YES Problem: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(f(f(a()))) -> g#(f(a())) active#(f(f(a()))) -> f#(g(f(a()))) active#(f(f(a()))) -> c#(f(g(f(a())))) active#(f(X)) -> active#(X) active#(f(X)) -> f#(active(X)) active#(g(X)) -> active#(X) active#(g(X)) -> g#(active(X)) f#(mark(X)) -> f#(X) g#(mark(X)) -> g#(X) proper#(f(X)) -> proper#(X) proper#(f(X)) -> f#(proper(X)) proper#(c(X)) -> proper#(X) proper#(c(X)) -> c#(proper(X)) proper#(g(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) f#(ok(X)) -> f#(X) c#(ok(X)) -> c#(X) g#(ok(X)) -> g#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(f(f(a()))) -> g#(f(a())) active#(f(f(a()))) -> f#(g(f(a()))) active#(f(f(a()))) -> c#(f(g(f(a())))) active#(f(X)) -> active#(X) active#(f(X)) -> f#(active(X)) active#(g(X)) -> active#(X) active#(g(X)) -> g#(active(X)) f#(mark(X)) -> f#(X) g#(mark(X)) -> g#(X) proper#(f(X)) -> proper#(X) proper#(f(X)) -> f#(proper(X)) proper#(c(X)) -> proper#(X) proper#(c(X)) -> c#(proper(X)) proper#(g(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) f#(ok(X)) -> f#(X) c#(ok(X)) -> c#(X) g#(ok(X)) -> g#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) 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#(g(X)) -> g#(active(X)) top#(ok(X)) -> active#(X) -> active#(g(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(f(X)) -> f#(active(X)) top#(ok(X)) -> active#(X) -> active#(f(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a())))) top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a()))) top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a())) 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#(g(X)) -> g#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(c(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(c(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) proper#(c(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) proper#(c(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) proper#(c(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) proper#(c(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(c(X)) -> c#(proper(X)) -> c#(ok(X)) -> c#(X) proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) proper#(g(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) proper#(g(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X) proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(X) proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) proper#(f(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) proper#(f(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X) proper#(f(X)) -> f#(proper(X)) -> f#(mark(X)) -> f#(X) c#(ok(X)) -> c#(X) -> c#(ok(X)) -> c#(X) f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X) f#(ok(X)) -> f#(X) -> f#(mark(X)) -> f#(X) f#(mark(X)) -> f#(X) -> f#(ok(X)) -> f#(X) f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X) g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X) g#(ok(X)) -> g#(X) -> g#(mark(X)) -> g#(X) g#(mark(X)) -> g#(X) -> g#(ok(X)) -> g#(X) g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X) active#(g(X)) -> g#(active(X)) -> g#(ok(X)) -> g#(X) active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X) active#(g(X)) -> active#(X) -> active#(g(X)) -> g#(active(X)) active#(g(X)) -> active#(X) -> active#(g(X)) -> active#(X) active#(g(X)) -> active#(X) -> active#(f(X)) -> f#(active(X)) active#(g(X)) -> active#(X) -> active#(f(X)) -> active#(X) active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a())))) active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a()))) active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a())) active#(f(f(a()))) -> c#(f(g(f(a())))) -> c#(ok(X)) -> c#(X) active#(f(f(a()))) -> f#(g(f(a()))) -> f#(ok(X)) -> f#(X) active#(f(f(a()))) -> f#(g(f(a()))) -> f#(mark(X)) -> f#(X) active#(f(f(a()))) -> g#(f(a())) -> g#(ok(X)) -> g#(X) active#(f(f(a()))) -> g#(f(a())) -> g#(mark(X)) -> g#(X) active#(f(X)) -> f#(active(X)) -> f#(ok(X)) -> f#(X) active#(f(X)) -> f#(active(X)) -> f#(mark(X)) -> f#(X) active#(f(X)) -> active#(X) -> active#(g(X)) -> g#(active(X)) active#(f(X)) -> active#(X) -> active#(g(X)) -> active#(X) active#(f(X)) -> active#(X) -> active#(f(X)) -> f#(active(X)) active#(f(X)) -> active#(X) -> active#(f(X)) -> active#(X) active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a())))) active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a()))) active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a())) EDG Processor: DPs: active#(f(f(a()))) -> g#(f(a())) active#(f(f(a()))) -> f#(g(f(a()))) active#(f(f(a()))) -> c#(f(g(f(a())))) active#(f(X)) -> active#(X) active#(f(X)) -> f#(active(X)) active#(g(X)) -> active#(X) active#(g(X)) -> g#(active(X)) f#(mark(X)) -> f#(X) g#(mark(X)) -> g#(X) proper#(f(X)) -> proper#(X) proper#(f(X)) -> f#(proper(X)) proper#(c(X)) -> proper#(X) proper#(c(X)) -> c#(proper(X)) proper#(g(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) f#(ok(X)) -> f#(X) c#(ok(X)) -> c#(X) g#(ok(X)) -> g#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a())) top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a()))) top#(ok(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a())))) top#(ok(X)) -> active#(X) -> active#(f(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(f(X)) -> f#(active(X)) top#(ok(X)) -> active#(X) -> active#(g(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(g(X)) -> g#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(c(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(c(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) proper#