MAYBE Problem: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Proof: DP Processor: DPs: active#(f(0())) -> s#(0()) active#(f(0())) -> f#(s(0())) active#(f(0())) -> cons#(0(),f(s(0()))) active#(f(0())) -> mark#(cons(0(),f(s(0())))) active#(f(s(0()))) -> p#(s(0())) active#(f(s(0()))) -> f#(p(s(0()))) active#(f(s(0()))) -> mark#(f(p(s(0())))) active#(p(s(0()))) -> mark#(0()) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(p(X)) -> mark#(X) mark#(p(X)) -> p#(mark(X)) mark#(p(X)) -> active#(p(mark(X))) f#(mark(X)) -> f#(X) f#(active(X)) -> f#(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) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) p#(mark(X)) -> p#(X) p#(active(X)) -> p#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) ADG Processor: DPs: active#(f(0())) -> s#(0()) active#(f(0())) -> f#(s(0())) active#(f(0())) -> cons#(0(),f(s(0()))) active#(f(0())) -> mark#(cons(0(),f(s(0())))) active#(f(s(0()))) -> p#(s(0())) active#(f(s(0()))) -> f#(p(s(0()))) active#(f(s(0()))) -> mark#(f(p(s(0())))) active#(p(s(0()))) -> mark#(0()) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(p(X)) -> mark#(X) mark#(p(X)) -> p#(mark(X)) mark#(p(X)) -> active#(p(mark(X))) f#(mark(X)) -> f#(X) f#(active(X)) -> f#(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) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) p#(mark(X)) -> p#(X) p#(active(X)) -> p#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) graph: p#(mark(X)) -> p#(X) -> p#(mark(X)) -> p#(X) p#(mark(X)) -> p#(X) -> p#(active(X)) -> p#(X) p#(active(X)) -> p#(X) -> p#(mark(X)) -> p#(X) p#(active(X)) -> p#(X) -> p#(active(X)) -> p#(X) mark#(p(X)) -> p#(mark(X)) -> p#(mark(X)) -> p#(X) mark#(p(X)) -> p#(mark(X)) -> p#(active(X)) -> p#(X) mark#(p(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X) mark#(p(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X)) mark#(p(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X))) mark#(p(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(p(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(p(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(p(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(p(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(p(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(p(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(p(X)) -> mark#(X) -> mark#(p(X)) -> mark#(X) mark#(p(X)) -> mark#(X) -> mark#(p(X)) -> p#(mark(X)) mark#(p(X)) -> mark#(X) -> mark#(p(X)) -> active#(p(mark(X))) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(0())) -> s#(0()) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(0())) -> f#(s(0())) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(0())) -> cons#(0(),f(s(0()))) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(0())) -> mark#(cons(0(),f(s(0())))) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(s(0()))) -> p#(s(0())) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(s(0()))) -> f#(p(s(0()))) mark#(p(X)) -> active#(p(mark(X))) -> active#(f(s(0()))) -> mark#(f(p(s(0())))) mark#(p(X)) -> active#(p(mark(X))) -> active#(p(s(0()))) -> mark#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> f#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> active#(f(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(p(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(p(X)) -> p#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(p(X)) -> active#(p(mark(X))) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(0())) -> s#(0()) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(0())) -> f#(s(0())) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(0())) -> cons#(0(),f(s(0()))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(0())) -> mark#(cons(0(),f(s(0())))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(s(0()))) -> p#(s(0())) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(s(0()))) -> f#(p(s(0()))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(f(s(0()))) -> mark#(f(p(s(0())))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) -> active#(p(s(0()))) -> mark#(0()) mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(p(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(p(X)) -> p#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(p(X)) -> active#(p(mark(X))) mark#(s(X)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(active(X)) -> s#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(0())) -> s#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(0())) -> f#(s(0())) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(0())) -> cons#(0(),f(s(0()))) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(0())) -> mark#(cons(0(),f(s(0())))) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(s(0()))) -> p#(s(0())) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(s(0()))) -> f#(p(s(0()))) mark#(s(X)) -> active#(s(mark(X))) -> active#(f(s(0()))) -> mark#(f(p(s(0())))) mark#(s(X)) -> active#(s(mark(X))) -> active#(p(s(0()))) -> mark#(0()) mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X) mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X))) mark#(f(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(f(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(f(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(f(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(f(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(f(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(f(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(f(X)) -> mark#(X) -> mark#(p(X)) -> mark#(X) mark#(f(X)) -> mark#(X) -> mark#(p(X)) -> p#(mark(X)) mark#(f(X)) -> mark#(X) -> mark#(p(X)) -> active#(p(mark(X))) mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X) mark#(f(X)) -> f#(mark(X)) -> f#(active(X)) -> f#(X) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(0())) -> s#(0()) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(0())) -> f#(s(0())) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(0())) -> cons#(0(),f(s(0()))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(0())) -> mark#(cons(0(),f(s(0())))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(s(0()))) -> p#(s(0())) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(s(0()))) -> f#(p(s(0()))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(s(0()))) -> mark#(f(p(s(0())))) mark#(f(X)) -> active#(f(mark(X))) -> active#(p(s(0()))) -> mark#(0()) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(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#(active(X1),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#(mark(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#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(mark(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#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X) f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X) f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X) f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) active#(p(s(0()))) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(f(s(0()))) -> mark#(f(p(s(0())))) -> mark#(f(X)) -> mark#(X) active#(f(s(0()))) -> mark#(f(p(s(0())))) -> mark#(f(X)) -> f#(mark(X)) active#(f(s(0()))) -> mark#(f(p(s(0())))) -> mark#(f(X)) -> active#(f(mark(X))) active#(f(0())) -> mark#(cons(0(),f(s(0())))) -> mark#(cons(X1,X2)) -> mark#(X1) active#(f(0())) -> mark#(cons(0(),f(s(0())))) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) active#(f(0())) -> mark#(cons(0(),f(s(0())))) -> mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) Restore Modifier: DPs: active#(f(0())) -> s#(0()) active#(f(0())) -> f#(s(0())) active#(f(0())) -> cons#(0(),f(s(0()))) active#(f(0())) -> mark#(cons(0(),f(s(0())))) active#(f(s(0()))) -> p#(s(0())) active#(f(s(0()))) -> f#(p(s(0()))) active#(f(s(0()))) -> mark#(f(p(s(0())))) active#(p(s(0()))) -> mark#(0()) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(0()) -> active#(0()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(p(X)) -> mark#(X) mark#(p(X)) -> p#(mark(X)) mark#(p(X)) -> active#(p(mark(X))) f#(mark(X)) -> f#(X) f#(active(X)) -> f#(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) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) p#(mark(X)) -> p#(X) p#(active(X)) -> p#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) SCC Processor: #sccs: 5 #rules: 20 #arcs: 129/961 DPs: mark#(p(X)) -> mark#(X) mark#(p(X)) -> active#(p(mark(X))) active#(f(s(0()))) -> mark#(f(p(s(0())))) mark#(f(X)) -> active#(f(mark(X))) active#(f(0())) -> mark#(cons(0(),f(s(0())))) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) mark#(f(X)) -> mark#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Open DPs: f#(active(X)) -> f#(X) f#(mark(X)) -> f#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Open DPs: s#(active(X)) -> s#(X) s#(mark(X)) -> s#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Open DPs: cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Open DPs: p#(mark(X)) -> p#(X) p#(active(X)) -> p#(X) TRS: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Open