118.58/124.56 [U61#](X1,X2,X3) = 0 118.58/124.56 [U62#](X1,X2,X3) = 0 118.58/124.56 [U63#](X1,X2,X3) = 0 118.58/124.56 [U64#](X1,X2,X3) = 0 118.58/124.56 [ACTIVE](X) = 2.X + 2 118.58/124.56 [ISNAT](X) = 0 118.58/124.56 [ISNATKIND](X) = 0 118.58/124.56 [MARK](X) = 2.X + 2 118.58/124.56 [PLUS](X1,X2) = 0 118.58/124.56 [S](X) = 0 118.58/124.56 118.58/124.56 Problem 1.23: 118.58/124.56 118.58/124.56 SCC Processor: 118.58/124.56 -> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 -> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 ->Strongly Connected Components: 118.58/124.56 ->->Cycle: 118.58/124.56 ->->-> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 ->->-> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 118.58/124.56 Problem 1.23: 118.58/124.56 118.58/124.56 Reduction Pairs Processor: 118.58/124.56 -> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> ACTIVE(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 -> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 -> Usable rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 ->Interpretation type: 118.58/124.56 Linear 118.58/124.56 ->Coefficients: 118.58/124.56 Natural Numbers 118.58/124.56 ->Dimension: 118.58/124.56 1 118.58/124.56 ->Bound: 118.58/124.56 2 118.58/124.56 ->Interpretation: 118.58/124.56 118.58/124.56 [U11](X1,X2,X3) = 2 118.58/124.56 [U12](X1,X2,X3) = 2 118.58/124.56 [U13](X1,X2,X3) = 0 118.58/124.56 [U14](X1,X2,X3) = 1 118.58/124.56 [U15](X1,X2) = 0 118.58/124.56 [U16](X) = 1 118.58/124.56 [U21](X1,X2) = 1 118.58/124.56 [U22](X1,X2) = 1 118.58/124.56 [U23](X) = 2 118.58/124.56 [U31](X1,X2) = 1 118.58/124.56 [U32](X) = 2 118.58/124.56 [U41](X) = 1 118.58/124.56 [U51](X1,X2) = 1 118.58/124.56 [U52](X1,X2) = 1 118.58/124.56 [U61](X1,X2,X3) = 1 118.58/124.56 [U62](X1,X2,X3) = 2 118.58/124.56 [U63](X1,X2,X3) = 2 118.58/124.56 [U64](X1,X2,X3) = 1 118.58/124.56 [active](X) = 2 118.58/124.56 [isNat](X) = 2 118.58/124.56 [isNatKind](X) = 1 118.58/124.56 [mark](X) = 2 118.58/124.56 [plus](X1,X2) = 1 118.58/124.56 [s](X) = 1 118.58/124.56 [0] = 1 118.58/124.56 [fSNonEmpty] = 0 118.58/124.56 [tt] = 1 118.58/124.56 [U11#](X1,X2,X3) = 0 118.58/124.56 [U12#](X1,X2,X3) = 0 118.58/124.56 [U13#](X1,X2,X3) = 0 118.58/124.56 [U14#](X1,X2,X3) = 0 118.58/124.56 [U15#](X1,X2) = 0 118.58/124.56 [U16#](X) = 0 118.58/124.56 [U21#](X1,X2) = 0 118.58/124.56 [U22#](X1,X2) = 0 118.58/124.56 [U23#](X) = 0 118.58/124.56 [U31#](X1,X2) = 0 118.58/124.56 [U32#](X) = 0 118.58/124.56 [U41#](X) = 0 118.58/124.56 [U51#](X1,X2) = 0 118.58/124.56 [U52#](X1,X2) = 0 118.58/124.56 [U61#](X1,X2,X3) = 0 118.58/124.56 [U62#](X1,X2,X3) = 0 118.58/124.56 [U63#](X1,X2,X3) = 0 118.58/124.56 [U64#](X1,X2,X3) = 0 118.58/124.56 [ACTIVE](X) = 2.X 118.58/124.56 [ISNAT](X) = 0 118.58/124.56 [ISNATKIND](X) = 0 118.58/124.56 [MARK](X) = 2 118.58/124.56 [PLUS](X1,X2) = 0 118.58/124.56 [S](X) = 0 118.58/124.56 118.58/124.56 Problem 1.23: 118.58/124.56 118.58/124.56 SCC Processor: 118.58/124.56 -> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 -> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 ->Strongly Connected Components: 118.58/124.56 ->->Cycle: 118.58/124.56 ->->-> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 ->->-> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 118.58/124.56 Problem 1.23: 118.58/124.56 118.58/124.56 Reduction Pairs Processor: 118.58/124.56 -> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U13(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 -> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 -> Usable rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 ->Interpretation type: 118.58/124.56 Linear 118.58/124.56 ->Coefficients: 118.58/124.56 Natural Numbers 118.58/124.56 ->Dimension: 118.58/124.56 1 118.58/124.56 ->Bound: 118.58/124.56 2 118.58/124.56 ->Interpretation: 118.58/124.56 118.58/124.56 [U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.56 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.56 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.56 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.56 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.56 [U16](X) = X 118.58/124.56 [U21](X1,X2) = 2.X1 + 2.X2 118.58/124.56 [U22](X1,X2) = 2.X1 + 2.X2 118.58/124.56 [U23](X) = X + 2 118.58/124.56 [U31](X1,X2) = X1 118.58/124.56 [U32](X) = X 118.58/124.56 [U41](X) = X 118.58/124.56 [U51](X1,X2) = X2 + 2 118.58/124.56 [U52](X1,X2) = X2 + 2 118.58/124.56 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.56 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.56 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.56 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.56 [active](X) = X 118.58/124.56 [isNat](X) = 2.X + 2 118.58/124.56 [isNatKind](X) = 2 118.58/124.56 [mark](X) = X 118.58/124.56 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.56 [s](X) = X + 1 118.58/124.56 [0] = 2 118.58/124.56 [fSNonEmpty] = 0 118.58/124.56 [tt] = 2 118.58/124.56 [U11#](X1,X2,X3) = 0 118.58/124.56 [U12#](X1,X2,X3) = 0 118.58/124.56 [U13#](X1,X2,X3) = 0 118.58/124.56 [U14#](X1,X2,X3) = 0 118.58/124.56 [U15#](X1,X2) = 0 118.58/124.56 [U16#](X) = 0 118.58/124.56 [U21#](X1,X2) = 0 118.58/124.56 [U22#](X1,X2) = 0 118.58/124.56 [U23#](X) = 0 118.58/124.56 [U31#](X1,X2) = 0 118.58/124.56 [U32#](X) = 0 118.58/124.56 [U41#](X) = 0 118.58/124.56 [U51#](X1,X2) = 0 118.58/124.56 [U52#](X1,X2) = 0 118.58/124.56 [U61#](X1,X2,X3) = 0 118.58/124.56 [U62#](X1,X2,X3) = 0 118.58/124.56 [U63#](X1,X2,X3) = 0 118.58/124.56 [U64#](X1,X2,X3) = 0 118.58/124.56 [ACTIVE](X) = 2.X 118.58/124.56 [ISNAT](X) = 0 118.58/124.56 [ISNATKIND](X) = 0 118.58/124.56 [MARK](X) = 2.X 118.58/124.56 [PLUS](X1,X2) = 0 118.58/124.56 [S](X) = 0 118.58/124.56 118.58/124.56 Problem 1.23: 118.58/124.56 118.58/124.56 SCC Processor: 118.58/124.56 -> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 -> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 ->Strongly Connected Components: 118.58/124.56 ->->Cycle: 118.58/124.56 ->->-> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 ->->-> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.56 s(active(X:S)) -> s(X:S) 118.58/124.56 s(mark(X:S)) -> s(X:S) 118.58/124.56 118.58/124.56 Problem 1.23: 118.58/124.56 118.58/124.56 Reduction Pairs Processor: 118.58/124.56 -> Pairs: 118.58/124.56 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.56 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> ACTIVE(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.56 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.56 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.56 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.56 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.56 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.56 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.56 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.56 MARK(s(X:S)) -> MARK(X:S) 118.58/124.56 -> Rules: 118.58/124.56 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.56 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.56 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.56 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.56 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.56 U16(active(X:S)) -> U16(X:S) 118.58/124.56 U16(mark(X:S)) -> U16(X:S) 118.58/124.56 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.56 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.56 U23(active(X:S)) -> U23(X:S) 118.58/124.56 U23(mark(X:S)) -> U23(X:S) 118.58/124.56 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.56 U32(active(X:S)) -> U32(X:S) 118.58/124.56 U32(mark(X:S)) -> U32(X:S) 118.58/124.56 U41(active(X:S)) -> U41(X:S) 118.58/124.56 U41(mark(X:S)) -> U41(X:S) 118.58/124.56 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.56 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.56 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.56 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.56 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.56 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.56 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.56 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.56 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.56 active(U16(tt)) -> mark(tt) 118.58/124.56 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.56 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.56 active(U23(tt)) -> mark(tt) 118.58/124.56 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.56 active(U32(tt)) -> mark(tt) 118.58/124.56 active(U41(tt)) -> mark(tt) 118.58/124.56 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.56 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.56 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.56 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.56 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.56 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.56 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.56 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.56 active(isNat(0)) -> mark(tt) 118.58/124.56 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.56 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.56 active(isNatKind(0)) -> mark(tt) 118.58/124.56 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.56 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.56 isNat(active(X:S)) -> isNat(X:S) 118.58/124.56 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.56 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.56 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.56 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.56 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.56 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.56 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.56 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.56 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.56 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.56 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.56 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.56 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.56 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.56 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.56 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.56 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.56 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.56 mark(0) -> active(0) 118.58/124.56 mark(tt) -> active(tt) 118.58/124.56 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.56 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 -> Usable rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 ->Interpretation type: 118.58/124.57 Linear 118.58/124.57 ->Coefficients: 118.58/124.57 Natural Numbers 118.58/124.57 ->Dimension: 118.58/124.57 1 118.58/124.57 ->Bound: 118.58/124.57 2 118.58/124.57 ->Interpretation: 118.58/124.57 118.58/124.57 [U11](X1,X2,X3) = 0 118.58/124.57 [U12](X1,X2,X3) = 0 118.58/124.57 [U13](X1,X2,X3) = 2 118.58/124.57 [U14](X1,X2,X3) = 1 118.58/124.57 [U15](X1,X2) = 1 118.58/124.57 [U16](X) = 2 118.58/124.57 [U21](X1,X2) = 2 118.58/124.57 [U22](X1,X2) = 2 118.58/124.57 [U23](X) = 0 118.58/124.57 [U31](X1,X2) = 