YES Problem: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Proof: DP Processor: DPs: active#(f(f(X))) -> g#(f(X)) active#(f(f(X))) -> f#(g(f(X))) active#(f(f(X))) -> c#(f(g(f(X)))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) active#(c(X)) -> d#(X) active#(c(X)) -> mark#(d(X)) active#(h(X)) -> d#(X) active#(h(X)) -> c#(d(X)) active#(h(X)) -> mark#(c(d(X))) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(c(X)) -> active#(c(X)) mark#(g(X)) -> active#(g(X)) mark#(d(X)) -> active#(d(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) c#(mark(X)) -> c#(X) c#(active(X)) -> c#(X) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) d#(mark(X)) -> d#(X) d#(active(X)) -> d#(X) h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) TDG Processor: DPs: active#(f(f(X))) -> g#(f(X)) active#(f(f(X))) -> f#(g(f(X))) active#(f(f(X))) -> c#(f(g(f(X)))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) active#(c(X)) -> d#(X) active#(c(X)) -> mark#(d(X)) active#(h(X)) -> d#(X) active#(h(X)) -> c#(d(X)) active#(h(X)) -> mark#(c(d(X))) mark#(f(X)) -> mark#(X) mark#(f(X)) -> f#(mark(X)) mark#(f(X)) -> active#(f(mark(X))) mark#(c(X)) -> active#(c(X)) mark#(g(X)) -> active#(g(X)) mark#(d(X)) -> active#(d(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) c#(mark(X)) -> c#(X) c#(active(X)) -> c#(X) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) d#(mark(X)) -> d#(X) d#(active(X)) -> d#(X) h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) graph: 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) d#(mark(X)) -> d#(X) -> d#(active(X)) -> d#(X) d#(mark(X)) -> d#(X) -> d#(mark(X)) -> d#(X) d#(active(X)) -> d#(X) -> d#(active(X)) -> d#(X) d#(active(X)) -> d#(X) -> d#(mark(X)) -> d#(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)) -> 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#(d(X)) -> active#(d(X)) mark#(h(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X)) mark#(h(X)) -> mark#(X) -> mark#(c(X)) -> active#(c(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)) -> active#(h(mark(X))) -> active#(h(X)) -> mark#(c(d(X))) mark#(h(X)) -> active#(h(mark(X))) -> active#(h(X)) -> c#(d(X)) mark#(h(X)) -> active#(h(mark(X))) -> active#(h(X)) -> d#(X) mark#(h(X)) -> active#(h(mark(X))) -> active#(c(X)) -> mark#(d(X)) mark#(h(X)) -> active#(h(mark(X))) -> active#(c(X)) -> d#(X) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(f(X))) -> c#(f(g(f(X)))) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(f(X))) -> f#(g(f(X))) mark#(h(X)) -> active#(h(mark(X))) -> active#(f(f(X))) -> g#(f(X)) mark#(d(X)) -> active#(d(X)) -> active#(h(X)) -> mark#(c(d(X))) mark#(d(X)) -> active#(d(X)) -> active#(h(X)) -> c#(d(X)) mark#(d(X)) -> active#(d(X)) -> active#(h(X)) -> d#(X) mark#(d(X)) -> active#(d(X)) -> active#(c(X)) -> mark#(d(X)) mark#(d(X)) -> active#(d(X)) -> active#(c(X)) -> d#(X) mark#(d(X)) -> active#(d(X)) -> active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(d(X)) -> active#(d(X)) -> active#(f(f(X))) -> c#(f(g(f(X)))) mark#(d(X)) -> active#(d(X)) -> active#(f(f(X))) -> f#(g(f(X))) mark#(d(X)) -> active#(d(X)) -> active#(f(f(X))) -> g#(f(X)) mark#(c(X)) -> active#(c(X)) -> active#(h(X)) -> mark#(c(d(X))) mark#(c(X)) -> active#(c(X)) -> active#(h(X)) -> c#(d(X)) mark#(c(X)) -> active#(c(X)) -> active#(h(X)) -> d#(X) mark#(c(X)) -> active#(c(X)) -> active#(c(X)) -> mark#(d(X)) mark#(c(X)) -> active#(c(X)) -> active#(c(X)) -> d#(X) mark#(c(X)) -> active#(c(X)) -> active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) -> active#(f(f(X))) -> c#(f(g(f(X)))) mark#(c(X)) -> active#(c(X)) -> active#(f(f(X))) -> f#(g(f(X))) mark#(c(X)) -> active#(c(X)) -> active#(f(f(X))) -> g#(f(X)) mark#(g(X)) -> active#(g(X)) -> active#(h(X)) -> mark#(c(d(X))) mark#(g(X)) -> active#(g(X)) -> active#(h(X)) -> c#(d(X)) mark#(g(X)) -> active#(g(X)) -> active#(h(X)) -> d#(X) mark#(g(X)) -> active#(g(X)) -> active#(c(X)) -> mark#(d(X)) mark#(g(X)) -> active#(g(X)) -> active#(c(X)) -> d#(X) mark#(g(X)) -> active#(g(X)) -> active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(g(X)) -> active#(g(X)) -> active#(f(f(X))) -> c#(f(g(f(X)))) mark#(g(X)) -> active#(g(X)) -> active#(f(f(X))) -> f#(g(f(X))) mark#(g(X)) -> active#(g(X)) -> active#(f(f(X))) -> g#(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#(d(X)) -> active#(d(X)) mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X)) mark#(f(X)) -> mark#(X) -> mark#(c(X)) -> active#(c(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)) -> f#(mark(X)) -> f#(active(X)) -> f#(X) mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X) mark#(f(X)) -> active#(f(mark(X))) -> active#(h(X)) -> mark#(c(d(X))) mark#(f(X)) -> active#(f(mark(X))) -> active#(h(X)) -> c#(d(X)) mark#(f(X)) -> active#(f(mark(X))) -> active#(h(X)) -> d#(X) mark#(f(X)) -> active#(f(mark(X))) -> active#(c(X)) -> mark#(d(X)) mark#(f(X)) -> active#(f(mark(X))) -> active#(c(X)) -> d#(X) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(f(X))) -> c#(f(g(f(X)))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(f(X))) -> f#(g(f(X))) mark#(f(X)) -> active#(f(mark(X))) -> active#(f(f(X))) -> g#(f(X)) c#(mark(X)) -> c#(X) -> c#(active(X)) -> c#(X) c#(mark(X)) -> c#(X) -> c#(mark(X)) -> c#(X) c#(active(X)) -> c#(X) -> c#(active(X)) -> c#(X) c#(active(X)) -> c#(X) -> c#(mark(X)) -> c#(X) 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) 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) active#(h(X)) -> d#(X) -> d#(active(X)) -> d#(X) active#(h(X)) -> d#(X) -> d#(mark(X)) -> d#(X) active#(h(X)) -> mark#(c(d(X))) -> mark#(h(X)) -> active#(h(mark(X))) active#(h(X)) -> mark#(c(d(X))) -> mark#(h(X)) -> h#(mark(X)) active#(h(X)) -> mark#(c(d(X))) -> mark#(h(X)) -> mark#(X) active#(h(X)) -> mark#(c(d(X))) -> mark#(d(X)) -> active#(d(X)) active#(h(X)) -> mark#(c(d(X))) -> mark#(g(X)) -> active#(g(X)) active#(h(X)) -> mark#(c(d(X))) -> mark#(c(X)) -> active#(c(X)) active#(h(X)) -> mark#(c(d(X))) -> mark#(f(X)) -> active#(f(mark(X))) active#(h(X)) -> mark#(c(d(X))) -> mark#(f(X)) -> f#(mark(X)) active#(h(X)) -> mark#(c(d(X))) -> mark#(f(X)) -> mark#(X) active#(h(X)) -> c#(d(X)) -> c#(active(X)) -> c#(X) active#(h(X)) -> c#(d(X)) -> c#(mark(X)) -> c#(X) active#(c(X)) -> d#(X) -> d#(active(X)) -> d#(X) active#(c(X)) -> d#(X) -> d#(mark(X)) -> d#(X) active#(c(X)) -> mark#(d(X)) -> mark#(