YES TRS: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} DP: Strict: { c#(ok(X)) -> c#(X), f#(mark(X)) -> f#(X), f#(ok(X)) -> f#(X), g#(ok(X)) -> g#(X), active#(c(X)) -> d#(X), active#(f(X)) -> f#(active(X)), active#(f(X)) -> active#(X), active#(f(f(X))) -> c#(f(g(f(X)))), active#(f(f(X))) -> f#(g(f(X))), active#(f(f(X))) -> g#(f(X)), active#(h(X)) -> c#(d(X)), active#(h(X)) -> active#(X), active#(h(X)) -> d#(X), active#(h(X)) -> h#(active(X)), d#(ok(X)) -> d#(X), h#(mark(X)) -> h#(X), h#(ok(X)) -> h#(X), proper#(c(X)) -> c#(proper(X)), proper#(c(X)) -> proper#(X), proper#(f(X)) -> f#(proper(X)), proper#(f(X)) -> proper#(X), proper#(g(X)) -> g#(proper(X)), proper#(g(X)) -> proper#(X), proper#(d(X)) -> d#(proper(X)), proper#(d(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X)), proper#(h(X)) -> proper#(X), top#(mark(X)) -> proper#(X), top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> active#(X), top#(ok(X)) -> top#(active(X))} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: {(active#(f(f(X))) -> f#(g(f(X))), f#(ok(X)) -> f#(X)) (active#(f(f(X))) -> f#(g(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)) (active#(f(X)) -> active#(X), active#(h(X)) -> h#(active(X))) (active#(f(X)) -> active#(X), active#(h(X)) -> d#(X)) (active#(f(X)) -> active#(X), active#(h(X)) -> active#(X)) (active#(f(X)) -> active#(X), active#(h(X)) -> c#(d(X))) (active#(f(X)) -> active#(X), active#(f(f(X))) -> g#(f(X))) (active#(f(X)) -> active#(X), active#(f(f(X))) -> f#(g(f(X)))) (active#(f(X)) -> active#(X), active#(f(f(X))) -> c#(f(g(f(X))))) (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#(c(X)) -> d#(X)) (active#(h(X)) -> d#(X), d#(ok(X)) -> d#(X)) (h#(mark(X)) -> h#(X), h#(ok(X)) -> h#(X)) (h#(mark(X)) -> h#(X), h#(mark(X)) -> h#(X)) (proper#(c(X)) -> proper#(X), proper#(h(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X))) (proper#(c(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(d(X)) -> d#(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)) -> 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#(g(X)) -> proper#(X), proper#(h(X)) -> proper#(X)) (proper#(g(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X))) (proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(g(X)) -> proper#(X), proper#(d(X)) -> d#(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)) -> 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#(h(X)) -> proper#(X), proper#(h(X)) -> proper#(X)) (proper#(h(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X))) (proper#(h(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(h(X)) -> proper#(X), proper#(d(X)) -> d#(proper(X))) (proper#(h(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(h(X)) -> proper#(X), proper#(g(X)) -> g#(proper(X))) (proper#(h(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(h(X)) -> proper#(X), proper#(f(X)) -> f#(proper(X))) (proper#(h(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(h(X)) -> proper#(X), proper#(c(X)) -> c#(proper(X))) (top#(ok(X)) -> active#(X), active#(h(X)) -> h#(active(X))) (top#(ok(X)) -> active#(X), active#(h(X)) -> d#(X)) (top#(ok(X)) -> active#(X), active#(h(X)) -> active#(X)) (top#(ok(X)) -> active#(X), active#(h(X)) -> c#(d(X))) (top#(ok(X)) -> active#(X), active#(f(f(X))) -> g#(f(X))) (top#(ok(X)) -> active#(X), active#(f(f(X))) -> f#(g(f(X)))) (top#(ok(X)) -> active#(X), active#(f(f(X))) -> c#(f(g(f(X))))) (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#(c(X)) -> d#(X)) (active#(f(f(X))) -> g#(f(X)), g#(ok(X)) -> g#(X)) (active#(h(X)) -> h#(active(X)), h#(ok(X)) -> h#(X)) (active#(h(X)) -> h#(active(X)