2 118.58/124.57 [U32](X) = 0 118.58/124.57 [U41](X) = 1 118.58/124.57 [U51](X1,X2) = 0 118.58/124.57 [U52](X1,X2) = 2 118.58/124.57 [U61](X1,X2,X3) = 0 118.58/124.57 [U62](X1,X2,X3) = 0 118.58/124.57 [U63](X1,X2,X3) = 2 118.58/124.57 [U64](X1,X2,X3) = 1 118.58/124.57 [active](X) = 2 118.58/124.57 [isNat](X) = 2 118.58/124.57 [isNatKind](X) = 2 118.58/124.57 [mark](X) = 2 118.58/124.57 [plus](X1,X2) = 2 118.58/124.57 [s](X) = 2 118.58/124.57 [0] = 1 118.58/124.57 [fSNonEmpty] = 0 118.58/124.57 [tt] = 2 118.58/124.57 [U11#](X1,X2,X3) = 0 118.58/124.57 [U12#](X1,X2,X3) = 0 118.58/124.57 [U13#](X1,X2,X3) = 0 118.58/124.57 [U14#](X1,X2,X3) = 0 118.58/124.57 [U15#](X1,X2) = 0 118.58/124.57 [U16#](X) = 0 118.58/124.57 [U21#](X1,X2) = 0 118.58/124.57 [U22#](X1,X2) = 0 118.58/124.57 [U23#](X) = 0 118.58/124.57 [U31#](X1,X2) = 0 118.58/124.57 [U32#](X) = 0 118.58/124.57 [U41#](X) = 0 118.58/124.57 [U51#](X1,X2) = 0 118.58/124.57 [U52#](X1,X2) = 0 118.58/124.57 [U61#](X1,X2,X3) = 0 118.58/124.57 [U62#](X1,X2,X3) = 0 118.58/124.57 [U63#](X1,X2,X3) = 0 118.58/124.57 [U64#](X1,X2,X3) = 0 118.58/124.57 [ACTIVE](X) = X 118.58/124.57 [ISNAT](X) = 0 118.58/124.57 [ISNATKIND](X) = 0 118.58/124.57 [MARK](X) = 2 118.58/124.57 [PLUS](X1,X2) = 0 118.58/124.57 [S](X) = 0 118.58/124.57 118.58/124.57 Problem 1.23: 118.58/124.57 118.58/124.57 SCC Processor: 118.58/124.57 -> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 -> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 ->Strongly Connected Components: 118.58/124.57 ->->Cycle: 118.58/124.57 ->->-> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 ->->-> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 118.58/124.57 Problem 1.23: 118.58/124.57 118.58/124.57 Reduction Pairs Processor: 118.58/124.57 -> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U14(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 -> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 -> Usable rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 ->Interpretation type: 118.58/124.57 Linear 118.58/124.57 ->Coefficients: 118.58/124.57 Natural Numbers 118.58/124.57 ->Dimension: 118.58/124.57 1 118.58/124.57 ->Bound: 118.58/124.57 2 118.58/124.57 ->Interpretation: 118.58/124.57 118.58/124.57 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.57 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.57 [U13](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.57 [U14](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.57 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.57 [U16](X) = X + 1 118.58/124.57 [U21](X1,X2) = X1 + 2.X2 118.58/124.57 [U22](X1,X2) = X1 + 2.X2 118.58/124.57 [U23](X) = X 118.58/124.57 [U31](X1,X2) = X1 118.58/124.57 [U32](X) = X 118.58/124.57 [U41](X) = X 118.58/124.57 [U51](X1,X2) = 2.X2 + 2 118.58/124.57 [U52](X1,X2) = 2.X2 + 2 118.58/124.57 [U61](X1,X2,X3) = X2 + 2.X3 + 2 118.58/124.57 [U62](X1,X2,X3) = X1 + X2 + 2.X3 118.58/124.57 [U63](X1,X2,X3) = X2 + 2.X3 + 2 118.58/124.57 [U64](X1,X2,X3) = X1 + X2 + 2.X3 118.58/124.57 [active](X) = X 118.58/124.57 [isNat](X) = 2.X + 2 118.58/124.57 [isNatKind](X) = 2 118.58/124.57 [mark](X) = X 118.58/124.57 [plus](X1,X2) = 2.X1 + X2 + 2 118.58/124.57 [s](X) = X 118.58/124.57 [0] = 2 118.58/124.57 [fSNonEmpty] = 0 118.58/124.57 [tt] = 2 118.58/124.57 [U11#](X1,X2,X3) = 0 118.58/124.57 [U12#](X1,X2,X3) = 0 118.58/124.57 [U13#](X1,X2,X3) = 0 118.58/124.57 [U14#](X1,X2,X3) = 0 118.58/124.57 [U15#](X1,X2) = 0 118.58/124.57 [U16#](X) = 0 118.58/124.57 [U21#](X1,X2) = 0 118.58/124.57 [U22#](X1,X2) = 0 118.58/124.57 [U23#](X) = 0 118.58/124.57 [U31#](X1,X2) = 0 118.58/124.57 [U32#](X) = 0 118.58/124.57 [U41#](X) = 0 118.58/124.57 [U51#](X1,X2) = 0 118.58/124.57 [U52#](X1,X2) = 0 118.58/124.57 [U61#](X1,X2,X3) = 0 118.58/124.57 [U62#](X1,X2,X3) = 0 118.58/124.57 [U63#](X1,X2,X3) = 0 118.58/124.57 [U64#](X1,X2,X3) = 0 118.58/124.57 [ACTIVE](X) = 2.X + 2 118.58/124.57 [ISNAT](X) = 0 118.58/124.57 [ISNATKIND](X) = 0 118.58/124.57 [MARK](X) = 2.X + 2 118.58/124.57 [PLUS](X1,X2) = 0 118.58/124.57 [S](X) = 0 118.58/124.57 118.58/124.57 Problem 1.23: 118.58/124.57 118.58/124.57 SCC Processor: 118.58/124.57 -> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 -> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 ->Strongly Connected Components: 118.58/124.57 ->->Cycle: 118.58/124.57 ->->-> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 ->->-> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 118.58/124.57 Problem 1.23: 118.58/124.57 118.58/124.57 Reduction Pairs Processor: 118.58/124.57 -> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> ACTIVE(U15(mark(X1:S),X2:S)) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 -> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 -> Usable rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 ->Interpretation type: 118.58/124.57 Linear 118.58/124.57 ->Coefficients: 118.58/124.57 Natural Numbers 118.58/124.57 ->Dimension: 118.58/124.57 1 118.58/124.57 ->Bound: 118.58/124.57 2 118.58/124.57 ->Interpretation: 118.58/124.57 118.58/124.57 [U11](X1,X2,X3) = 0 118.58/124.57 [U12](X1,X2,X3) = 2 118.58/124.57 [U13](X1,X2,X3) = 2 118.58/124.57 [U14](X1,X2,X3) = 0 118.58/124.57 [U15](X1,X2) = 0 118.58/124.57 [U16](X) = 0 118.58/124.57 [U21](X1,X2) = 1 118.58/124.57 [U22](X1,X2) = 0 118.58/124.57 [U23](X) = 0 118.58/124.57 [U31](X1,X2) = 1 118.58/124.57 [U32](X) = 2 118.58/124.57 [U41](X) = 0 118.58/124.57 [U51](X1,X2) = 2 118.58/124.57 [U52](X1,X2) = 2 118.58/124.57 [U61](X1,X2,X3) = 0 118.58/124.57 [U62](X1,X2,X3) = 2 118.58/124.57 [U63](X1,X2,X3) = 2 118.58/124.57 [U64](X1,X2,X3) = 0 118.58/124.57 [active](X) = 2 118.58/124.57 [isNat](X) = 0 118.58/124.57 [isNatKind](X) = 1 118.58/124.57 [mark](X) = 2 118.58/124.57 [plus](X1,X2) = 0 118.58/124.57 [s](X) = 0 118.58/124.57 [0] = 0 118.58/124.57 [fSNonEmpty] = 0 118.58/124.57 [tt] = 0 118.58/124.57 [U11#](X1,X2,X3) = 0 118.58/124.57 [U12#](X1,X2,X3) = 0 118.58/124.57 [U13#](X1,X2,X3) = 0 118.58/124.57 [U14#](X1,X2,X3) = 0 118.58/124.57 [U15#](X1,X2) = 0 118.58/124.57 [U16#](X) = 0 118.58/124.57 [U21#](X1,X2) = 0 118.58/124.57 [U22#](X1,X2) = 0 118.58/124.57 [U23#](X) = 0 118.58/124.57 [U31#](X1,X2) = 0 118.58/124.57 [U32#](X) = 0 118.58/124.57 [U41#](X) = 0 118.58/124.57 [U51#](X1,X2) = 0 118.58/124.57 [U52#](X1,X2) = 0 118.58/124.57 [U61#](X1,X2,X3) = 0 118.58/124.57 [U62#](X1,X2,X3) = 0 118.58/124.57 [U63#](X1,X2,X3) = 0 118.58/124.57 [U64#](X1,X2,X3) = 0 118.58/124.57 [ACTIVE](X) = 2.X 118.58/124.57 [ISNAT](X) = 0 118.58/124.57 [ISNATKIND](X) = 0 118.58/124.57 [MARK](X) = 2 118.58/124.57 [PLUS](X1,X2) = 0 118.58/124.57 [S](X) = 0 118.58/124.57 118.58/124.57 Problem 1.23: 118.58/124.57 118.58/124.57 SCC Processor: 118.58/124.57 -> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 -> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 ->Strongly Connected Components: 118.58/124.57 ->->Cycle: 118.58/124.57 ->->-> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 ->->-> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.57 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.57 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.57 U23(active(X:S)) -> U23(X:S) 118.58/124.57 U23(mark(X:S)) -> U23(X:S) 118.58/124.57 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.57 U32(active(X:S)) -> U32(X:S) 118.58/124.57 U32(mark(X:S)) -> U32(X:S) 118.58/124.57 U41(active(X:S)) -> U41(X:S) 118.58/124.57 U41(mark(X:S)) -> U41(X:S) 118.58/124.57 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.57 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.57 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.57 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.57 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.57 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.57 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.57 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.57 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.57 active(U16(tt)) -> mark(tt) 118.58/124.57 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.57 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.57 active(U23(tt)) -> mark(tt) 118.58/124.57 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.57 active(U32(tt)) -> mark(tt) 118.58/124.57 active(U41(tt)) -> mark(tt) 118.58/124.57 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.57 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.57 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.57 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.57 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.57 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.57 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.57 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.57 active(isNat(0)) -> mark(tt) 118.58/124.57 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.57 active(isNatKind(0)) -> mark(tt) 118.58/124.57 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.57 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.57 isNat(active(X:S)) -> isNat(X:S) 118.58/124.57 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.57 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.57 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.57 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.57 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.57 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.57 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.57 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.57 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.57 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.57 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.57 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.57 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.57 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.57 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.57 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.57 mark(0) -> active(0) 118.58/124.57 mark(tt) -> active(tt) 118.58/124.57 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.57 s(active(X:S)) -> s(X:S) 118.58/124.57 s(mark(X:S)) -> s(X:S) 118.58/124.57 118.58/124.57 Problem 1.23: 118.58/124.57 118.58/124.57 Reduction Pairs Processor: 118.58/124.57 -> Pairs: 118.58/124.57 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.57 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.57 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.57 MARK(U15(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.57 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.57 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.57 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.57 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.57 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.57 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.57 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.57 MARK(s(X:S)) -> MARK(X:S) 118.58/124.57 -> Rules: 118.58/124.57 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.57 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.57 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.57 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.57 