(c(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) proper#(c(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) proper#(c(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) proper#(c(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(c(X)) -> c#(proper(X)) -> c#(ok(X)) -> c#(X) proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) proper#(g(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) proper#(g(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(X) proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X) proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X) proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X)) proper#(f(X)) -> proper#(X) -> proper#(c(X)) -> proper#(X) proper#(f(X)) -> proper#(X) -> proper#(c(X)) -> c#(proper(X)) proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X) proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X)) proper#(f(X)) -> f#(proper(X)) -> f#(mark(X)) -> f#(X) proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X) c#(ok(X)) -> c#(X) -> c#(ok(X)) -> c#(X) f#(ok(X)) -> f#(X) -> f#(mark(X)) -> f#(X) f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X) f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X) f#(mark(X)) -> f#(X) -> f#(ok(X)) -> f#(X) g#(ok(X)) -> g#(X) -> g#(mark(X)) -> g#(X) g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X) g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X) g#(mark(X)) -> g#(X) -> g#(ok(X)) -> g#(X) active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X) active#(g(X)) -> g#(active(X)) -> g#(ok(X)) -> g#(X) active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a())) active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a()))) active#(g(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a())))) active#(g(X)) -> active#(X) -> active#(f(X)) -> active#(X) active#(g(X)) -> active#(X) -> active#(f(X)) -> f#(active(X)) active#(g(X)) -> active#(X) -> active#(g(X)) -> active#(X) active#(g(X)) -> active#(X) -> active#(g(X)) -> g#(active(X)) active#(f(X)) -> f#(active(X)) -> f#(mark(X)) -> f#(X) active#(f(X)) -> f#(active(X)) -> f#(ok(X)) -> f#(X) active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> g#(f(a())) active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> f#(g(f(a()))) active#(f(X)) -> active#(X) -> active#(f(f(a()))) -> c#(f(g(f(a())))) active#(f(X)) -> active#(X) -> active#(f(X)) -> active#(X) active#(f(X)) -> active#(X) -> active#(f(X)) -> f#(active(X)) active#(f(X)) -> active#(X) -> active#(g(X)) -> active#(X) active#(f(X)) -> active#(X) -> active#(g(X)) -> g#(active(X)) CDG Processor: DPs: active#(f(f(a()))) -> g#(f(a())) active#(f(f(a()))) -> f#(g(f(a()))) active#(f(f(a()))) -> c#(f(g(f(a())))) active#(f(X)) -> active#(X) active#(f(X)) -> f#(active(X)) active#(g(X)) -> active#(X) active#(g(X)) -> g#(active(X)) f#(mark(X)) -> f#(X) g#(mark(X)) -> g#(X) proper#(f(X)) -> proper#(X) proper#(f(X)) -> f#(proper(X)) proper#(c(X)) -> proper#(X) proper#(c(X)) -> c#(proper(X)) proper#(g(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) f#(ok(X)) -> f#(X) c#(ok(X)) -> c#(X) g#(ok(X)) -> g#(X) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) 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#(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) proper#(c(X)) -> c#(proper(X)) -> c#(ok(X)) -> c#(X) proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X) proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X) active#(g(X)) -> g#(active(X)) -> g#(mark(X)) -> g#(X) active#(f(X)) -> f#(active(X)) -> f#(mark(X)) -> f#(X) SCC Processor: #sccs: 1 #rules: 2 #arcs: 13/484 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [top#](x0) = [1 0 0]x0, [1] [top](x0) = [0] [1], [0 0 1] [1] [ok](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [proper](x0) = x0 , [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0 0 0] [1] [c](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [1 0 0] [g](x0) = [1 0 1]x0 [0 0 1] , [0 0 1] [active](x0) = [0 1 1]x0 [0 0 1] , [1 0 0] [1] [f](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1] [a] = [0] [0] orientation: top#(ok(X)) = [0 0 1]X + [1] >= [0 0 1]X = top#(active(X)) top#(mark(X)) = [1 0 0]X + [1] >= [1 0 0]X = top#(proper(X)) [2] [2] active(f(f(a()))) = [2] >= [0] = mark(c(f(g(f(a()))))) [2] [0] [0 0 1] [1] [0 0 1] [1] active(f(X)) = [0 0 1]X + [1] >= [0 0 0]X + [0] = f(active(X)) [0 0 1] [1] [0 0 1] [1] [0 0 1] [0 0 1] active(g(X)) = [1 0 2]X >= [0 0 2]X = g(active(X)) [0 0 1] [0 0 1] [1 0 0] [2] [1 0 0] [2] f(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(f(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] g(mark(X)) = [1 0 0]X + [1] >= [0 0 0]X + [0] = mark(g(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] proper(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(proper(X)) [0 0 1] [1] [0 0 1] [1] [1] [1] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [0 0 0] [1] [0 0 0] [1] proper(c(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = c(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] proper(g(X)) = [1 0 1]X >= [1 0 1]X = g(proper(X)) [0 0 1] [0 0 1] [0 0 1] [2] [0 0 1] [2] f(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(f(X)) [0 0 0] [1] [0 0 0] [0] [1] [1] c(ok(X)) = [0] >= [0] = ok(c(X)) [0] [0] [0 0 1] [1] [0 0 1] [1] g(ok(X)) = [0 0 1]X + [1] >= [0 0 0]X + [0] = ok(g(X)) [0 0 0] [0] [0 0 0] [0] [1] [1] top(mark(X)) = [0] >= [0] = top(proper(X)) [1] [1] [1] [1] top(ok(X)) = [0] >= [0] = top(active(X)) [1] [1] problem: DPs: TRS: active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed