MAYBE 0.18/0.23 MAYBE 0.18/0.23 0.18/0.23 Problem: 0.18/0.23 active(U11(tt(),V2)) -> mark(U12(isNat(V2))) 0.18/0.23 active(U12(tt())) -> mark(tt()) 0.18/0.23 active(U21(tt())) -> mark(tt()) 0.18/0.23 active(U31(tt(),N)) -> mark(N) 0.18/0.23 active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) 0.18/0.23 active(U42(tt(),M,N)) -> mark(s(plus(N,M))) 0.18/0.23 active(isNat(0())) -> mark(tt()) 0.18/0.23 active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) 0.18/0.23 active(isNat(s(V1))) -> mark(U21(isNat(V1))) 0.18/0.23 active(plus(N,0())) -> mark(U31(isNat(N),N)) 0.18/0.23 active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) 0.18/0.23 active(U11(X1,X2)) -> U11(active(X1),X2) 0.18/0.23 active(U12(X)) -> U12(active(X)) 0.18/0.23 active(U21(X)) -> U21(active(X)) 0.18/0.23 active(U31(X1,X2)) -> U31(active(X1),X2) 0.18/0.23 active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) 0.18/0.23 active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) 0.18/0.23 active(s(X)) -> s(active(X)) 0.18/0.23 active(plus(X1,X2)) -> plus(active(X1),X2) 0.18/0.23 active(plus(X1,X2)) -> plus(X1,active(X2)) 0.18/0.23 U11(mark(X1),X2) -> mark(U11(X1,X2)) 0.18/0.23 U12(mark(X)) -> mark(U12(X)) 0.18/0.23 U21(mark(X)) -> mark(U21(X)) 0.18/0.23 U31(mark(X1),X2) -> mark(U31(X1,X2)) 0.18/0.23 U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) 0.18/0.23 U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) 0.18/0.23 s(mark(X)) -> mark(s(X)) 0.18/0.23 plus(mark(X1),X2) -> mark(plus(X1,X2)) 0.18/0.23 plus(X1,mark(X2)) -> mark(plus(X1,X2)) 0.18/0.23 proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) 0.18/0.23 proper(tt()) -> ok(tt()) 0.18/0.23 proper(U12(X)) -> U12(proper(X)) 0.18/0.23 proper(isNat(X)) -> isNat(proper(X)) 0.18/0.23 proper(U21(X)) -> U21(proper(X)) 0.18/0.23 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) 0.18/0.23 proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) 0.18/0.23 proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) 0.18/0.23 proper(s(X)) -> s(proper(X)) 0.18/0.23 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) 0.18/0.23 proper(0()) -> ok(0()) 0.18/0.23 U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) 0.18/0.23 U12(ok(X)) -> ok(U12(X)) 0.18/0.23 isNat(ok(X)) -> ok(isNat(X)) 0.18/0.23 U21(ok(X)) -> ok(U21(X)) 0.18/0.23 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) 0.18/0.23 U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) 0.18/0.23 U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) 0.18/0.23 s(ok(X)) -> ok(s(X)) 0.18/0.23 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) 0.18/0.23 top(mark(X)) -> top(proper(X)) 0.18/0.23 top(ok(X)) -> top(active(X)) 0.18/0.23 0.18/0.23 Proof: 0.18/0.23 Open 0.18/0.23 EOF