MAYBE Problem: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(U12(tt(),M,N)) -> plus#(N,M) active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(U22(tt(),M,N)) -> x#(N,M) active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(x(N,s(M))) -> U21#(tt(),M,N) active#(U11(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(plus(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(plus(X1,X2)) -> active#(X2) active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> x#(active(X1),X2) active#(x(X1,X2)) -> active#(X2) active#(x(X1,X2)) -> x#(X1,active(X2)) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) s#(mark(X)) -> s#(X) plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(plus(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) s#(ok(X)) -> s#(X) plus#(ok(X1),ok(X2)) -> plus#(X1,X2) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) x#(ok(X1),ok(X2)) -> x#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(U12(tt(),M,N)) -> plus#(N,M) active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(U22(tt(),M,N)) -> x#(N,M) active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(x(N,s(M))) -> U21#(tt(),M,N) active#(U11(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(plus(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(plus(X1,X2)) -> active#(X2) active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> x#(active(X1),X2) active#(x(X1,X2)) -> active#(X2) active#(x(X1,X2)) -> x#(X1,active(X2)) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) s#(mark(X)) -> s#(X) plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(plus(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) s#(ok(X)) -> s#(X) plus#(ok(X1),ok(X2)) -> plus#(X1,X2) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) x#(ok(X1),ok(X2)) -> x#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> active#(X) -> active#(x(X1,X2)) -> x#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(x(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(x(X1,X2)) -> x#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(x(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) top#(ok(X)) -> active#(X) -> active#(U22(X1,X2,X3)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) top#(ok(X)) -> active#(X) -> active#(U21(X1,X2,X3)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) top#(ok(X)) -> active#(X) -> active#(U12(X1,X2,X3)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) top#(ok(X)) -> active#(X) -> active#(U11(X1,X2,X3)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(x(N,s(M))) -> U21#(tt(),M,N) top#(ok(X)) -> active#(X) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) top#(ok(X)) -> active#(X) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) top#(ok(X)) -> active#(X) -> active#(U22(tt(),M,N)) -> x#(N,M) top#(ok(X)) -> active#(X) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) top#(ok(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) top#(ok(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> plus#(N,M) top#(ok(X)) -> active#(X) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(x(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(x(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) top#(mark(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> proper#(X3) top#(mark(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) top#(mark(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> proper#(X3) top#(mark(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) top#(mark(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> proper#(X3) top#(mark(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) top#(mark(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X2) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X2) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X1) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X1) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) -> x#(X1,mark(X2)) -> x#(X1,X2) proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) -> x#(mark(X1),X2) -> x#(X1,X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> s#(proper(X)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> proper#(X) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) -> U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) -> U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> s#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> proper#(X) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) -> U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) proper#(s(X)) -> proper#(X) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(x(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(x(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(s(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(s(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(s(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(s(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(s(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(s(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(s(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X) proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) -> plus#(X1,mark(X2)) -> plus#(X1,X2) proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) -> plus#(mark(X1),X2) -> plus#(X1,X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> s#(proper(X)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> proper#(X) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) -> U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> s#(proper(X)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(s(X)) -> proper#(X) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X3) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X2) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> x#(proper(X1),proper(X2)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(x(X1,X2)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(plus(X1,X2)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) -> proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) -> U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3)) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) -> U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) -> U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) x#(ok(X1),ok(X2)) -> x#(X1,X2) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) x#(ok(X1),ok(X2)) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(ok(X1),ok(X2)) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) -> U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) -> U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) -> U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) -> U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) plus#(ok(X1),ok(X2)) -> plus#(X1,X2) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) plus#(ok(X1),ok(X2)) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(ok(X1),ok(X2)) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) -> U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) active#(x(X1,X2)) -> x#(active(X1),X2) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) active#(