MAYBE 0.18/0.29 MAYBE 0.18/0.29 0.18/0.29 Problem: 0.18/0.29 active(zeros()) -> mark(cons(0(),zeros())) 0.18/0.29 active(U11(tt())) -> mark(tt()) 0.18/0.29 active(U21(tt())) -> mark(tt()) 0.18/0.29 active(U31(tt())) -> mark(tt()) 0.18/0.29 active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) 0.18/0.29 active(U42(tt())) -> mark(tt()) 0.18/0.29 active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) 0.18/0.29 active(U52(tt())) -> mark(tt()) 0.18/0.29 active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) 0.18/0.29 active(U62(tt())) -> mark(tt()) 0.18/0.29 active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) 0.18/0.29 active(U72(tt(),L)) -> mark(s(length(L))) 0.18/0.29 active(U81(tt())) -> mark(nil()) 0.18/0.29 active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) 0.18/0.29 active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) 0.18/0.29 active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) 0.18/0.29 active(isNat(0())) -> mark(tt()) 0.18/0.29 active(isNat(length(V1))) -> mark(U11(isNatList(V1))) 0.18/0.29 active(isNat(s(V1))) -> mark(U21(isNat(V1))) 0.18/0.29 active(isNatIList(V)) -> mark(U31(isNatList(V))) 0.18/0.29 active(isNatIList(zeros())) -> mark(tt()) 0.18/0.29 active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) 0.18/0.29 active(isNatList(nil())) -> mark(tt()) 0.18/0.29 active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) 0.18/0.29 active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) 0.18/0.29 active(length(nil())) -> mark(0()) 0.18/0.29 active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) 0.18/0.29 active(take(0(),IL)) -> mark(U81(isNatIList(IL))) 0.18/0.29 active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) 0.18/0.29 active(cons(X1,X2)) -> cons(active(X1),X2) 0.18/0.29 active(U11(X)) -> U11(active(X)) 0.18/0.29 active(U21(X)) -> U21(active(X)) 0.18/0.29 active(U31(X)) -> U31(active(X)) 0.18/0.29 active(U41(X1,X2)) -> U41(active(X1),X2) 0.18/0.29 active(U42(X)) -> U42(active(X)) 0.18/0.29 active(U51(X1,X2)) -> U51(active(X1),X2) 0.18/0.29 active(U52(X)) -> U52(active(X)) 0.18/0.29 active(U61(X1,X2)) -> U61(active(X1),X2) 0.18/0.29 active(U62(X)) -> U62(active(X)) 0.18/0.29 active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3) 0.18/0.29 active(U72(X1,X2)) -> U72(active(X1),X2) 0.18/0.29 active(s(X)) -> s(active(X)) 0.18/0.29 active(length(X)) -> length(active(X)) 0.18/0.29 active(U81(X)) -> U81(active(X)) 0.18/0.29 active(U91(X1,X2,X3,X4)) -> U91(active(X1),X2,X3,X4) 0.18/0.29 active(U92(X1,X2,X3,X4)) -> U92(active(X1),X2,X3,X4) 0.18/0.29 active(U93(X1,X2,X3,X4)) -> U93(active(X1),X2,X3,X4) 0.18/0.29 active(take(X1,X2)) -> take(active(X1),X2) 0.18/0.29 active(take(X1,X2)) -> take(X1,active(X2)) 0.18/0.29 cons(mark(X1),X2) -> mark(cons(X1,X2)) 0.18/0.29 U11(mark(X)) -> mark(U11(X)) 0.18/0.29 U21(mark(X)) -> mark(U21(X)) 0.18/0.29 U31(mark(X)) -> mark(U31(X)) 0.18/0.29 U41(mark(X1),X2) -> mark(U41(X1,X2)) 0.18/0.29 U42(mark(X)) -> mark(U42(X)) 0.18/0.29 U51(mark(X1),X2) -> mark(U51(X1,X2)) 0.18/0.29 U52(mark(X)) -> mark(U52(X)) 0.18/0.29 U61(mark(X1),X2) -> mark(U61(X1,X2)) 0.18/0.29 U62(mark(X)) -> mark(U62(X)) 0.18/0.29 U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3)) 0.18/0.29 U72(mark(X1),X2) -> mark(U72(X1,X2)) 0.18/0.29 s(mark(X)) -> mark(s(X)) 0.18/0.29 length(mark(X)) -> mark(length(X)) 0.18/0.29 U81(mark(X)) -> mark(U81(X)) 0.18/0.29 U91(mark(X1),X2,X3,X4) -> mark(U91(X1,X2,X3,X4)) 0.18/0.29 U92(mark(X1),X2,X3,X4) -> mark(U92(X1,X2,X3,X4)) 0.18/0.29 U93(mark(X1),X2,X3,X4) -> mark(U93(X1,X2,X3,X4)) 0.18/0.29 take(mark(X1),X2) -> mark(take(X1,X2)) 0.18/0.29 take(X1,mark(X2)) -> mark(take(X1,X2)) 0.18/0.29 proper(zeros()) -> ok(zeros()) 0.18/0.29 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 0.18/0.29 proper(0()) -> ok(0()) 0.18/0.29 proper(U11(X)) -> U11(proper(X)) 0.18/0.29 proper(tt()) -> ok(tt()) 0.18/0.29 proper(U21(X)) -> U21(proper(X)) 0.18/0.29 proper(U31(X)) -> U31(proper(X)) 0.18/0.29 proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) 0.18/0.29 proper(U42(X)) -> U42(proper(X)) 0.18/0.29 proper(isNatIList(X)) -> isNatIList(proper(X)) 0.18/0.29 proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) 0.18/0.29 proper(U52(X)) -> U52(proper(X)) 0.18/0.29 proper(isNatList(X)) -> isNatList(proper(X)) 0.18/0.29 proper(U61(X1,X2)) -> U61(proper(X1),proper(X2)) 0.18/0.29 proper(U62(X)) -> U62(proper(X)) 0.18/0.29 proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3)) 0.18/0.29 proper(U72(X1,X2)) -> U72(proper(X1),proper(X2)) 0.18/0.29 proper(isNat(X)) -> isNat(proper(X)) 0.18/0.29 proper(s(X)) -> s(proper(X)) 0.18/0.29 proper(length(X)) -> length(proper(X)) 0.18/0.29 proper(U81(X)) -> U81(proper(X)) 0.18/0.29 proper(nil()) -> ok(nil()) 0.18/0.29 proper(U91(X1,X2,X3,X4)) -> U91(proper(X1),proper(X2),proper(X3),proper(X4)) 0.18/0.29 proper(U92(X1,X2,X3,X4)) -> U92(proper(X1),proper(X2),proper(X3),proper(X4)) 0.18/0.29 proper(U93(X1,X2,X3,X4)) -> U93(proper(X1),proper(X2),proper(X3),proper(X4)) 0.18/0.29 proper(take(X1,X2)) -> take(proper(X1),proper(X2)) 0.18/0.29 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 0.18/0.29 U11(ok(X)) -> ok(U11(X)) 0.18/0.29 U21(ok(X)) -> ok(U21(X)) 0.18/0.29 U31(ok(X)) -> ok(U31(X)) 0.18/0.29 U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) 0.18/0.29 U42(ok(X)) -> ok(U42(X)) 0.18/0.29 isNatIList(ok(X)) -> ok(isNatIList(X)) 0.18/0.29 U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) 0.18/0.29 U52(ok(X)) -> ok(U52(X)) 0.18/0.29 isNatList(ok(X)) -> ok(isNatList(X)) 0.18/0.29 U61(ok(X1),ok(X2)) -> ok(U61(X1,X2)) 0.18/0.29 U62(ok(X)) -> ok(U62(X)) 0.18/0.29 U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3)) 0.18/0.29 U72(ok(X1),ok(X2)) -> ok(U72(X1,X2)) 0.18/0.29 isNat(ok(X)) -> ok(isNat(X)) 0.18/0.29 s(ok(X)) -> ok(s(X)) 0.18/0.29 length(ok(X)) -> ok(length(X)) 0.18/0.29 U81(ok(X)) -> ok(U81(X)) 0.18/0.29 U91(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U91(X1,X2,X3,X4)) 0.18/0.29 U92(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U92(X1,X2,X3,X4)) 0.18/0.29 U93(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U93(X1,X2,X3,X4)) 0.18/0.29 take(ok(X1),ok(X2)) -> ok(take(X1,X2)) 0.18/0.29 top(mark(X)) -> top(proper(X)) 0.18/0.29 top(ok(X)) -> top(active(X)) 0.18/0.29 0.18/0.29 Proof: 0.18/0.29 Open 0.28/0.30 EOF