YES Problem: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Proof: DP Processor: DPs: active#(f(X)) -> h#(f(X)) active#(f(X)) -> g#(h(f(X))) active#(f(X)) -> mark#(g(h(f(X)))) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(g(X)) -> active#(g(X)) mark#(h(X)) -> mark#(X) mark#(h(X)) -> h#(mark(X)) mark#(h(X)) -> active#(h(mark(X))) f#(mark(X)) -> f#(X) f#(active(X)) -> f#(X) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) TRS: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) TDG Processor: DPs: active#(f(X)) -> h#(f(X)) active#(f(X)) -> g#(h(f(X))) active#(f(X)) -> mark#(g(h(f(X)))) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(g(X)) -> active#(g(X)) mark#(h(X)) -> mark#(X) mark#(h(X)) -> h#(mark(X)) mark#(h(X)) -> active#(h(mark(X))) f#(mark(X)) -> f#(X) f#(active(X)) -> f#(X) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) TRS: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) graph: f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X) f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X) f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X) f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X) mark#(g(X)) -> active#(g(X)) -> active#(f(X)) -> mark#(g(h(f(X)))) mark#(g(X)) -> active#(g(X)) -> active#(f(X)) -> g#(h(f(X))) mark#(g(X)) -> active#(g(X)) -> active#(f(X)) -> h#(f(X)) mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> active#(h(mark(X))) mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> h#(mark(X)) mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> mark#(X) mark#(h(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X)) mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X))) mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X)) mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X) mark#(h(X)) -> h#(mark(X)) -> h#(active(X)) -> h#(X) mark#(h(X)) -> h#(mark(X)) -> h#(mark(X)) -> h#(X) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(X)) -> mark#(g(h(f(X)))) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(X)) -> g#(h(f(X))) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(X)) -> h#(f(X)) mark#(f(X)) -> f#(mark(X)) -> f#(active(X)) -> f#(X) mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X) mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> active#(h(mark(X))) mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> h#(mark(X)) mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> mark#(X) mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X)) mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X))) mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> mark#(g(h(f(X)))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> g#(h(f(X))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> h#(f(X)) g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X) g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X) g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X) h#(mark(X)) -> h#(X) -> h#(active(X)) -> h#(X) h#(mark(X)) -> h#(X) -> h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) -> h#(active(X)) -> h#(X) h#(active(X)) -> h#(X) -> h#(mark(X)) -> h#(X) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(h(X)) -> active#(h(mark(X))) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(h(X)) -> h#(mark(X)) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(h(X)) -> mark#(X) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(g(X)) -> active#(g(X)) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(f(X)) -> active#(f(mark(X))) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(f(X)) -> f#(mark(X)) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(f(X)) -> mark#(X) active#(f(X)) -> g#(h(f(X))) -> g#(active(X)) -> g#(X) active#(f(X)) -> g#(h(f(X))) -> g#(mark(X)) -> g#(X) active#(f(X)) -> h#(f(X)) -> h#(active(X)) -> h#(X) active#(f(X)) -> h#(f(X)) -> h#(mark(X)) -> h#(X) CDG Processor: DPs: active#(f(X)) -> h#(f(X)) active#(f(X)) -> g#(h(f(X))) active#(f(X)) -> mark#(g(h(f(X)))) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(g(X)) -> active#(g(X)) mark#(h(X)) -> mark#(X) mark#(h(X)) -> h#(mark(X)) mark#(h(X)) -> active#(h(mark(X))) f#(mark(X)) -> f#(X) f#(active(X)) -> f#(X) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) TRS: active(f(X)) -> mark(g(h(f(X)))) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) graph: mark#(h(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X)) mark#(h(X)) -> h#(mark(X)) -> h#(mark(X)) -> h#(X) mark#(h(X)) -> h#(mark(X)) -> h#(active(X)) -> h#(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)) -> mark#(X) -> mark#(g(X)) -> active#(g(X)) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> h#(f(X)) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> g#(h(f(X))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> mark#(g(h(f(X)))) active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(g(X)) -> active#(g(X)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 10/256