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.57 U16(active(X:S)) -> U16(X:S) 118.58/124.57 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 -> Usable rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 ->Interpretation type: 118.58/124.58 Linear 118.58/124.58 ->Coefficients: 118.58/124.58 Natural Numbers 118.58/124.58 ->Dimension: 118.58/124.58 1 118.58/124.58 ->Bound: 118.58/124.58 2 118.58/124.58 ->Interpretation: 118.58/124.58 118.58/124.58 [U11](X1,X2,X3) = 2.X1 + X2 + 2.X3 118.58/124.58 [U12](X1,X2,X3) = 2.X1 + X2 + 2.X3 118.58/124.58 [U13](X1,X2,X3) = X1 + X2 + 2.X3 + 2 118.58/124.58 [U14](X1,X2,X3) = 2.X1 + X2 + 2.X3 118.58/124.58 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.58 [U16](X) = 2.X 118.58/124.58 [U21](X1,X2) = X1 + X2 118.58/124.58 [U22](X1,X2) = X1 + X2 118.58/124.58 [U23](X) = X 118.58/124.58 [U31](X1,X2) = X1 118.58/124.58 [U32](X) = X 118.58/124.58 [U41](X) = X 118.58/124.58 [U51](X1,X2) = X1 + X2 + 2 118.58/124.58 [U52](X1,X2) = 2.X1 + X2 118.58/124.58 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.58 [U62](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.58 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.58 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.58 [active](X) = X 118.58/124.58 [isNat](X) = X + 2 118.58/124.58 [isNatKind](X) = 2 118.58/124.58 [mark](X) = X 118.58/124.58 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.58 [s](X) = X 118.58/124.58 [0] = 2 118.58/124.58 [fSNonEmpty] = 0 118.58/124.58 [tt] = 2 118.58/124.58 [U11#](X1,X2,X3) = 0 118.58/124.58 [U12#](X1,X2,X3) = 0 118.58/124.58 [U13#](X1,X2,X3) = 0 118.58/124.58 [U14#](X1,X2,X3) = 0 118.58/124.58 [U15#](X1,X2) = 0 118.58/124.58 [U16#](X) = 0 118.58/124.58 [U21#](X1,X2) = 0 118.58/124.58 [U22#](X1,X2) = 0 118.58/124.58 [U23#](X) = 0 118.58/124.58 [U31#](X1,X2) = 0 118.58/124.58 [U32#](X) = 0 118.58/124.58 [U41#](X) = 0 118.58/124.58 [U51#](X1,X2) = 0 118.58/124.58 [U52#](X1,X2) = 0 118.58/124.58 [U61#](X1,X2,X3) = 0 118.58/124.58 [U62#](X1,X2,X3) = 0 118.58/124.58 [U63#](X1,X2,X3) = 0 118.58/124.58 [U64#](X1,X2,X3) = 0 118.58/124.58 [ACTIVE](X) = 2.X + 1 118.58/124.58 [ISNAT](X) = 0 118.58/124.58 [ISNATKIND](X) = 0 118.58/124.58 [MARK](X) = 2.X + 1 118.58/124.58 [PLUS](X1,X2) = 0 118.58/124.58 [S](X) = 0 118.58/124.58 118.58/124.58 Problem 1.23: 118.58/124.58 118.58/124.58 SCC Processor: 118.58/124.58 -> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 -> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 ->Strongly Connected Components: 118.58/124.58 ->->Cycle: 118.58/124.58 ->->-> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 ->->-> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 118.58/124.58 Problem 1.23: 118.58/124.58 118.58/124.58 Reduction Pairs Processor: 118.58/124.58 -> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U16(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 -> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 -> Usable rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 ->Interpretation type: 118.58/124.58 Linear 118.58/124.58 ->Coefficients: 118.58/124.58 Natural Numbers 118.58/124.58 ->Dimension: 118.58/124.58 1 118.58/124.58 ->Bound: 118.58/124.58 2 118.58/124.58 ->Interpretation: 118.58/124.58 118.58/124.58 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.58 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.58 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.58 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.58 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.58 [U16](X) = X + 2 118.58/124.58 [U21](X1,X2) = X1 + 2.X2 118.58/124.58 [U22](X1,X2) = X1 + 2.X2 118.58/124.58 [U23](X) = X 118.58/124.58 [U31](X1,X2) = X1 118.58/124.58 [U32](X) = X 118.58/124.58 [U41](X) = X 118.58/124.58 [U51](X1,X2) = 2.X2 + 2 118.58/124.58 [U52](X1,X2) = X2 + 2 118.58/124.58 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.58 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.58 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.58 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.58 [active](X) = X 118.58/124.58 [isNat](X) = 2.X + 2 118.58/124.58 [isNatKind](X) = 2 118.58/124.58 [mark](X) = X 118.58/124.58 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.58 [s](X) = X 118.58/124.58 [0] = 0 118.58/124.58 [fSNonEmpty] = 0 118.58/124.58 [tt] = 2 118.58/124.58 [U11#](X1,X2,X3) = 0 118.58/124.58 [U12#](X1,X2,X3) = 0 118.58/124.58 [U13#](X1,X2,X3) = 0 118.58/124.58 [U14#](X1,X2,X3) = 0 118.58/124.58 [U15#](X1,X2) = 0 118.58/124.58 [U16#](X) = 0 118.58/124.58 [U21#](X1,X2) = 0 118.58/124.58 [U22#](X1,X2) = 0 118.58/124.58 [U23#](X) = 0 118.58/124.58 [U31#](X1,X2) = 0 118.58/124.58 [U32#](X) = 0 118.58/124.58 [U41#](X) = 0 118.58/124.58 [U51#](X1,X2) = 0 118.58/124.58 [U52#](X1,X2) = 0 118.58/124.58 [U61#](X1,X2,X3) = 0 118.58/124.58 [U62#](X1,X2,X3) = 0 118.58/124.58 [U63#](X1,X2,X3) = 0 118.58/124.58 [U64#](X1,X2,X3) = 0 118.58/124.58 [ACTIVE](X) = 2.X 118.58/124.58 [ISNAT](X) = 0 118.58/124.58 [ISNATKIND](X) = 0 118.58/124.58 [MARK](X) = 2.X 118.58/124.58 [PLUS](X1,X2) = 0 118.58/124.58 [S](X) = 0 118.58/124.58 118.58/124.58 Problem 1.23: 118.58/124.58 118.58/124.58 SCC Processor: 118.58/124.58 -> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 -> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 ->Strongly Connected Components: 118.58/124.58 ->->Cycle: 118.58/124.58 ->->-> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 ->->-> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 118.58/124.58 Problem 1.23: 118.58/124.58 118.58/124.58 Reduction Pairs Processor: 118.58/124.58 -> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> ACTIVE(U21(mark(X1:S),X2:S)) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 -> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 -> Usable rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 ->Interpretation type: 118.58/124.58 Linear 118.58/124.58 ->Coefficients: 118.58/124.58 Natural Numbers 118.58/124.58 ->Dimension: 118.58/124.58 1 118.58/124.58 ->Bound: 118.58/124.58 2 118.58/124.58 ->Interpretation: 118.58/124.58 118.58/124.58 [U11](X1,X2,X3) = 0 118.58/124.58 [U12](X1,X2,X3) = 0 118.58/124.58 [U13](X1,X2,X3) = 0 118.58/124.58 [U14](X1,X2,X3) = 0 118.58/124.58 [U15](X1,X2) = 0 118.58/124.58 [U16](X) = 0 118.58/124.58 [U21](X1,X2) = 0 118.58/124.58 [U22](X1,X2) = 0 118.58/124.58 [U23](X) = 0 118.58/124.58 [U31](X1,X2) = 2 118.58/124.58 [U32](X) = 0 118.58/124.58 [U41](X) = 0 118.58/124.58 [U51](X1,X2) = 0 118.58/124.58 [U52](X1,X2) = 0 118.58/124.58 [U61](X1,X2,X3) = 0 118.58/124.58 [U62](X1,X2,X3) = 0 118.58/124.58 [U63](X1,X2,X3) = 2 118.58/124.58 [U64](X1,X2,X3) = 0 118.58/124.58 [active](X) = 2 118.58/124.58 [isNat](X) = 2 118.58/124.58 [isNatKind](X) = 2 118.58/124.58 [mark](X) = 2 118.58/124.58 [plus](X1,X2) = 2 118.58/124.58 [s](X) = 2 118.58/124.58 [0] = 0 118.58/124.58 [fSNonEmpty] = 0 118.58/124.58 [tt] = 0 118.58/124.58 [U11#](X1,X2,X3) = 0 118.58/124.58 [U12#](X1,X2,X3) = 0 118.58/124.58 [U13#](X1,X2,X3) = 0 118.58/124.58 [U14#](X1,X2,X3) = 0 118.58/124.58 [U15#](X1,X2) = 0 118.58/124.58 [U16#](X) = 0 118.58/124.58 [U21#](X1,X2) = 0 118.58/124.58 [U22#](X1,X2) = 0 118.58/124.58 [U23#](X) = 0 118.58/124.58 [U31#](X1,X2) = 0 118.58/124.58 [U32#](X) = 0 118.58/124.58 [U41#](X) = 0 118.58/124.58 [U51#](X1,X2) = 0 118.58/124.58 [U52#](X1,X2) = 0 118.58/124.58 [U61#](X1,X2,X3) = 0 118.58/124.58 [U62#](X1,X2,X3) = 0 118.58/124.58 [U63#](X1,X2,X3) = 0 118.58/124.58 [U64#](X1,X2,X3) = 0 118.58/124.58 [ACTIVE](X) = X 118.58/124.58 [ISNAT](X) = 0 118.58/124.58 [ISNATKIND](X) = 0 118.58/124.58 [MARK](X) = 2 118.58/124.58 [PLUS](X1,X2) = 0 118.58/124.58 [S](X) = 0 118.58/124.58 118.58/124.58 Problem 1.23: 118.58/124.58 118.58/124.58 SCC Processor: 118.58/124.58 -> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 -> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.58 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.58 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.58 active(U16(tt)) -> mark(tt) 118.58/124.58 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.58 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.58 active(U23(tt)) -> mark(tt) 118.58/124.58 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.58 active(U32(tt)) -> mark(tt) 118.58/124.58 active(U41(tt)) -> mark(tt) 118.58/124.58 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.58 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.58 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.58 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.58 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.58 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.58 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.58 active(isNat(0)) -> mark(tt) 118.58/124.58 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.58 active(isNatKind(0)) -> mark(tt) 118.58/124.58 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.58 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.58 isNat(active(X:S)) -> isNat(X:S) 118.58/124.58 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.58 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.58 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.58 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.58 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.58 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.58 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.58 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.58 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.58 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.58 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.58 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.58 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.58 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.58 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.58 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.58 mark(0) -> active(0) 118.58/124.58 mark(tt) -> active(tt) 118.58/124.58 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.58 s(active(X:S)) -> s(X:S) 118.58/124.58 s(mark(X:S)) -> s(X:S) 118.58/124.58 ->Strongly Connected Components: 118.58/124.58 ->->Cycle: 118.58/124.58 ->->-> Pairs: 118.58/124.58 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.58 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.58 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.58 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.58 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.58 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.58 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.58 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.58 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.58 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.58 MARK(s(X:S)) -> MARK(X:S) 118.58/124.58 ->->-> Rules: 118.58/124.58 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.58 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.58 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.58 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.58 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.58 U16(active(X:S)) -> U16(X:S) 