YES Problem: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Proof: DP Processor: DPs: active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> 2nd#(mark(X)) mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 2nd#(mark(X)) -> 2nd#(X) 2nd#(active(X)) -> 2nd#(X) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) TDG Processor: DPs: active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> 2nd#(mark(X)) mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 2nd#(mark(X)) -> 2nd#(X) 2nd#(active(X)) -> 2nd#(X) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) graph: 2nd#(mark(X)) -> 2nd#(X) -> 2nd#(active(X)) -> 2nd#(X) 2nd#(mark(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X) 2nd#(active(X)) -> 2nd#(X) -> 2nd#(active(X)) -> 2nd#(X) 2nd#(active(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) from#(mark(X)) -> from#(X) -> from#(active(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) -> from#(active(X)) -> from#(X) from#(active(X)) -> from#(X) -> from#(mark(X)) -> from#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(active(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> from#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> 2nd#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> from#(s(X)) mark#(s(X)) -> active#(s(mark(X))) -> active#(from(X)) -> s#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(from(X)) -> from#(mark(X)) -> from#(active(X)) -> from#(X) mark#(from(X)) -> from#(mark(X)) -> from#(mark(X)) -> from#(X) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> from#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> 2nd#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> from#(s(X)) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> s#(X) mark#(from(X)) -> active#(from(mark(X))) -> active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(2nd(X)) -> 2nd#(mark(X)) -> 2nd#(active(X)) -> 2nd#(X) mark#(2nd(X)) -> 2nd#(mark(X)) -> 2nd#(mark(X)) -> 2nd#(X) mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> from#(mark(X)) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> 2nd#(mark(X)) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> active#(2nd(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(2nd(X)) -> active#(2nd(mark(X))) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(2nd(X)) -> active#(2nd(mark(X))) -> active#(from(X)) -> from#(s(X)) mark#(2nd(X)) -> active#(2nd(mark(X))) -> active#(from(X)) -> s#(X) mark#(2nd(X)) -> active#(2nd(mark(X))) -> active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(active(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> 2nd#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> mark#(X) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> cons#(X,from(s(X))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> from#(s(X)) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(from(X)) -> s#(X) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(from(X)) -> from#(s(X)) -> from#(active(X)) -> from#(X) active#(from(X)) -> from#(s(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> s#(X) -> s#(active(X)) -> s#(X) active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> s#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(s(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> from#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(from(X)) -> mark#(X) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(2nd(X)) -> active#(2nd(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(2nd(X)) -> 2nd#(mark(X)) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(2nd(X)) -> mark#(X) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(s(X)) -> active#(s(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(s(X)) -> s#(mark(X)) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(s(X)) -> mark#(X) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(from(X)) -> active#(from(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(from(X)) -> from#(mark(X)) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(from(X)) -> mark#(X) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(cons(X1,X2)) -> mark#(X1) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(2nd(X)) -> active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(2nd(X)) -> 2nd#(mark(X)) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(2nd(X)) -> mark#(X) SCC Processor: #sccs: 5 #rules: 20 #arcs: 138/729 DPs: mark#(s(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> active#(s(mark(X))) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) CDG Processor: DPs: mark#(s(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(from(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> active#(s(mark(X))) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) graph: mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(from(X)) -> active#(from(mark(X))) -> active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> active#(from(mark(X))) mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(2nd(X)) -> active#(2nd(mark(X))) -> active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(2nd(X)) -> active#(2nd(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> active#(from(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(from(X)) -> mark#(cons(X,from(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(2nd(X)) -> mark#(X) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(2nd(X)) -> active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(cons(X1,X2)) -> mark#(X1) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(from(X)) -> mark#(X) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(from(X)) -> active#(from(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(s(X)) -> mark#(X) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) -> mark#(s(X)) -> active#(s(mark(X))) SCC Processor: #sccs: 1 #rules: 8 #arcs: 44/100 DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) mark#(2nd(X)) -> active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(2nd(X)) -> mark#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [s](x0) = x0, [from](x0) = 2x0, [mark](x0) = x0, [active](x0) = x0, [2nd](x0) = x0 + 7, [cons](x0, x1) = x0 + x1 orientation: mark#(s(X)) = X >= X = mark#(X) mark#(from(X)) = 2X >= 2X = active#(from(mark(X))) active#(from(X)) = 2X >= 2X = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(from(X)) = 2X >= X = mark#(X) mark#(2nd(X)) = X + 7 >= X + 7 = active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) = X + Y + Z + 7 >= Y = mark#(Y) mark#(2nd(X)) = X + 7 >= X = mark#(X) active(2nd(cons(X,cons(Y,Z)))) = X + Y + Z + 7 >= Y = mark(Y) active(from(X)) = 2X >= 2X = mark(cons(X,from(s(X)))) mark(2nd(X)) = X + 7 >= X + 7 = active(2nd(mark(X))) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(from(X)) = 2X >= 2X = active(from(mark(X))) mark(s(X)) = X >= X = active(s(mark(X))) 2nd(mark(X)) = X + 7 >= X + 7 = 2nd(X) 2nd(active(X)) = X + 7 >= X + 7 = 2nd(X) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) from(mark(X)) = 2X >= 2X = from(X) from(active(X)) = 2X >= 2X = from(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) problem: DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) -> mark#(Y) mark#(2nd(X)) -> mark#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [s](x0) = x0 + 0, [from](x0) = x0 + 0, [mark](x0) = x0, [active](x0) = x0 + 0, [2nd](x0) = 4x0 + 0, [cons](x0, x1) = x0 + x1 + 0 orientation: mark#(s(X)) = X + 0 >= X = mark#(X) mark#(from(X)) = X + 0 >= X + 0 = active#(from(mark(X))) active#(from(X)) = X + 0 >= X + 0 = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(2nd(X)) = 4X + 0 >= 4X + 0 = active#(2nd(mark(X))) active#(2nd(cons(X,cons(Y,Z)))) = 4X + 4Y + 4Z + 4 >= Y = mark#(Y) mark#(2nd(X)) = 4X + 0 >= X = mark#(X) active(2nd(cons(X,cons(Y,Z)))) = 4X + 4Y + 4Z + 4 >= Y = mark(Y) active(from(X)) = X + 0 >= X + 0 = mark(cons(X,from(s(X)))) mark(2nd(X)) = 4X + 0 >= 4X + 0 = active(2nd(mark(X))) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(cons(mark(X1),X2)) mark(from(X)) = X + 0 >= X + 0 = active(from(mark(X))) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) 2nd(mark(X)) = 4X + 0 >= 4X + 0 = 2nd(X) 2nd(active(X)) = 4X + 4 >= 4X + 0 = 2nd(X) cons(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(X1,X2) from(mark(X)) = X + 0 >= X + 0 = from(X) from(active(X)) = X + 0 >= X + 0 = from(X) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) problem: DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) mark#(2nd(X)) -> active#(2nd(mark(X))) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) SCC Processor: #sccs: 1 #rules: 4 #arcs: 33/25 DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) -> mark#(X1) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [s](x0) = x0, [from](x0) = 1x0, [mark](x0) = x0, [active](x0) = x0, [2nd](x0) = x0 + 1, [cons](x0, x1) = 1x0 + x1 orientation: mark#(s(X)) = X >= X = mark#(X) mark#(from(X)) = 1X >= 1X = active#(from(mark(X))) active#(from(X)) = 1X >= 1X = mark#(cons(X,from(s(X)))) mark#(cons(X1,X2)) = 1X1 + X2 >= X1 = mark#(X1) active(2nd(cons(X,cons(Y,Z)))) = 1X + 1Y + Z + 1 >= Y = mark(Y) active(from(X)) = 1X >= 1X = mark(cons(X,from(s(X)))) mark(2nd(X)) = X + 1 >= X + 1 = active(2nd(mark(X))) mark(cons(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = active(cons(mark(X1),X2)) mark(from(X)) = 1X >= 1X = active(from(mark(X))) mark(s(X)) = X >= X = active(s(mark(X))) 2nd(mark(X)) = X + 1 >= X + 1 = 2nd(X) 2nd(active(X)) = X + 1 >= X + 1 = 2nd(X) cons(mark(X1),X2) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) cons(active(X1),X2) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = 1X1 + X2 >= 1X1 + X2 = cons(X1,X2) from(mark(X)) = 1X >= 1X = from(X) from(active(X)) = 1X >= 1X = from(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) problem: DPs: mark#(s(X)) -> mark#(X) mark#(from(X)) -> active#(from(mark(X))) active#(from(X)) -> mark#(cons(X,from(s(X)))) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) SCC Processor: #sccs: 1 #rules: 1 #arcs: 8/9 DPs: mark#(s(X)) -> mark#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Qed DPs: from#(mark(X)) -> from#(X) from#(active(X)) -> from#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Qed DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Qed DPs: 2nd#(mark(X)) -> 2nd#(X) 2nd#(active(X)) -> 2nd#(X) TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Subterm Criterion Processor: simple projection: pi(2nd#) = 0 problem: DPs: TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Qed