x(X1,X2)) -> x#(active(X1),X2) -> x#(X1,mark(X2)) -> x#(X1,X2) active#(x(X1,X2)) -> x#(active(X1),X2) -> x#(mark(X1),X2) -> x#(X1,X2) active#(x(X1,X2)) -> x#(X1,active(X2)) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) active#(x(X1,X2)) -> x#(X1,active(X2)) -> x#(X1,mark(X2)) -> x#(X1,X2) active#(x(X1,X2)) -> x#(X1,active(X2)) -> x#(mark(X1),X2) -> x#(X1,X2) active#(x(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(x(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> active#(X2) active#(x(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(x(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X2) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X2) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(x(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> active#(X2) active#(x(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(x(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(x(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(x(X1,X2)) -> active#(X2) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X2) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X2) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(x(X1,X2)) -> active#(X2) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(x(X1,X2)) -> active#(X2) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(x(X1,X2)) -> active#(X2) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(x(X1,X2)) -> active#(X2) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(x(X1,X2)) -> active#(X2) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(x(X1,X2)) -> active#(X2) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(x(X1,X2)) -> active#(X2) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(x(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(x(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X2) active#(x(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(x(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(x(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X2) active#(x(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(x(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(x(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(x(X1,X2)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(x(X1,X2)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(x(X1,X2)) -> active#(X1) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(x(X1,X2)) -> active#(X1) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(x(X1,X2)) -> active#(X1) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(x(X1,X2)) -> active#(X1) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(x(X1,X2)) -> active#(X1) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(x(X1,X2)) -> active#(X1) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(x(X1,X2)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(x(N,s(M))) -> U21#(tt(),M,N) -> U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) active#(x(N,s(M))) -> U21#(tt(),M,N) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) active#(U22(tt(),M,N)) -> x#(N,M) -> x#(ok(X1),ok(X2)) -> x#(X1,X2) active#(U22(tt(),M,N)) -> x#(N,M) -> x#(X1,mark(X2)) -> x#(X1,X2) active#(U22(tt(),M,N)) -> x#(N,M) -> x#(mark(X1),X2) -> x#(X1,X2) active#(U22(tt(),M,N)) -> plus#(x(N,M),N) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) active#(U22(tt(),M,N)) -> plus#(x(N,M),N) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(U22(tt(),M,N)) -> plus#(x(N,M),N) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) -> U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) -> U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X2) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X2) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(U22(X1,X2,X3)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(U21(tt(),M,N)) -> U22#(tt(),M,N) -> U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) active#(U21(tt(),M,N)) -> U22#(tt(),M,N) -> U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) -> U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X2) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X1) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X2) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X1) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(U21(X1,X2,X3)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X) active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X) active#(s(X)) -> active#(X) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(x(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(x(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(s(X)) -> active#(X) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(s(X)) -> active#(X) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(plus(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(s(X)) -> active#(X) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(s(X)) -> active#(X) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(s(X)) -> active#(X) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(s(X)) -> active#(X) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(s(X)) -> active#(X) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(s(X)) -> active#(X) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(s(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(s(X)) -> active#(X) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(s(X)) -> active#(X) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(plus(X1,X2)) -> plus#(active(X1),X2) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) active#(plus(X1,X2)) -> plus#(active(X1),X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(plus(X1,X2)) -> plus#(active(X1),X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(plus(X1,X2)) -> plus#(X1,active(X2)) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) active#(plus(X1,X2)) -> plus#(X1,active(X2)) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(plus(X1,X2)) -> plus#(X1,active(X2)) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(plus(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(plus(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> active#(X2) active#(plus(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(plus(X1,X2)) -> active#(X2) -> active#(x(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X2) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X2) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(plus(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> active#(X2) active#(plus(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(plus(X1,X2)) -> active#(X2) -> active#(plus(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(plus(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(plus(X1,X2)) -> active#(X2) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X2) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X2) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(plus(X1,X2)) -> active#(X2) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(plus(X1,X2)) -> active#(X2) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(plus(X1,X2)) -> active#(X2) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(plus(X1,X2)) -> active#(X2) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(plus(X1,X2)) -> active#(X2) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(plus(X1,X2)) -> active#(X2) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(plus(X1,X2)) -> active#(X2) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(plus(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(plus(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X2) active#(plus(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(plus(X1,X2)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(plus(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X2) active#(plus(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(plus(X1,X2)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(plus(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(plus(X1,X2)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(plus(X1,X2)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(plus(X1,X2)) -> active#(X1) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(plus(X1,X2)) -> active#(X1) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(plus(X1,X2)) -> active#(X1) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(plus(X1,X2)) -> active#(X1) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(plus(X1,X2)) -> active#(X1) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(plus(X1,X2)) -> active#(X1) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(plus(X1,X2)) -> active#(X1) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(plus(X1,X2)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(plus(N,s(M))) -> U11#(tt(),M,N) -> U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) active#(plus(N,s(M))) -> U11#(tt(),M,N) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) active#(U12(tt(),M,N)) -> s#(plus(N,M)) -> s#(ok(X)) -> s#(X) active#(U12(tt(),M,N)) -> s#(plus(N,M)) -> s#(mark(X)) -> s#(X) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(ok(X1),ok(X2)) -> plus#(X1,X2) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) -> U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X2) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X2) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(U12(X1,X2,X3)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) -> U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(X1,active(X2)) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X2) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> x#(active(X1),X2) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(x(X1,X2)) -> active#(X1) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U22(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U21(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(X1,active(X2)) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X2) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> plus#(active(X1),X2) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(plus(X1,X2)) -> active#(X1) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U12(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U11(X1,X2,X3)) -> active#(X1) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(x(N,s(M))) -> U21#(tt(),M,N) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(plus(N,s(M))) -> U11#(tt(),M,N) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> plus#(x(N,M),N) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U22(tt(),M,N)) -> x#(N,M) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U21(tt(),M,N)) -> U22#(tt(),M,N) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U12(tt(),M,N)) -> plus#(N,M) active#(U11(X1,X2,X3)) -> active#(X1) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) SCC Processor: #sccs: 10 #rules: 44 #arcs: 795/4900 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(U11(X1,X2,X3)) -> active#(X1) active#(U12(X1,X2,X3)) -> active#(X1) active#(s(X)) -> active#(X) active#(plus(X1,X2)) -> active#(X1) active#(plus(X1,X2)) -> active#(X2) active#(U21(X1,X2,X3)) -> active#(X1) active#(U22(X1,X2,X3)) -> active#(X1) active#(x(X1,X2)) -> active#(X1) active#(x(X1,X2)) -> active#(X2) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(active#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(U11(X1,X2,X3)) -> proper#(X3) proper#(U11(X1,X2,X3)) -> proper#(X2) proper#(U11(X1,X2,X3)) -> proper#(X1) proper#(U12(X1,X2,X3)) -> proper#(X3) proper#(U12(X1,X2,X3)) -> proper#(X2) proper#(U12(X1,X2,X3)) -> proper#(X1) proper#(s(X)) -> proper#(X) proper#(plus(X1,X2)) -> proper#(X2) proper#(plus(X1,X2)) -> proper#(X1) proper#(U21(X1,X2,X3)) -> proper#(X3) proper#(U21(X1,X2,X3)) -> proper#(X2) proper#(U21(X1,X2,X3)) -> proper#(X1) proper#(U22(X1,X2,X3)) -> proper#(X3) proper#(U22(X1,X2,X3)) -> proper#(X2) proper#(U22(X1,X2,X3)) -> proper#(X1) proper#(x(X1,X2)) -> proper#(X2) proper#(x(X1,X2)) -> proper#(X1) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) x#(ok(X1),ok(X2)) -> x#(X1,X2) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(x#) = 1 problem: DPs: x#(mark(X1),X2) -> x#(X1,X2) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(x#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U22#) = 2 problem: DPs: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U22#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U21#) = 2 problem: DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U21#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(ok(X1),ok(X2)) -> plus#(X1,X2) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(plus#) = 1 problem: DPs: plus#(mark(X1),X2) -> plus#(X1,X2) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(plus#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: s#(mark(X)) -> s#(X) s#(ok(X)) -> s#(X) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U12#) = 2 problem: DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U12#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U11#) = 2 problem: DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(U11#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(U21(tt(),M,N)) -> mark(U22(tt(),M,N)) active(U22(tt(),M,N)) -> mark(plus(x(N,M),N)) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(U21(tt(),M,N)) active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3) active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3) active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3) active(x(X1,X2)) -> x(active(X1),X2) active(x(X1,X2)) -> x(X1,active(X2)) U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3)) U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3)) U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3)) x(mark(X1),X2) -> mark(x(X1,X2)) x(X1,mark(X2)) -> mark(x(X1,X2)) proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3)) proper(tt()) -> ok(tt()) proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3)) proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3)) proper(x(X1,X2)) -> x(proper(X1),proper(X2)) proper(0()) -> ok(0()) U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3)) U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3)) U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3)) x(ok(X1),ok(X2)) -> ok(x(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed