MAYBE 0.16/0.26 MAYBE 0.16/0.26 0.16/0.26 Problem: 0.16/0.26 active(U11(tt(),V1,V2)) -> mark(U12(isNat(V1),V2)) 0.16/0.26 active(U12(tt(),V2)) -> mark(U13(isNat(V2))) 0.16/0.26 active(U13(tt())) -> mark(tt()) 0.16/0.26 active(U21(tt(),V1)) -> mark(U22(isNat(V1))) 0.16/0.26 active(U22(tt())) -> mark(tt()) 0.16/0.26 active(U31(tt(),N)) -> mark(N) 0.16/0.26 active(U41(tt(),M,N)) -> mark(s(plus(N,M))) 0.16/0.26 active(and(tt(),X)) -> mark(X) 0.16/0.26 active(isNat(0())) -> mark(tt()) 0.16/0.26 active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)) 0.16/0.26 active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) 0.16/0.26 active(isNatKind(0())) -> mark(tt()) 0.16/0.26 active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2))) 0.16/0.26 active(isNatKind(s(V1))) -> mark(isNatKind(V1)) 0.16/0.26 active(plus(N,0())) -> mark(U31(and(isNat(N),isNatKind(N)),N)) 0.16/0.26 active(plus(N,s(M))) -> mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) 0.16/0.26 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) 0.16/0.26 active(U12(X1,X2)) -> U12(active(X1),X2) 0.16/0.26 active(U13(X)) -> U13(active(X)) 0.16/0.26 active(U21(X1,X2)) -> U21(active(X1),X2) 0.16/0.26 active(U22(X)) -> U22(active(X)) 0.16/0.26 active(U31(X1,X2)) -> U31(active(X1),X2) 0.16/0.26 active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) 0.16/0.26 active(s(X)) -> s(active(X)) 0.16/0.26 active(plus(X1,X2)) -> plus(active(X1),X2) 0.16/0.26 active(plus(X1,X2)) -> plus(X1,active(X2)) 0.16/0.26 active(and(X1,X2)) -> and(active(X1),X2) 0.16/0.26 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) 0.16/0.26 U12(mark(X1),X2) -> mark(U12(X1,X2)) 0.16/0.26 U13(mark(X)) -> mark(U13(X)) 0.16/0.26 U21(mark(X1),X2) -> mark(U21(X1,X2)) 0.16/0.26 U22(mark(X)) -> mark(U22(X)) 0.16/0.26 U31(mark(X1),X2) -> mark(U31(X1,X2)) 0.16/0.26 U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) 0.16/0.26 s(mark(X)) -> mark(s(X)) 0.16/0.26 plus(mark(X1),X2) -> mark(plus(X1,X2)) 0.16/0.26 plus(X1,mark(X2)) -> mark(plus(X1,X2)) 0.16/0.26 and(mark(X1),X2) -> mark(and(X1,X2)) 0.16/0.26 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) 0.16/0.26 proper(tt()) -> ok(tt()) 0.16/0.26 proper(U12(X1,X2)) -> U12(proper(X1),proper(X2)) 0.16/0.26 proper(isNat(X)) -> isNat(proper(X)) 0.16/0.26 proper(U13(X)) -> U13(proper(X)) 0.16/0.26 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2)) 0.16/0.26 proper(U22(X)) -> U22(proper(X)) 0.16/0.26 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) 0.16/0.26 proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) 0.16/0.26 proper(s(X)) -> s(proper(X)) 0.16/0.26 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 0.16/0.26 proper(and(X1,X2)) -> and(proper(X1),proper(X2)) 0.16/0.26 proper(0()) -> ok(0()) 0.16/0.26 proper(isNatKind(X)) -> isNatKind(proper(X)) 0.16/0.26 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) 0.16/0.26 U12(ok(X1),ok(X2)) -> ok(U12(X1,X2)) 0.16/0.26 isNat(ok(X)) -> ok(isNat(X)) 0.16/0.26 U13(ok(X)) -> ok(U13(X)) 0.16/0.26 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2)) 0.16/0.26 U22(ok(X)) -> ok(U22(X)) 0.16/0.26 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) 0.16/0.26 U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) 0.16/0.26 s(ok(X)) -> ok(s(X)) 0.16/0.26 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 0.16/0.26 and(ok(X1),ok(X2)) -> ok(and(X1,X2)) 0.16/0.26 isNatKind(ok(X)) -> ok(isNatKind(X)) 0.16/0.26 top(mark(X)) -> top(proper(X)) 0.16/0.26 top(ok(X)) -> top(active(X)) 0.16/0.26 0.16/0.26 Proof: 0.16/0.26 Open 0.16/0.26 EOF