118.58/124.58 U16(mark(X:S)) -> U16(X:S) 118.58/124.58 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.58 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.58 U23(active(X:S)) -> U23(X:S) 118.58/124.58 U23(mark(X:S)) -> U23(X:S) 118.58/124.58 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.58 U32(active(X:S)) -> U32(X:S) 118.58/124.58 U32(mark(X:S)) -> U32(X:S) 118.58/124.58 U41(active(X:S)) -> U41(X:S) 118.58/124.58 U41(mark(X:S)) -> U41(X:S) 118.58/124.58 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.58 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.58 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.58 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.58 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.58 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.58 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.58 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 118.58/124.59 Problem 1.23: 118.58/124.59 118.58/124.59 Reduction Pairs Processor: 118.58/124.59 -> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 -> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 -> Usable rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 ->Interpretation type: 118.58/124.59 Linear 118.58/124.59 ->Coefficients: 118.58/124.59 Natural Numbers 118.58/124.59 ->Dimension: 118.58/124.59 1 118.58/124.59 ->Bound: 118.58/124.59 2 118.58/124.59 ->Interpretation: 118.58/124.59 118.58/124.59 [U11](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U12](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U13](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U14](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U15](X1,X2) = 2 118.58/124.59 [U16](X) = 2 118.58/124.59 [U21](X1,X2) = X1 + X2 + 1 118.58/124.59 [U22](X1,X2) = X1 + X2 + 1 118.58/124.59 [U23](X) = X + 1 118.58/124.59 [U31](X1,X2) = X1 118.58/124.59 [U32](X) = X 118.58/124.59 [U41](X) = X 118.58/124.59 [U51](X1,X2) = X1 + X2 + 2 118.58/124.59 [U52](X1,X2) = 2.X1 + X2 118.58/124.59 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.59 [active](X) = X 118.58/124.59 [isNat](X) = X + 2 118.58/124.59 [isNatKind](X) = 2 118.58/124.59 [mark](X) = X 118.58/124.59 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.59 [s](X) = X + 1 118.58/124.59 [0] = 2 118.58/124.59 [fSNonEmpty] = 0 118.58/124.59 [tt] = 2 118.58/124.59 [U11#](X1,X2,X3) = 0 118.58/124.59 [U12#](X1,X2,X3) = 0 118.58/124.59 [U13#](X1,X2,X3) = 0 118.58/124.59 [U14#](X1,X2,X3) = 0 118.58/124.59 [U15#](X1,X2) = 0 118.58/124.59 [U16#](X) = 0 118.58/124.59 [U21#](X1,X2) = 0 118.58/124.59 [U22#](X1,X2) = 0 118.58/124.59 [U23#](X) = 0 118.58/124.59 [U31#](X1,X2) = 0 118.58/124.59 [U32#](X) = 0 118.58/124.59 [U41#](X) = 0 118.58/124.59 [U51#](X1,X2) = 0 118.58/124.59 [U52#](X1,X2) = 0 118.58/124.59 [U61#](X1,X2,X3) = 0 118.58/124.59 [U62#](X1,X2,X3) = 0 118.58/124.59 [U63#](X1,X2,X3) = 0 118.58/124.59 [U64#](X1,X2,X3) = 0 118.58/124.59 [ACTIVE](X) = 2.X + 2 118.58/124.59 [ISNAT](X) = 0 118.58/124.59 [ISNATKIND](X) = 0 118.58/124.59 [MARK](X) = 2.X + 2 118.58/124.59 [PLUS](X1,X2) = 0 118.58/124.59 [S](X) = 0 118.58/124.59 118.58/124.59 Problem 1.23: 118.58/124.59 118.58/124.59 SCC Processor: 118.58/124.59 -> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 -> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 ->Strongly Connected Components: 118.58/124.59 ->->Cycle: 118.58/124.59 ->->-> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 ->->-> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 118.58/124.59 Problem 1.23: 118.58/124.59 118.58/124.59 Reduction Pairs Processor: 118.58/124.59 -> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> ACTIVE(U22(mark(X1:S),X2:S)) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 -> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 -> Usable rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 ->Interpretation type: 118.58/124.59 Linear 118.58/124.59 ->Coefficients: 118.58/124.59 Natural Numbers 118.58/124.59 ->Dimension: 118.58/124.59 1 118.58/124.59 ->Bound: 118.58/124.59 2 118.58/124.59 ->Interpretation: 118.58/124.59 118.58/124.59 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.59 [U12](X1,X2,X3) = 2.X2 + 2.X3 118.58/124.59 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.59 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.59 [U15](X1,X2) = 2.X2 118.58/124.59 [U16](X) = 0 118.58/124.59 [U21](X1,X2) = 2.X2 + 2 118.58/124.59 [U22](X1,X2) = X1 + 2.X2 + 2 118.58/124.59 [U23](X) = X 118.58/124.59 [U31](X1,X2) = 2.X1 118.58/124.59 [U32](X) = X 118.58/124.59 [U41](X) = 2.X 118.58/124.59 [U51](X1,X2) = 2.X2 + 2 118.58/124.59 [U52](X1,X2) = 2.X2 + 2 118.58/124.59 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.59 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.59 [active](X) = X 118.58/124.59 [isNat](X) = 2.X + 2 118.58/124.59 [isNatKind](X) = 0 118.58/124.59 [mark](X) = X 118.58/124.59 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.59 [s](X) = X 118.58/124.59 [0] = 2 118.58/124.59 [fSNonEmpty] = 0 118.58/124.59 [tt] = 0 118.58/124.59 [U11#](X1,X2,X3) = 0 118.58/124.59 [U12#](X1,X2,X3) = 0 118.58/124.59 [U13#](X1,X2,X3) = 0 118.58/124.59 [U14#](X1,X2,X3) = 0 118.58/124.59 [U15#](X1,X2) = 0 118.58/124.59 [U16#](X) = 0 118.58/124.59 [U21#](X1,X2) = 0 118.58/124.59 [U22#](X1,X2) = 0 118.58/124.59 [U23#](X) = 0 118.58/124.59 [U31#](X1,X2) = 0 118.58/124.59 [U32#](X) = 0 118.58/124.59 [U41#](X) = 0 118.58/124.59 [U51#](X1,X2) = 0 118.58/124.59 [U52#](X1,X2) = 0 118.58/124.59 [U61#](X1,X2,X3) = 0 118.58/124.59 [U62#](X1,X2,X3) = 0 118.58/124.59 [U63#](X1,X2,X3) = 0 118.58/124.59 [U64#](X1,X2,X3) = 0 118.58/124.59 [ACTIVE](X) = X + 2 118.58/124.59 [ISNAT](X) = 0 118.58/124.59 [ISNATKIND](X) = 0 118.58/124.59 [MARK](X) = 2.X + 2 118.58/124.59 [PLUS](X1,X2) = 0 118.58/124.59 [S](X) = 0 118.58/124.59 118.58/124.59 Problem 1.23: 118.58/124.59 118.58/124.59 SCC Processor: 118.58/124.59 -> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 -> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 ->Strongly Connected Components: 118.58/124.59 ->->Cycle: 118.58/124.59 ->->-> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 ->->-> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 118.58/124.59 Problem 1.23: 118.58/124.59 118.58/124.59 Reduction Pairs Processor: 118.58/124.59 -> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 -> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 -> Usable rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 ->Interpretation type: 118.58/124.59 Linear 118.58/124.59 ->Coefficients: 118.58/124.59 Natural Numbers 118.58/124.59 ->Dimension: 118.58/124.59 1 118.58/124.59 ->Bound: 118.58/124.59 2 118.58/124.59 ->Interpretation: 118.58/124.59 118.58/124.59 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.59 [U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.59 [U13](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.59 [U14](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.59 [U15](X1,X2) = X1 + 2.X2 + 2 118.58/124.59 [U16](X) = X + 2 118.58/124.59 [U21](X1,X2) = 2.X1 + 2.X2 118.58/124.59 [U22](X1,X2) = X1 + 2.X2 + 2 118.58/124.59 [U23](X) = X + 2 118.58/124.59 [U31](X1,X2) = X1 118.58/124.59 [U32](X) = X 118.58/124.59 [U41](X) = X 118.58/124.59 [U51](X1,X2) = 2.X2 + 2 118.58/124.59 [U52](X1,X2) = 2.X2 + 2 118.58/124.59 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.59 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.59 [active](X) = X 118.58/124.59 [isNat](X) = 2.X + 2 118.58/124.59 [isNatKind](X) = 2 118.58/124.59 [mark](X) = X 118.58/124.59 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.59 [s](X) = X + 1 118.58/124.59 [0] = 2 118.58/124.59 [fSNonEmpty] = 0 118.58/124.59 [tt] = 2 118.58/124.59 [U11#](X1,X2,X3) = 0 118.58/124.59 [U12#](X1,X2,X3) = 0 118.58/124.59 [U13#](X1,X2,X3) = 0 118.58/124.59 [U14#](X1,X2,X3) = 0 118.58/124.59 [U15#](X1,X2) = 0 118.58/124.59 [U16#](X) = 0 118.58/124.59 [U21#](X1,X2) = 0 118.58/124.59 [U22#](X1,X2) = 0 118.58/124.59 [U23#](X) = 0 118.58/124.59 [U31#](X1,X2) = 0 118.58/124.59 [U32#](X) = 0 118.58/124.59 [U41#](X) = 0 118.58/124.59 [U51#](X1,X2) = 0 118.58/124.59 [U52#](X1,X2) = 0 118.58/124.59 [U61#](X1,X2,X3) = 0 118.58/124.59 [U62#](X1,X2,X3) = 0 118.58/124.59 [U63#](X1,X2,X3) = 0 118.58/124.59 [U64#](X1,X2,X3) = 0 118.58/124.59 [ACTIVE](X) = 2.X + 2 118.58/124.59 [ISNAT](X) = 0 118.58/124.59 [ISNATKIND](X) = 0 118.58/124.59 [MARK](X) = 2.X + 2 118.58/124.59 [PLUS](X1,X2) = 0 118.58/124.59 [S](X) = 0 118.58/124.59 118.58/124.59 Problem 1.23: 118.58/124.59 118.58/124.59 SCC Processor: 118.58/124.59 -> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 -> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.59 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.59 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.59 U16(active(X:S)) -> U16(X:S) 118.58/124.59 U16(mark(X:S)) -> U16(X:S) 118.58/124.59 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.59 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.59 U23(active(X:S)) -> U23(X:S) 118.58/124.59 U23(mark(X:S)) -> U23(X:S) 118.58/124.59 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.59 U32(active(X:S)) -> U32(X:S) 118.58/124.59 U32(mark(X:S)) -> U32(X:S) 118.58/124.59 U41(active(X:S)) -> U41(X:S) 118.58/124.59 U41(mark(X:S)) -> U41(X:S) 118.58/124.59 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.59 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.59 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.59 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.59 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.59 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.59 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.59 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.59 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.59 active(U16(tt)) -> mark(tt) 118.58/124.59 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.59 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.59 active(U23(tt)) -> mark(tt) 118.58/124.59 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.59 active(U32(tt)) -> mark(tt) 118.58/124.59 active(U41(tt)) -> mark(tt) 118.58/124.59 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.59 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.59 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.59 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.59 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.59 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.59 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.59 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.59 active(isNat(0)) -> mark(tt) 118.58/124.59 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.59 active(isNatKind(0)) -> mark(tt) 118.58/124.59 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.59 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.59 isNat(active(X:S)) -> isNat(X:S) 118.58/124.59 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.59 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.59 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.59 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.59 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.59 