h(X)) -> active#(h(mark(X))) active#(c(X)) -> mark#(d(X)) -> mark#(h(X)) -> h#(mark(X)) active#(c(X)) -> mark#(d(X)) -> mark#(h(X)) -> mark#(X) active#(c(X)) -> mark#(d(X)) -> mark#(d(X)) -> active#(d(X)) active#(c(X)) -> mark#(d(X)) -> mark#(g(X)) -> active#(g(X)) active#(c(X)) -> mark#(d(X)) -> mark#(c(X)) -> active#(c(X)) active#(c(X)) -> mark#(d(X)) -> mark#(f(X)) -> active#(f(mark(X))) active#(c(X)) -> mark#(d(X)) -> mark#(f(X)) -> f#(mark(X)) active#(c(X)) -> mark#(d(X)) -> mark#(f(X)) -> mark#(X) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(h(X)) -> active#(h(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(h(X)) -> h#(mark(X)) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(h(X)) -> mark#(X) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(d(X)) -> active#(d(X)) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(g(X)) -> active#(g(X)) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(c(X)) -> active#(c(X)) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(f(X)) -> f#(mark(X)) active#(f(f(X))) -> mark#(c(f(g(f(X))))) -> mark#(f(X)) -> mark#(X) active#(f(f(X))) -> c#(f(g(f(X)))) -> c#(active(X)) -> c#(X) active#(f(f(X))) -> c#(f(g(f(X)))) -> c#(mark(X)) -> c#(X) active#(f(f(X))) -> f#(g(f(X))) -> f#(active(X)) -> f#(X) active#(f(f(X))) -> f#(g(f(X))) -> f#(mark(X)) -> f#(X) active#(f(f(X))) -> g#(f(X)) -> g#(active(X)) -> g#(X) active#(f(f(X))) -> g#(f(X)) -> g#(mark(X)) -> g#(X) SCC Processor: #sccs: 6 #rules: 20 #arcs: 126/784 DPs: mark#(h(X)) -> mark#(X) mark#(f(X)) -> mark#(X) mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) active#(c(X)) -> mark#(d(X)) mark#(g(X)) -> active#(g(X)) active#(h(X)) -> mark#(c(d(X))) mark#(d(X)) -> active#(d(X)) mark#(h(X)) -> active#(h(mark(X))) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1, [h](x0) = x0 + 1, [d](x0) = x0, [mark](x0) = x0, [c](x0) = x0, [g](x0) = x0, [active](x0) = x0, [f](x0) = x0 + 1 orientation: mark#(h(X)) = X + 2 >= X + 1 = mark#(X) mark#(f(X)) = X + 2 >= X + 1 = mark#(X) mark#(f(X)) = X + 2 >= X + 2 = active#(f(mark(X))) active#(f(f(X))) = X + 3 >= X + 3 = mark#(c(f(g(f(X))))) mark#(c(X)) = X + 1 >= X + 1 = active#(c(X)) active#(c(X)) = X + 1 >= X + 1 = mark#(d(X)) mark#(g(X)) = X + 1 >= X + 1 = active#(g(X)) active#(h(X)) = X + 2 >= X + 1 = mark#(c(d(X))) mark#(d(X)) = X + 1 >= X + 1 = active#(d(X)) mark#(h(X)) = X + 2 >= X + 2 = active#(h(mark(X))) active(f(f(X))) = X + 2 >= X + 2 = mark(c(f(g(f(X))))) active(c(X)) = X >= X = mark(d(X)) active(h(X)) = X + 1 >= X = mark(c(d(X))) mark(f(X)) = X + 1 >= X + 1 = active(f(mark(X))) mark(c(X)) = X >= X = active(c(X)) mark(g(X)) = X >= X = active(g(X)) mark(d(X)) = X >= X = active(d(X)) mark(h(X)) = X + 1 >= X + 1 = active(h(mark(X))) f(mark(X)) = X + 1 >= X + 1 = f(X) f(active(X)) = X + 1 >= X + 1 = f(X) c(mark(X)) = X >= X = c(X) c(active(X)) = X >= X = c(X) g(mark(X)) = X >= X = g(X) g(active(X)) = X >= X = g(X) d(mark(X)) = X >= X = d(X) d(active(X)) = X >= X = d(X) h(mark(X)) = X + 1 >= X + 1 = h(X) h(active(X)) = X + 1 >= X + 1 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) active#(c(X)) -> mark#(d(X)) mark#(g(X)) -> active#(g(X)) mark#(d(X)) -> active#(d(X)) mark#(h(X)) -> active#(h(mark(X))) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [h](x0) = 1, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 0, [g](x0) = 0, [active](x0) = 0, [f](x0) = 0 orientation: mark#(f(X)) = 0 >= 0 = active#(f(mark(X))) active#(f(f(X))) = 0 >= 0 = mark#(c(f(g(f(X))))) mark#(c(X)) = 0 >= 0 = active#(c(X)) active#(c(X)) = 0 >= 0 = mark#(d(X)) mark#(g(X)) = 0 >= 0 = active#(g(X)) mark#(d(X)) = 0 >= 0 = active#(d(X)) mark#(h(X)) = 1 >= 0 = active#(h(mark(X))) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 0 >= 0 = f(X) f(active(X)) = 0 >= 0 = f(X) c(mark(X)) = 0 >= 0 = c(X) c(active(X)) = 0 >= 0 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 1 >= 1 = h(X) h(active(X)) = 1 >= 1 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) active#(c(X)) -> mark#(d(X)) mark#(g(X)) -> active#(g(X)) mark#(d(X)) -> active#(d(X)) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [h](x0) = 0, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 1, [g](x0) = 1, [active](x0) = 0, [f](x0) = 1 orientation: mark#(f(X)) = 1 >= 1 = active#(f(mark(X))) active#(f(f(X))) = 1 >= 1 = mark#(c(f(g(f(X))))) mark#(c(X)) = 1 >= 1 = active#(c(X)) active#(c(X)) = 1 >= 1 = mark#(d(X)) mark#(g(X)) = 1 >= 1 = active#(g(X)) mark#(d(X)) = 1 >= 0 = active#(d(X)) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 1 >= 1 = g(X) g(active(X)) = 1 >= 1 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 0 >= 0 = h(X) h(active(X)) = 0 >= 0 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) active#(c(X)) -> mark#(d(X)) mark#(g(X)) -> active#(g(X)) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [h](x0) = 0, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 0, [g](x0) = 1, [active](x0) = 0, [f](x0) = 0 orientation: mark#(f(X)) = 0 >= 0 = active#(f(mark(X))) active#(f(f(X))) = 0 >= 0 = mark#(c(f(g(f(X))))) mark#(c(X)) = 0 >= 0 = active#(c(X)) active#(c(X)) = 0 >= 0 = mark#(d(X)) mark#(g(X)) = 1 >= 0 = active#(g(X)) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 0 >= 0 = f(X) f(active(X)) = 0 >= 0 = f(X) c(mark(X)) = 0 >= 0 = c(X) c(active(X)) = 0 >= 0 = c(X) g(mark(X)) = 1 >= 1 = g(X) g(active(X)) = 1 >= 1 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 0 >= 0 = h(X) h(active(X)) = 0 >= 0 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) active#(c(X)) -> mark#(d(X)) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 1, [h](x0) = 0, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 1, [g](x0) = 0, [active](x0) = 0, [f](x0) = 1 orientation: mark#(f(X)) = 1 >= 1 = active#(f(mark(X))) active#(f(f(X))) = 1 >= 1 = mark#(c(f(g(f(X))))) mark#(c(X)) = 1 >= 1 = active#(c(X)) active#(c(X)) = 1 >= 0 = mark#(d(X)) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 0 >= 0 = h(X) h(active(X)) = 0 >= 0 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) mark#(c(X)) -> active#(c(X)) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [h](x0) = 0, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 0, [g](x0) = 0, [active](x0) = 0, [f](x0) = 1 orientation: mark#(f(X)) = 1 >= 1 = active#(f(mark(X))) active#(f(f(X))) = 1 >= 1 = mark#(c(f(g(f(X))))) mark#(c(X)) = 1 >= 0 = active#(c(X)) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 0 >= 0 = c(X) c(active(X)) = 0 >= 0 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 0 >= 0 = h(X) h(active(X)) = 0 >= 0 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) active#(f(f(X))) -> mark#(c(f(g(f(X))))) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 1, [h](x0) = 0, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 0, [g](x0) = 0, [active](x0) = 0, [f](x0) = 1 orientation: mark#(f(X)) = 1 >= 1 = active#(f(mark(X))) active#(f(f(X))) = 1 >= 0 = mark#(c(f(g(f(X))))) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 0 >= 0 = c(X) c(active(X)) = 0 >= 0 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 0 >= 0 = h(X) h(active(X)) = 0 >= 0 = h(X) problem: DPs: mark#(f(X)) -> active#(f(mark(X))) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = 0, [h](x0) = 0, [d](x0) = 0, [mark](x0) = 0, [c](x0) = 0, [g](x0) = 0, [active](x0) = 0, [f](x0) = 0 orientation: mark#(f(X)) = 1 >= 0 = active#(f(mark(X))) active(f(f(X))) = 0 >= 0 = mark(c(f(g(f(X))))) active(c(X)) = 0 >= 0 = mark(d(X)) active(h(X)) = 0 >= 0 = mark(c(d(X))) mark(f(X)) = 0 >= 0 = active(f(mark(X))) mark(c(X)) = 0 >= 0 = active(c(X)) mark(g(X)) = 0 >= 0 = active(g(X)) mark(d(X)) = 0 >= 0 = active(d(X)) mark(h(X)) = 0 >= 0 = active(h(mark(X))) f(mark(X)) = 0 >= 0 = f(X) f(active(X)) = 0 >= 0 = f(X) c(mark(X)) = 0 >= 0 = c(X) c(active(X)) = 0 >= 0 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 0 >= 0 = d(X) d(active(X)) = 0 >= 0 = d(X) h(mark(X)) = 0 >= 0 = h(X) h(active(X)) = 0 >= 0 = h(X) problem: DPs: TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Qed DPs: c#(mark(X)) -> c#(X) c#(active(X)) -> c#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [c#](x0) = x0 + 1, [h](x0) = 1, [d](x0) = 1, [mark](x0) = x0 + 1, [c](x0) = 1, [g](x0) = 0, [active](x0) = x0 + 1, [f](x0) = 1 orientation: c#(mark(X)) = X + 2 >= X + 1 = c#(X) c#(active(X)) = X + 2 >= X + 1 = c#(X) active(f(f(X))) = 2 >= 2 = mark(c(f(g(f(X))))) active(c(X)) = 2 >= 2 = mark(d(X)) active(h(X)) = 2 >= 2 = mark(c(d(X))) mark(f(X)) = 2 >= 2 = active(f(mark(X))) mark(c(X)) = 2 >= 2 = active(c(X)) mark(g(X)) = 1 >= 1 = active(g(X)) mark(d(X)) = 2 >= 2 = active(d(X)) mark(h(X)) = 2 >= 2 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 1 >= 1 = d(X) d(active(X)) = 1 >= 1 = d(X) h(mark(X)) = 1 >= 1 = h(X) h(active(X)) = 1 >= 1 = h(X) problem: DPs: TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Qed DPs: g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [g#](x0) = x0 + 1, [h](x0) = 1, [d](x0) = 1, [mark](x0) = x0 + 1, [c](x0) = 1, [g](x0) = 0, [active](x0) = x0 + 1, [f](x0) = 1 orientation: g#(mark(X)) = X + 2 >= X + 1 = g#(X) g#(active(X)) = X + 2 >= X + 1 = g#(X) active(f(f(X))) = 2 >= 2 = mark(c(f(g(f(X))))) active(c(X)) = 2 >= 2 = mark(d(X)) active(h(X)) = 2 >= 2 = mark(c(d(X))) mark(f(X)) = 2 >= 2 = active(f(mark(X))) mark(c(X)) = 2 >= 2 = active(c(X)) mark(g(X)) = 1 >= 1 = active(g(X)) mark(d(X)) = 2 >= 2 = active(d(X)) mark(h(X)) = 2 >= 2 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 1 >= 1 = d(X) d(active(X)) = 1 >= 1 = d(X) h(mark(X)) = 1 >= 1 = h(X) h(active(X)) = 1 >= 1 = h(X) problem: DPs: TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Qed DPs: f#(mark(X)) -> f#(X) f#(active(X)) -> f#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [f#](x0) = x0 + 1, [h](x0) = 1, [d](x0) = 1, [mark](x0) = x0 + 1, [c](x0) = 1, [g](x0) = 0, [active](x0) = x0 + 1, [f](x0) = 1 orientation: f#(mark(X)) = X + 2 >= X + 1 = f#(X) f#(active(X)) = X + 2 >= X + 1 = f#(X) active(f(f(X))) = 2 >= 2 = mark(c(f(g(f(X))))) active(c(X)) = 2 >= 2 = mark(d(X)) active(h(X)) = 2 >= 2 = mark(c(d(X))) mark(f(X)) = 2 >= 2 = active(f(mark(X))) mark(c(X)) = 2 >= 2 = active(c(X)) mark(g(X)) = 1 >= 1 = active(g(X)) mark(d(X)) = 2 >= 2 = active(d(X)) mark(h(X)) = 2 >= 2 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 1 >= 1 = d(X) d(active(X)) = 1 >= 1 = d(X) h(mark(X)) = 1 >= 1 = h(X) h(active(X)) = 1 >= 1 = h(X) problem: DPs: TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Qed DPs: d#(mark(X)) -> d#(X) d#(active(X)) -> d#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [d#](x0) = x0 + 1, [h](x0) = 1, [d](x0) = 1, [mark](x0) = x0 + 1, [c](x0) = 1, [g](x0) = 0, [active](x0) = x0 + 1, [f](x0) = 1 orientation: d#(mark(X)) = X + 2 >= X + 1 = d#(X) d#(active(X)) = X + 2 >= X + 1 = d#(X) active(f(f(X))) = 2 >= 2 = mark(c(f(g(f(X))))) active(c(X)) = 2 >= 2 = mark(d(X)) active(h(X)) = 2 >= 2 = mark(c(d(X))) mark(f(X)) = 2 >= 2 = active(f(mark(X))) mark(c(X)) = 2 >= 2 = active(c(X)) mark(g(X)) = 1 >= 1 = active(g(X)) mark(d(X)) = 2 >= 2 = active(d(X)) mark(h(X)) = 2 >= 2 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 1 >= 1 = d(X) d(active(X)) = 1 >= 1 = d(X) h(mark(X)) = 1 >= 1 = h(X) h(active(X)) = 1 >= 1 = h(X) problem: DPs: TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Qed DPs: h#(mark(X)) -> h#(X) h#(active(X)) -> h#(X) TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Matrix Interpretation Processor: dimension: 1 interpretation: [h#](x0) = x0 + 1, [h](x0) = 1, [d](x0) = 1, [mark](x0) = x0 + 1, [c](x0) = 1, [g](x0) = 0, [active](x0) = x0 + 1, [f](x0) = 1 orientation: h#(mark(X)) = X + 2 >= X + 1 = h#(X) h#(active(X)) = X + 2 >= X + 1 = h#(X) active(f(f(X))) = 2 >= 2 = mark(c(f(g(f(X))))) active(c(X)) = 2 >= 2 = mark(d(X)) active(h(X)) = 2 >= 2 = mark(c(d(X))) mark(f(X)) = 2 >= 2 = active(f(mark(X))) mark(c(X)) = 2 >= 2 = active(c(X)) mark(g(X)) = 1 >= 1 = active(g(X)) mark(d(X)) = 2 >= 2 = active(d(X)) mark(h(X)) = 2 >= 2 = active(h(mark(X))) f(mark(X)) = 1 >= 1 = f(X) f(active(X)) = 1 >= 1 = f(X) c(mark(X)) = 1 >= 1 = c(X) c(active(X)) = 1 >= 1 = c(X) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) d(mark(X)) = 1 >= 1 = d(X) d(active(X)) = 1 >= 1 = d(X) h(mark(X)) = 1 >= 1 = h(X) h(active(X)) = 1 >= 1 = h(X) problem: DPs: TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) active(c(X)) -> mark(d(X)) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(c(X)) -> active(c(X)) mark(g(X)) -> active(g(X)) mark(d(X)) -> active(d(X)) mark(h(X)) -> active(h(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) c(mark(X)) -> c(X) c(active(X)) -> c(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) d(mark(X)) -> d(X) d(active(X)) -> d(X) h(mark(X)) -> h(X) h(active(X)) -> h(X) Qed