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.59 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.59 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.59 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.59 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.59 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.59 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.59 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.59 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.59 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.59 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.59 mark(0) -> active(0) 118.58/124.59 mark(tt) -> active(tt) 118.58/124.59 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.59 s(active(X:S)) -> s(X:S) 118.58/124.59 s(mark(X:S)) -> s(X:S) 118.58/124.59 ->Strongly Connected Components: 118.58/124.59 ->->Cycle: 118.58/124.59 ->->-> Pairs: 118.58/124.59 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.59 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.59 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.59 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.59 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.59 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.59 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.59 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.59 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.59 MARK(s(X:S)) -> MARK(X:S) 118.58/124.59 ->->-> Rules: 118.58/124.59 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.59 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.59 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 118.58/124.60 Problem 1.23: 118.58/124.60 118.58/124.60 Reduction Pairs Processor: 118.58/124.60 -> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U23(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 -> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 -> Usable rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 ->Interpretation type: 118.58/124.60 Linear 118.58/124.60 ->Coefficients: 118.58/124.60 Natural Numbers 118.58/124.60 ->Dimension: 118.58/124.60 1 118.58/124.60 ->Bound: 118.58/124.60 2 118.58/124.60 ->Interpretation: 118.58/124.60 118.58/124.60 [U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.60 [U12](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.60 [U13](X1,X2,X3) = X2 + 2.X3 + 2 118.58/124.60 [U14](X1,X2,X3) = X3 + 2 118.58/124.60 [U15](X1,X2) = X2 + 2 118.58/124.60 [U16](X) = 2 118.58/124.60 [U21](X1,X2) = 2.X1 + 2.X2 118.58/124.60 [U22](X1,X2) = 2.X1 + 2.X2 118.58/124.60 [U23](X) = X + 2 118.58/124.60 [U31](X1,X2) = X1 118.58/124.60 [U32](X) = X 118.58/124.60 [U41](X) = X 118.58/124.60 [U51](X1,X2) = 2.X2 + 1 118.58/124.60 [U52](X1,X2) = 2.X2 + 1 118.58/124.60 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.60 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.60 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.60 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.60 [active](X) = X 118.58/124.60 [isNat](X) = 2.X + 2 118.58/124.60 [isNatKind](X) = 2 118.58/124.60 [mark](X) = X 118.58/124.60 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.60 [s](X) = X + 1 118.58/124.60 [0] = 2 118.58/124.60 [fSNonEmpty] = 0 118.58/124.60 [tt] = 2 118.58/124.60 [U11#](X1,X2,X3) = 0 118.58/124.60 [U12#](X1,X2,X3) = 0 118.58/124.60 [U13#](X1,X2,X3) = 0 118.58/124.60 [U14#](X1,X2,X3) = 0 118.58/124.60 [U15#](X1,X2) = 0 118.58/124.60 [U16#](X) = 0 118.58/124.60 [U21#](X1,X2) = 0 118.58/124.60 [U22#](X1,X2) = 0 118.58/124.60 [U23#](X) = 0 118.58/124.60 [U31#](X1,X2) = 0 118.58/124.60 [U32#](X) = 0 118.58/124.60 [U41#](X) = 0 118.58/124.60 [U51#](X1,X2) = 0 118.58/124.60 [U52#](X1,X2) = 0 118.58/124.60 [U61#](X1,X2,X3) = 0 118.58/124.60 [U62#](X1,X2,X3) = 0 118.58/124.60 [U63#](X1,X2,X3) = 0 118.58/124.60 [U64#](X1,X2,X3) = 0 118.58/124.60 [ACTIVE](X) = 2.X + 2 118.58/124.60 [ISNAT](X) = 0 118.58/124.60 [ISNATKIND](X) = 0 118.58/124.60 [MARK](X) = 2.X + 2 118.58/124.60 [PLUS](X1,X2) = 0 118.58/124.60 [S](X) = 0 118.58/124.60 118.58/124.60 Problem 1.23: 118.58/124.60 118.58/124.60 SCC Processor: 118.58/124.60 -> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 -> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 ->Strongly Connected Components: 118.58/124.60 ->->Cycle: 118.58/124.60 ->->-> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 ->->-> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 118.58/124.60 Problem 1.23: 118.58/124.60 118.58/124.60 Reduction Pairs Processor: 118.58/124.60 -> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> ACTIVE(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 -> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 -> Usable rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 ->Interpretation type: 118.58/124.60 Linear 118.58/124.60 ->Coefficients: 118.58/124.60 Natural Numbers 118.58/124.60 ->Dimension: 118.58/124.60 1 118.58/124.60 ->Bound: 118.58/124.60 2 118.58/124.60 ->Interpretation: 118.58/124.60 118.58/124.60 [U11](X1,X2,X3) = 0 118.58/124.60 [U12](X1,X2,X3) = X1 118.58/124.60 [U13](X1,X2,X3) = 2.X1 118.58/124.60 [U14](X1,X2,X3) = 2.X1 118.58/124.60 [U15](X1,X2) = 0 118.58/124.60 [U16](X) = 0 118.58/124.60 [U21](X1,X2) = 0 118.58/124.60 [U22](X1,X2) = 0 118.58/124.60 [U23](X) = 0 118.58/124.60 [U31](X1,X2) = 2.X1 118.58/124.60 [U32](X) = X 118.58/124.60 [U41](X) = 2.X 118.58/124.60 [U51](X1,X2) = 2.X2 + 2 118.58/124.60 [U52](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.60 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.60 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.60 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.60 [U64](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.60 [active](X) = X 118.58/124.60 [isNat](X) = 0 118.58/124.60 [isNatKind](X) = 0 118.58/124.60 [mark](X) = X 118.58/124.60 [plus](X1,X2) = 2.X1 + 2.X2 118.58/124.60 [s](X) = X + 2 118.58/124.60 [0] = 2 118.58/124.60 [fSNonEmpty] = 0 118.58/124.60 [tt] = 0 118.58/124.60 [U11#](X1,X2,X3) = 0 118.58/124.60 [U12#](X1,X2,X3) = 0 118.58/124.60 [U13#](X1,X2,X3) = 0 118.58/124.60 [U14#](X1,X2,X3) = 0 118.58/124.60 [U15#](X1,X2) = 0 118.58/124.60 [U16#](X) = 0 118.58/124.60 [U21#](X1,X2) = 0 118.58/124.60 [U22#](X1,X2) = 0 118.58/124.60 [U23#](X) = 0 118.58/124.60 [U31#](X1,X2) = 0 118.58/124.60 [U32#](X) = 0 118.58/124.60 [U41#](X) = 0 118.58/124.60 [U51#](X1,X2) = 0 118.58/124.60 [U52#](X1,X2) = 0 118.58/124.60 [U61#](X1,X2,X3) = 0 118.58/124.60 [U62#](X1,X2,X3) = 0 118.58/124.60 [U63#](X1,X2,X3) = 0 118.58/124.60 [U64#](X1,X2,X3) = 0 118.58/124.60 [ACTIVE](X) = 2 118.58/124.60 [ISNAT](X) = 0 118.58/124.60 [ISNATKIND](X) = 0 118.58/124.60 [MARK](X) = 2.X + 2 118.58/124.60 [PLUS](X1,X2) = 0 118.58/124.60 [S](X) = 0 118.58/124.60 118.58/124.60 Problem 1.23: 118.58/124.60 118.58/124.60 SCC Processor: 118.58/124.60 -> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 -> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 ->Strongly Connected Components: 118.58/124.60 ->->Cycle: 118.58/124.60 ->->-> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 ->->-> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 118.58/124.60 Problem 1.23: 118.58/124.60 118.58/124.60 Reduction Pairs Processor: 118.58/124.60 -> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U64(X1:S,X2:S,X3:S)) -> MARK(X1:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 -> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 -> Usable rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.60 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.60 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.60 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.60 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.60 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.60 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.60 mark(0) -> active(0) 118.58/124.60 mark(tt) -> active(tt) 118.58/124.60 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.60 s(active(X:S)) -> s(X:S) 118.58/124.60 s(mark(X:S)) -> s(X:S) 118.58/124.60 ->Interpretation type: 118.58/124.60 Linear 118.58/124.60 ->Coefficients: 118.58/124.60 Natural Numbers 118.58/124.60 ->Dimension: 118.58/124.60 1 118.58/124.60 ->Bound: 118.58/124.60 2 118.58/124.60 ->Interpretation: 118.58/124.60 118.58/124.60 [U11](X1,X2,X3) = 2 118.58/124.60 [U12](X1,X2,X3) = X1 118.58/124.60 [U13](X1,X2,X3) = 2 118.58/124.60 [U14](X1,X2,X3) = 2 118.58/124.60 [U15](X1,X2) = X1 118.58/124.60 [U16](X) = X 118.58/124.60 [U21](X1,X2) = X1 118.58/124.60 [U22](X1,X2) = 2 118.58/124.60 [U23](X) = 2 118.58/124.60 [U31](X1,X2) = X1 118.58/124.60 [U32](X) = X 118.58/124.60 [U41](X) = X 118.58/124.60 [U51](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.60 [U52](X1,X2) = 2.X2 + 2 118.58/124.60 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.60 [U62](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.60 [U63](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 118.58/124.60 [U64](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.60 [active](X) = X 118.58/124.60 [isNat](X) = 2 118.58/124.60 [isNatKind](X) = 2 118.58/124.60 [mark](X) = X 118.58/124.60 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.60 [s](X) = X + 2 118.58/124.60 [0] = 2 118.58/124.60 [fSNonEmpty] = 0 118.58/124.60 [tt] = 2 118.58/124.60 [U11#](X1,X2,X3) = 0 118.58/124.60 [U12#](X1,X2,X3) = 0 118.58/124.60 [U13#](X1,X2,X3) = 0 118.58/124.60 [U14#](X1,X2,X3) = 0 118.58/124.60 [U15#](X1,X2) = 0 118.58/124.60 [U16#](X) = 0 118.58/124.60 [U21#](X1,X2) = 0 118.58/124.60 [U22#](X1,X2) = 0 118.58/124.60 [U23#](X) = 0 118.58/124.60 [U31#](X1,X2) = 0 118.58/124.60 [U32#](X) = 0 118.58/124.60 [U41#](X) = 0 118.58/124.60 [U51#](X1,X2) = 0 118.58/124.60 [U52#](X1,X2) = 0 118.58/124.60 [U61#](X1,X2,X3) = 0 118.58/124.60 [U62#](X1,X2,X3) = 0 118.58/124.60 [U63#](X1,X2,X3) = 0 118.58/124.60 [U64#](X1,X2,X3) = 0 118.58/124.60 [ACTIVE](X) = X + 2 118.58/124.60 [ISNAT](X) = 0 118.58/124.60 [ISNATKIND](X) = 0 118.58/124.60 [MARK](X) = X + 2 118.58/124.60 [PLUS](X1,X2) = 0 118.58/124.60 [S](X) = 0 118.58/124.60 118.58/124.60 Problem 1.23: 118.58/124.60 118.58/124.60 SCC Processor: 118.58/124.60 -> Pairs: 118.58/124.60 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.60 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.60 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.60 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.60 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.60 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.60 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.60 MARK(s(X:S)) -> MARK(X:S) 118.58/124.60 -> Rules: 118.58/124.60 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.60 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.60 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.60 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.60 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.60 U16(active(X:S)) -> U16(X:S) 118.58/124.60 U16(mark(X:S)) -> U16(X:S) 118.58/124.60 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.60 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.60 U23(active(X:S)) -> U23(X:S) 118.58/124.60 U23(mark(X:S)) -> U23(X:S) 118.58/124.60 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.60 U32(active(X:S)) -> U32(X:S) 118.58/124.60 U32(mark(X:S)) -> U32(X:S) 118.58/124.60 U41(active(X:S)) -> U41(X:S) 118.58/124.60 U41(mark(X:S)) -> U41(X:S) 118.58/124.60 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.60 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.60 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.60 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.60 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.60 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.60 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.60 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.60 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.60 active(U16(tt)) -> mark(tt) 118.58/124.60 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.60 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.60 active(U23(tt)) -> mark(tt) 118.58/124.60 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.60 active(U32(tt)) -> mark(tt) 118.58/124.60 active(U41(tt)) -> mark(tt) 118.58/124.60 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.60 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.60 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.60 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.60 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.60 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.60 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.60 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.60 active(isNat(0)) -> mark(tt) 118.58/124.60 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.60 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.60 active(isNatKind(0)) -> mark(tt) 118.58/124.60 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.60 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.60 isNat(active(X:S)) -> isNat(X:S) 118.58/124.60 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.60 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.60 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.60 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.60 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.60 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.60 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.60 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.60 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.60 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.60 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 ->Strongly Connected Components: 118.58/124.61 ->->Cycle: 118.58/124.61 ->->-> Pairs: 118.58/124.61 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.61 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 ->->-> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 118.58/124.61 Problem 1.23: 118.58/124.61 118.58/124.61 Reduction Pairs Processor: 118.58/124.61 -> Pairs: 118.58/124.61 ACTIVE(U31(tt,V2:S)) -> MARK(U32(isNatKind(V2:S))) 118.58/124.61 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 -> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 -> Usable rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 ->Interpretation type: 118.58/124.61 Linear 118.58/124.61 ->Coefficients: 118.58/124.61 Natural Numbers 118.58/124.61 ->Dimension: 118.58/124.61 1 118.58/124.61 ->Bound: 118.58/124.61 2 118.58/124.61 ->Interpretation: 118.58/124.61 118.58/124.61 [U11](X1,X2,X3) = 2 118.58/124.61 [U12](X1,X2,X3) = 2 118.58/124.61 [U13](X1,X2,X3) = 2 118.58/124.61 [U14](X1,X2,X3) = 2 118.58/124.61 [U15](X1,X2) = 2 118.58/124.61 [U16](X) = X 118.58/124.61 [U21](X1,X2) = 2 118.58/124.61 [U22](X1,X2) = 2 118.58/124.61 [U23](X) = 2 118.58/124.61 [U31](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.61 [U32](X) = X + 2 118.58/124.61 [U41](X) = X + 2 118.58/124.61 [U51](X1,X2) = 2.X1 + 2.X2 118.58/124.61 [U52](X1,X2) = 2.X2 + 1 118.58/124.61 [U61](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.61 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [U63](X1,X2,X3) = X1 + 2.X2 + 2.X3 118.58/124.61 [U64](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [active](X) = X 118.58/124.61 [isNat](X) = 2 118.58/124.61 [isNatKind](X) = 2.X + 1 118.58/124.61 [mark](X) = X 118.58/124.61 [plus](X1,X2) = 2.X1 + 2.X2 + 1 118.58/124.61 [s](X) = X + 1 118.58/124.61 [0] = 2 118.58/124.61 [fSNonEmpty] = 0 118.58/124.61 [tt] = 2 118.58/124.61 [U11#](X1,X2,X3) = 0 118.58/124.61 [U12#](X1,X2,X3) = 0 118.58/124.61 [U13#](X1,X2,X3) = 0 118.58/124.61 [U14#](X1,X2,X3) = 0 118.58/124.61 [U15#](X1,X2) = 0 118.58/124.61 [U16#](X) = 0 118.58/124.61 [U21#](X1,X2) = 0 118.58/124.61 [U22#](X1,X2) = 0 118.58/124.61 [U23#](X) = 0 118.58/124.61 [U31#](X1,X2) = 0 118.58/124.61 [U32#](X) = 0 118.58/124.61 [U41#](X) = 0 118.58/124.61 [U51#](X1,X2) = 0 118.58/124.61 [U52#](X1,X2) = 0 118.58/124.61 [U61#](X1,X2,X3) = 0 118.58/124.61 [U62#](X1,X2,X3) = 0 118.58/124.61 [U63#](X1,X2,X3) = 0 118.58/124.61 [U64#](X1,X2,X3) = 0 118.58/124.61 [ACTIVE](X) = 2.X + 2 118.58/124.61 [ISNAT](X) = 0 118.58/124.61 [ISNATKIND](X) = 0 118.58/124.61 [MARK](X) = 2.X + 2 118.58/124.61 [PLUS](X1,X2) = 0 118.58/124.61 [S](X) = 0 118.58/124.61 118.58/124.61 Problem 1.23: 118.58/124.61 118.58/124.61 SCC Processor: 118.58/124.61 -> Pairs: 118.58/124.61 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 -> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 ->Strongly Connected Components: 118.58/124.61 ->->Cycle: 118.58/124.61 ->->-> Pairs: 118.58/124.61 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 ->->-> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 118.58/124.61 Problem 1.23: 118.58/124.61 118.58/124.61 Reduction Pairs Processor: 118.58/124.61 -> Pairs: 118.58/124.61 ACTIVE(isNatKind(plus(V1:S,V2:S))) -> MARK(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 -> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 -> Usable rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 ->Interpretation type: 118.58/124.61 Linear 118.58/124.61 ->Coefficients: 118.58/124.61 Natural Numbers 118.58/124.61 ->Dimension: 118.58/124.61 1 118.58/124.61 ->Bound: 118.58/124.61 2 118.58/124.61 ->Interpretation: 118.58/124.61 118.58/124.61 [U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 118.58/124.61 [U12](X1,X2,X3) = X1 + 2.X3 + 2 118.58/124.61 [U13](X1,X2,X3) = X1 + 2 118.58/124.61 [U14](X1,X2,X3) = 2 118.58/124.61 [U15](X1,X2) = 2 118.58/124.61 [U16](X) = 2 118.58/124.61 [U21](X1,X2) = 2.X2 118.58/124.61 [U22](X1,X2) = 2.X2 118.58/124.61 [U23](X) = X 118.58/124.61 [U31](X1,X2) = X1 + 2.X2 + 2 118.58/124.61 [U32](X) = X + 1 118.58/124.61 [U41](X) = X 118.58/124.61 [U51](X1,X2) = 2.X2 + 2 118.58/124.61 [U52](X1,X2) = X2 + 2 118.58/124.61 [U61](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [U64](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [active](X) = X 118.58/124.61 [isNat](X) = 2.X 118.58/124.61 [isNatKind](X) = 2.X + 2 118.58/124.61 [mark](X) = X 118.58/124.61 [plus](X1,X2) = 2.X1 + 2.X2 + 2 118.58/124.61 [s](X) = X 118.58/124.61 [0] = 2 118.58/124.61 [fSNonEmpty] = 0 118.58/124.61 [tt] = 2 118.58/124.61 [U11#](X1,X2,X3) = 0 118.58/124.61 [U12#](X1,X2,X3) = 0 118.58/124.61 [U13#](X1,X2,X3) = 0 118.58/124.61 [U14#](X1,X2,X3) = 0 118.58/124.61 [U15#](X1,X2) = 0 118.58/124.61 [U16#](X) = 0 118.58/124.61 [U21#](X1,X2) = 0 118.58/124.61 [U22#](X1,X2) = 0 118.58/124.61 [U23#](X) = 0 118.58/124.61 [U31#](X1,X2) = 0 118.58/124.61 [U32#](X) = 0 118.58/124.61 [U41#](X) = 0 118.58/124.61 [U51#](X1,X2) = 0 118.58/124.61 [U52#](X1,X2) = 0 118.58/124.61 [U61#](X1,X2,X3) = 0 118.58/124.61 [U62#](X1,X2,X3) = 0 118.58/124.61 [U63#](X1,X2,X3) = 0 118.58/124.61 [U64#](X1,X2,X3) = 0 118.58/124.61 [ACTIVE](X) = 2.X + 2 118.58/124.61 [ISNAT](X) = 0 118.58/124.61 [ISNATKIND](X) = 0 118.58/124.61 [MARK](X) = 2.X + 2 118.58/124.61 [PLUS](X1,X2) = 0 118.58/124.61 [S](X) = 0 118.58/124.61 118.58/124.61 Problem 1.23: 118.58/124.61 118.58/124.61 SCC Processor: 118.58/124.61 -> Pairs: 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 -> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 ->Strongly Connected Components: 118.58/124.61 ->->Cycle: 118.58/124.61 ->->-> Pairs: 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 ->->-> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 118.58/124.61 Problem 1.23: 118.58/124.61 118.58/124.61 Reduction Pairs Processor: 118.58/124.61 -> Pairs: 118.58/124.61 ACTIVE(isNatKind(s(V1:S))) -> MARK(U41(isNatKind(V1:S))) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 -> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 -> Usable rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.61 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.61 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.61 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.61 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.61 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.61 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.61 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.61 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.61 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.61 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.61 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.61 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.61 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.61 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.61 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.61 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.61 mark(0) -> active(0) 118.58/124.61 mark(tt) -> active(tt) 118.58/124.61 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.61 s(active(X:S)) -> s(X:S) 118.58/124.61 s(mark(X:S)) -> s(X:S) 118.58/124.61 ->Interpretation type: 118.58/124.61 Linear 118.58/124.61 ->Coefficients: 118.58/124.61 Natural Numbers 118.58/124.61 ->Dimension: 118.58/124.61 1 118.58/124.61 ->Bound: 118.58/124.61 2 118.58/124.61 ->Interpretation: 118.58/124.61 118.58/124.61 [U11](X1,X2,X3) = 2 118.58/124.61 [U12](X1,X2,X3) = 2 118.58/124.61 [U13](X1,X2,X3) = 2 118.58/124.61 [U14](X1,X2,X3) = 2 118.58/124.61 [U15](X1,X2) = 2 118.58/124.61 [U16](X) = X 118.58/124.61 [U21](X1,X2) = 2 118.58/124.61 [U22](X1,X2) = 2 118.58/124.61 [U23](X) = 2 118.58/124.61 [U31](X1,X2) = X1 + 2.X2 118.58/124.61 [U32](X) = X 118.58/124.61 [U41](X) = X 118.58/124.61 [U51](X1,X2) = 2.X1 + 2.X2 118.58/124.61 [U52](X1,X2) = X1 + X2 + 1 118.58/124.61 [U61](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 118.58/124.61 [U62](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [U63](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [U64](X1,X2,X3) = 2.X2 + 2.X3 + 2 118.58/124.61 [active](X) = X 118.58/124.61 [isNat](X) = 2 118.58/124.61 [isNatKind](X) = X + 2 118.58/124.61 [mark](X) = X 118.58/124.61 [plus](X1,X2) = 2.X1 + 2.X2 118.58/124.61 [s](X) = X + 2 118.58/124.61 [0] = 2 118.58/124.61 [fSNonEmpty] = 0 118.58/124.61 [tt] = 2 118.58/124.61 [U11#](X1,X2,X3) = 0 118.58/124.61 [U12#](X1,X2,X3) = 0 118.58/124.61 [U13#](X1,X2,X3) = 0 118.58/124.61 [U14#](X1,X2,X3) = 0 118.58/124.61 [U15#](X1,X2) = 0 118.58/124.61 [U16#](X) = 0 118.58/124.61 [U21#](X1,X2) = 0 118.58/124.61 [U22#](X1,X2) = 0 118.58/124.61 [U23#](X) = 0 118.58/124.61 [U31#](X1,X2) = 0 118.58/124.61 [U32#](X) = 0 118.58/124.61 [U41#](X) = 0 118.58/124.61 [U51#](X1,X2) = 0 118.58/124.61 [U52#](X1,X2) = 0 118.58/124.61 [U61#](X1,X2,X3) = 0 118.58/124.61 [U62#](X1,X2,X3) = 0 118.58/124.61 [U63#](X1,X2,X3) = 0 118.58/124.61 [U64#](X1,X2,X3) = 0 118.58/124.61 [ACTIVE](X) = 2.X 118.58/124.61 [ISNAT](X) = 0 118.58/124.61 [ISNATKIND](X) = 0 118.58/124.61 [MARK](X) = 2.X + 2 118.58/124.61 [PLUS](X1,X2) = 0 118.58/124.61 [S](X) = 0 118.58/124.61 118.58/124.61 Problem 1.23: 118.58/124.61 118.58/124.61 SCC Processor: 118.58/124.61 -> Pairs: 118.58/124.61 MARK(U31(X1:S,X2:S)) -> ACTIVE(U31(mark(X1:S),X2:S)) 118.58/124.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.61 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.61 MARK(isNatKind(X:S)) -> ACTIVE(isNatKind(X:S)) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.61 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.61 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 118.58/124.61 MARK(s(X:S)) -> MARK(X:S) 118.58/124.61 -> Rules: 118.58/124.61 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.61 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.61 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.61 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.61 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.61 U16(active(X:S)) -> U16(X:S) 118.58/124.61 U16(mark(X:S)) -> U16(X:S) 118.58/124.61 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.61 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.61 U23(active(X:S)) -> U23(X:S) 118.58/124.61 U23(mark(X:S)) -> U23(X:S) 118.58/124.61 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.61 U32(active(X:S)) -> U32(X:S) 118.58/124.61 U32(mark(X:S)) -> U32(X:S) 118.58/124.61 U41(active(X:S)) -> U41(X:S) 118.58/124.61 U41(mark(X:S)) -> U41(X:S) 118.58/124.61 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.61 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.61 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.61 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.61 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.61 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.61 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.61 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.61 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.61 active(U16(tt)) -> mark(tt) 118.58/124.61 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.61 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.61 active(U23(tt)) -> mark(tt) 118.58/124.61 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.61 active(U32(tt)) -> mark(tt) 118.58/124.61 active(U41(tt)) -> mark(tt) 118.58/124.61 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.61 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.61 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.61 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.61 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.61 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.61 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.61 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.61 active(isNat(0)) -> mark(tt) 118.58/124.61 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.61 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.61 active(isNatKind(0)) -> mark(tt) 118.58/124.61 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.61 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.61 isNat(active(X:S)) -> isNat(X:S) 118.58/124.61 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.62 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.62 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.62 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.62 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.62 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.62 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.62 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.62 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.62 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.62 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.62 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.62 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.62 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.62 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.62 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.62 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.62 mark(0) -> active(0) 118.58/124.62 mark(tt) -> active(tt) 118.58/124.62 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 s(active(X:S)) -> s(X:S) 118.58/124.62 s(mark(X:S)) -> s(X:S) 118.58/124.62 ->Strongly Connected Components: 118.58/124.62 ->->Cycle: 118.58/124.62 ->->-> Pairs: 118.58/124.62 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.62 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.62 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.62 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.62 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.62 MARK(s(X:S)) -> MARK(X:S) 118.58/124.62 ->->-> Rules: 118.58/124.62 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.62 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.62 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.62 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.62 U16(active(X:S)) -> U16(X:S) 118.58/124.62 U16(mark(X:S)) -> U16(X:S) 118.58/124.62 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.62 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.62 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.62 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.62 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.62 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.62 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.62 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.62 U23(active(X:S)) -> U23(X:S) 118.58/124.62 U23(mark(X:S)) -> U23(X:S) 118.58/124.62 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.62 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.62 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.62 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.62 U32(active(X:S)) -> U32(X:S) 118.58/124.62 U32(mark(X:S)) -> U32(X:S) 118.58/124.62 U41(active(X:S)) -> U41(X:S) 118.58/124.62 U41(mark(X:S)) -> U41(X:S) 118.58/124.62 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.62 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.62 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.62 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.62 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.62 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.62 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.62 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.62 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.62 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.62 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.62 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.62 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.62 active(U16(tt)) -> mark(tt) 118.58/124.62 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.62 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.62 active(U23(tt)) -> mark(tt) 118.58/124.62 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.62 active(U32(tt)) -> mark(tt) 118.58/124.62 active(U41(tt)) -> mark(tt) 118.58/124.62 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.62 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.62 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.62 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.62 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.62 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.62 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.62 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.62 active(isNat(0)) -> mark(tt) 118.58/124.62 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.62 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.62 active(isNatKind(0)) -> mark(tt) 118.58/124.62 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.62 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.62 isNat(active(X:S)) -> isNat(X:S) 118.58/124.62 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.62 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.62 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.62 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.62 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.62 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.62 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.62 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.62 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.62 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.62 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.62 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.62 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.62 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.62 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.62 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.62 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.62 mark(0) -> active(0) 118.58/124.62 mark(tt) -> active(tt) 118.58/124.62 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 s(active(X:S)) -> s(X:S) 118.58/124.62 s(mark(X:S)) -> s(X:S) 118.58/124.62 118.58/124.62 Problem 1.23: 118.58/124.62 118.58/124.62 Subterm Processor: 118.58/124.62 -> Pairs: 118.58/124.62 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.62 MARK(U32(X:S)) -> MARK(X:S) 118.58/124.62 MARK(U41(X:S)) -> MARK(X:S) 118.58/124.62 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 118.58/124.62 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 118.58/124.62 MARK(s(X:S)) -> MARK(X:S) 118.58/124.62 -> Rules: 118.58/124.62 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.62 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.62 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.62 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.62 U16(active(X:S)) -> U16(X:S) 118.58/124.62 U16(mark(X:S)) -> U16(X:S) 118.58/124.62 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.62 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.62 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.62 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.62 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.62 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.62 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.62 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.62 U23(active(X:S)) -> U23(X:S) 118.58/124.62 U23(mark(X:S)) -> U23(X:S) 118.58/124.62 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.62 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.62 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.62 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.62 U32(active(X:S)) -> U32(X:S) 118.58/124.62 U32(mark(X:S)) -> U32(X:S) 118.58/124.62 U41(active(X:S)) -> U41(X:S) 118.58/124.62 U41(mark(X:S)) -> U41(X:S) 118.58/124.62 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.62 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.62 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.62 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.62 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.62 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.62 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.62 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.62 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.62 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.62 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.62 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.62 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.62 active(U16(tt)) -> mark(tt) 118.58/124.62 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.62 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.62 active(U23(tt)) -> mark(tt) 118.58/124.62 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.62 active(U32(tt)) -> mark(tt) 118.58/124.62 active(U41(tt)) -> mark(tt) 118.58/124.62 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.62 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.62 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.62 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.62 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.62 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.62 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.62 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.62 active(isNat(0)) -> mark(tt) 118.58/124.62 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.62 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.62 active(isNatKind(0)) -> mark(tt) 118.58/124.62 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.62 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.62 isNat(active(X:S)) -> isNat(X:S) 118.58/124.62 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.62 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.62 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.62 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.62 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.62 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.62 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.62 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.62 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.62 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.62 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.62 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.62 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.62 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.62 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.62 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.62 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.62 mark(0) -> active(0) 118.58/124.62 mark(tt) -> active(tt) 118.58/124.62 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 s(active(X:S)) -> s(X:S) 118.58/124.62 s(mark(X:S)) -> s(X:S) 118.58/124.62 ->Projection: 118.58/124.62 pi(MARK) = 1 118.58/124.62 118.58/124.62 Problem 1.23: 118.58/124.62 118.58/124.62 SCC Processor: 118.58/124.62 -> Pairs: 118.58/124.62 Empty 118.58/124.62 -> Rules: 118.58/124.62 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S) 118.58/124.62 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S) 118.58/124.62 U13(active(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(mark(X1:S),X2:S,X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,active(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,mark(X2:S),X3:S) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,X2:S,active(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U13(X1:S,X2:S,mark(X3:S)) -> U13(X1:S,X2:S,X3:S) 118.58/124.62 U14(active(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(mark(X1:S),X2:S,X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,active(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,mark(X2:S),X3:S) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,X2:S,active(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U14(X1:S,X2:S,mark(X3:S)) -> U14(X1:S,X2:S,X3:S) 118.58/124.62 U15(active(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.62 U15(mark(X1:S),X2:S) -> U15(X1:S,X2:S) 118.58/124.62 U15(X1:S,active(X2:S)) -> U15(X1:S,X2:S) 118.58/124.62 U15(X1:S,mark(X2:S)) -> U15(X1:S,X2:S) 118.58/124.62 U16(active(X:S)) -> U16(X:S) 118.58/124.62 U16(mark(X:S)) -> U16(X:S) 118.58/124.62 U21(active(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.62 U21(mark(X1:S),X2:S) -> U21(X1:S,X2:S) 118.58/124.62 U21(X1:S,active(X2:S)) -> U21(X1:S,X2:S) 118.58/124.62 U21(X1:S,mark(X2:S)) -> U21(X1:S,X2:S) 118.58/124.62 U22(active(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.62 U22(mark(X1:S),X2:S) -> U22(X1:S,X2:S) 118.58/124.62 U22(X1:S,active(X2:S)) -> U22(X1:S,X2:S) 118.58/124.62 U22(X1:S,mark(X2:S)) -> U22(X1:S,X2:S) 118.58/124.62 U23(active(X:S)) -> U23(X:S) 118.58/124.62 U23(mark(X:S)) -> U23(X:S) 118.58/124.62 U31(active(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.62 U31(mark(X1:S),X2:S) -> U31(X1:S,X2:S) 118.58/124.62 U31(X1:S,active(X2:S)) -> U31(X1:S,X2:S) 118.58/124.62 U31(X1:S,mark(X2:S)) -> U31(X1:S,X2:S) 118.58/124.62 U32(active(X:S)) -> U32(X:S) 118.58/124.62 U32(mark(X:S)) -> U32(X:S) 118.58/124.62 U41(active(X:S)) -> U41(X:S) 118.58/124.62 U41(mark(X:S)) -> U41(X:S) 118.58/124.62 U51(active(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.62 U51(mark(X1:S),X2:S) -> U51(X1:S,X2:S) 118.58/124.62 U51(X1:S,active(X2:S)) -> U51(X1:S,X2:S) 118.58/124.62 U51(X1:S,mark(X2:S)) -> U51(X1:S,X2:S) 118.58/124.62 U52(active(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.62 U52(mark(X1:S),X2:S) -> U52(X1:S,X2:S) 118.58/124.62 U52(X1:S,active(X2:S)) -> U52(X1:S,X2:S) 118.58/124.62 U52(X1:S,mark(X2:S)) -> U52(X1:S,X2:S) 118.58/124.62 U61(active(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(mark(X1:S),X2:S,X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,active(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,mark(X2:S),X3:S) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,X2:S,active(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U61(X1:S,X2:S,mark(X3:S)) -> U61(X1:S,X2:S,X3:S) 118.58/124.62 U62(active(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(mark(X1:S),X2:S,X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,active(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,mark(X2:S),X3:S) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,X2:S,active(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U62(X1:S,X2:S,mark(X3:S)) -> U62(X1:S,X2:S,X3:S) 118.58/124.62 U63(active(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(mark(X1:S),X2:S,X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,active(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,mark(X2:S),X3:S) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,X2:S,active(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U63(X1:S,X2:S,mark(X3:S)) -> U63(X1:S,X2:S,X3:S) 118.58/124.62 U64(active(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(mark(X1:S),X2:S,X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,active(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,mark(X2:S),X3:S) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,X2:S,active(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 U64(X1:S,X2:S,mark(X3:S)) -> U64(X1:S,X2:S,X3:S) 118.58/124.62 active(U11(tt,V1:S,V2:S)) -> mark(U12(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.62 active(U12(tt,V1:S,V2:S)) -> mark(U13(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.62 active(U13(tt,V1:S,V2:S)) -> mark(U14(isNatKind(V2:S),V1:S,V2:S)) 118.58/124.62 active(U14(tt,V1:S,V2:S)) -> mark(U15(isNat(V1:S),V2:S)) 118.58/124.62 active(U15(tt,V2:S)) -> mark(U16(isNat(V2:S))) 118.58/124.62 active(U16(tt)) -> mark(tt) 118.58/124.62 active(U21(tt,V1:S)) -> mark(U22(isNatKind(V1:S),V1:S)) 118.58/124.62 active(U22(tt,V1:S)) -> mark(U23(isNat(V1:S))) 118.58/124.62 active(U23(tt)) -> mark(tt) 118.58/124.62 active(U31(tt,V2:S)) -> mark(U32(isNatKind(V2:S))) 118.58/124.62 active(U32(tt)) -> mark(tt) 118.58/124.62 active(U41(tt)) -> mark(tt) 118.58/124.62 active(U51(tt,N:S)) -> mark(U52(isNatKind(N:S),N:S)) 118.58/124.62 active(U52(tt,N:S)) -> mark(N:S) 118.58/124.62 active(U61(tt,M:S,N:S)) -> mark(U62(isNatKind(M:S),M:S,N:S)) 118.58/124.62 active(U62(tt,M:S,N:S)) -> mark(U63(isNat(N:S),M:S,N:S)) 118.58/124.62 active(U63(tt,M:S,N:S)) -> mark(U64(isNatKind(N:S),M:S,N:S)) 118.58/124.62 active(U64(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S))) 118.58/124.62 active(isNat(plus(V1:S,V2:S))) -> mark(U11(isNatKind(V1:S),V1:S,V2:S)) 118.58/124.62 active(isNat(s(V1:S))) -> mark(U21(isNatKind(V1:S),V1:S)) 118.58/124.62 active(isNat(0)) -> mark(tt) 118.58/124.62 active(isNatKind(plus(V1:S,V2:S))) -> mark(U31(isNatKind(V1:S),V2:S)) 118.58/124.62 active(isNatKind(s(V1:S))) -> mark(U41(isNatKind(V1:S))) 118.58/124.62 active(isNatKind(0)) -> mark(tt) 118.58/124.62 active(plus(N:S,s(M:S))) -> mark(U61(isNat(M:S),M:S,N:S)) 118.58/124.62 active(plus(N:S,0)) -> mark(U51(isNat(N:S),N:S)) 118.58/124.62 isNat(active(X:S)) -> isNat(X:S) 118.58/124.62 isNat(mark(X:S)) -> isNat(X:S) 118.58/124.62 isNatKind(active(X:S)) -> isNatKind(X:S) 118.58/124.62 isNatKind(mark(X:S)) -> isNatKind(X:S) 118.58/124.62 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U13(X1:S,X2:S,X3:S)) -> active(U13(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U14(X1:S,X2:S,X3:S)) -> active(U14(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U15(X1:S,X2:S)) -> active(U15(mark(X1:S),X2:S)) 118.58/124.62 mark(U16(X:S)) -> active(U16(mark(X:S))) 118.58/124.62 mark(U21(X1:S,X2:S)) -> active(U21(mark(X1:S),X2:S)) 118.58/124.62 mark(U22(X1:S,X2:S)) -> active(U22(mark(X1:S),X2:S)) 118.58/124.62 mark(U23(X:S)) -> active(U23(mark(X:S))) 118.58/124.62 mark(U31(X1:S,X2:S)) -> active(U31(mark(X1:S),X2:S)) 118.58/124.62 mark(U32(X:S)) -> active(U32(mark(X:S))) 118.58/124.62 mark(U41(X:S)) -> active(U41(mark(X:S))) 118.58/124.62 mark(U51(X1:S,X2:S)) -> active(U51(mark(X1:S),X2:S)) 118.58/124.62 mark(U52(X1:S,X2:S)) -> active(U52(mark(X1:S),X2:S)) 118.58/124.62 mark(U61(X1:S,X2:S,X3:S)) -> active(U61(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U62(X1:S,X2:S,X3:S)) -> active(U62(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U63(X1:S,X2:S,X3:S)) -> active(U63(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(U64(X1:S,X2:S,X3:S)) -> active(U64(mark(X1:S),X2:S,X3:S)) 118.58/124.62 mark(isNat(X:S)) -> active(isNat(X:S)) 118.58/124.62 mark(isNatKind(X:S)) -> active(isNatKind(X:S)) 118.58/124.62 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 118.58/124.62 mark(s(X:S)) -> active(s(mark(X:S))) 118.58/124.62 mark(0) -> active(0) 118.58/124.62 mark(tt) -> active(tt) 118.58/124.62 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 118.58/124.62 s(active(X:S)) -> s(X:S) 118.58/124.62 s(mark(X:S)) -> s(X:S) 118.58/124.62 ->Strongly Connected Components: 118.58/124.62 There is no strongly connected component 118.58/124.62 118.58/124.62 The problem is finite. 118.62/124.63 EOF