), h#(mark(X)) -> h#(X)) (proper#(f(X)) -> f#(proper(X)), f#(ok(X)) -> f#(X)) (proper#(f(X)) -> f#(proper(X)), f#(mark(X)) -> f#(X)) (proper#(d(X)) -> d#(proper(X)), d#(ok(X)) -> d#(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)) (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))) (proper#(h(X)) -> h#(proper(X)), h#(mark(X)) -> h#(X)) (proper#(h(X)) -> h#(proper(X)), h#(ok(X)) -> h#(X)) (proper#(g(X)) -> g#(proper(X)), g#(ok(X)) -> g#(X)) (proper#(c(X)) -> c#(proper(X)), c#(ok(X)) -> c#(X)) (active#(h(X)) -> c#(d(X)), c#(ok(X)) -> c#(X)) (active#(f(X)) -> f#(active(X)), f#(mark(X)) -> f#(X)) (active#(f(X)) -> f#(active(X)), f#(ok(X)) -> f#(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)) (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#(d(X)) -> d#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (top#(mark(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(h(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(c(X)) -> c#(proper(X))) (proper#(d(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(f(X)) -> f#(proper(X))) (proper#(d(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(g(X)) -> g#(proper(X))) (proper#(d(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(d(X)) -> d#(proper(X))) (proper#(d(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X))) (proper#(d(X)) -> proper#(X), proper#(h(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)) -> proper#(X), proper#(g(X)) -> g#(proper(X))) (proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(d(X)) -> d#(proper(X))) (proper#(f(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(h(X)) -> h#(proper(X))) (proper#(f(X)) -> proper#(X), proper#(h(X)) -> proper#(X)) (h#(ok(X)) -> h#(X), h#(mark(X)) -> h#(X)) (h#(ok(X)) -> h#(X), h#(ok(X)) -> h#(X)) (d#(ok(X)) -> d#(X), d#(ok(X)) -> d#(X)) (active#(h(X)) -> active#(X), active#(c(X)) -> d#(X)) (active#(h(X)) -> active#(X), active#(f(X)) -> f#(active(X))) (active#(h(X)) -> active#(X), active#(f(X)) -> active#(X)) (active#(h(X)) -> active#(X), active#(f(f(X))) -> c#(f(g(f(X))))) (active#(h(X)) -> active#(X), active#(f(f(X))) -> f#(g(f(X)))) (active#(h(X)) -> active#(X), active#(f(f(X))) -> g#(f(X))) (active#(h(X)) -> active#(X), active#(h(X)) -> c#(d(X))) (active#(h(X)) -> active#(X), active#(h(X)) -> active#(X)) (active#(h(X)) -> active#(X), active#(h(X)) -> d#(X)) (active#(h(X)) -> active#(X), active#(h(X)) -> h#(active(X))) (active#(c(X)) -> d#(X), d#(ok(X)) -> d#(X)) (f#(ok(X)) -> f#(X), f#(mark(X)) -> f#(X)) (f#(ok(X)) -> f#(X), f#(ok(X)) -> f#(X)) (c#(ok(X)) -> c#(X), c#(ok(X)) -> c#(X)) (active#(f(f(X))) -> c#(f(g(f(X)))), c#(ok(X)) -> c#(X))} SCCS: Scc: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Scc: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X), proper#(h(X)) -> proper#(X)} Scc: {h#(mark(X)) -> h#(X), h#(ok(X)) -> h#(X)} Scc: {d#(ok(X)) -> d#(X)} Scc: {active#(f(X)) -> active#(X), active#(h(X)) -> active#(X)} Scc: {g#(ok(X)) -> g#(X)} Scc: {f#(mark(X)) -> f#(X), f#(ok(X)) -> f#(X)} Scc: {c#(ok(X)) -> c#(X)} SCC: Strict: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} POLY: Argument Filtering: pi(top#) = 0, pi(top) = [], pi(ok) = [0], pi(proper) = [], pi(h) = 0, pi(d) = 0, pi(active) = 0, pi(g) = 0, pi(f) = 0, pi(c) = 0, pi(mark) = 0 Usable Rules: {} Interpretation: [ok](x0) = x0 + 1, [proper] = 0 Strict: {top#(mark(X)) -> top#(proper(X))} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: {(top#(mark(X)) -> top#(proper(X)), top#(mark(X)) -> top#(proper(X)))} SCCS: Scc: {top#(mark(X)) -> top#(proper(X))} SCC: Strict: {top#(mark(X)) -> top#(proper(X))} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} POLY: Argument Filtering: pi(top#) = 0, pi(top) = [], pi(ok) = [], pi(proper) = [], pi(h) = 0, pi(d) = [], pi(active) = [], pi(g) = [], pi(f) = 0, pi(c) = [], pi(mark) = [] Usable Rules: {} Interpretation: [proper] = 0, [mark] = 1 Strict: {} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} Qed SCC: Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X), proper#(h(X)) -> proper#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X)} EDG: {(proper#(f(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(g(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(g(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(g(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(g(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(d(X)) -> proper#(X))} SCCS: Scc: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X)} SCC: Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(g(X)) -> proper#(X), proper#(d(X)) -> proper#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(d(X)) -> proper#(X)} EDG: {(proper#(f(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(d(X)) -> proper#(X), proper#(d(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(d(X)) -> proper#(X))} SCCS: Scc: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(d(X)) -> proper#(X)} SCC: Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X), proper#(d(X)) -> proper#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X)} EDG: {(proper#(f(X)) -> proper#(X), proper#(f(X)) -> proper#(X)) (proper#(f(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(c(X)) -> proper#(X)) (proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X))} SCCS: Scc: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X)} SCC: Strict: {proper#(c(X)) -> proper#(X), proper#(f(X)) -> proper#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(f(X)) -> proper#(X)} EDG: {(proper#(f(X)) -> proper#(X), proper#(f(X)) -> proper#(X))} SCCS: Scc: {proper#(f(X)) -> proper#(X)} SCC: Strict: {proper#(f(X)) -> proper#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {} Qed SCC: Strict: {h#(mark(X)) -> h#(X), h#(ok(X)) -> h#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(h#) = 0 Strict: {h#(ok(X)) -> h#(X)} EDG: {(h#(ok(X)) -> h#(X), h#(ok(X)) -> h#(X))} SCCS: Scc: {h#(ok(X)) -> h#(X)} SCC: Strict: {h#(ok(X)) -> h#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(h#) = 0 Strict: {} Qed SCC: Strict: {d#(ok(X)) -> d#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(d#) = 0 Strict: {} Qed SCC: Strict: {active#(f(X)) -> active#(X), active#(h(X)) -> active#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(h(X)) -> active#(X)} EDG: {(active#(h(X)) -> active#(X), active#(h(X)) -> active#(X))} SCCS: Scc: {active#(h(X)) -> active#(X)} SCC: Strict: {active#(h(X)) -> active#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {} Qed SCC: Strict: {g#(ok(X)) -> g#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(g#) = 0 Strict: {} Qed SCC: Strict: {f#(mark(X)) -> f#(X), f#(ok(X)) -> f#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(f#) = 0 Strict: {f#(ok(X)) -> f#(X)} EDG: {(f#(ok(X)) -> f#(X), f#(ok(X)) -> f#(X))} SCCS: Scc: {f#(ok(X)) -> f#(X)} SCC: Strict: {f#(ok(X)) -> f#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(f#) = 0 Strict: {} Qed SCC: Strict: {c#(ok(X)) -> c#(X)} Weak: { c(ok(X)) -> ok(c(X)), f(mark(X)) -> mark(f(X)), f(ok(X)) -> ok(f(X)), g(ok(X)) -> ok(g(X)), active(c(X)) -> mark(d(X)), active(f(X)) -> f(active(X)), active(f(f(X))) -> mark(c(f(g(f(X))))), active(h(X)) -> mark(c(d(X))), active(h(X)) -> h(active(X)), d(ok(X)) -> ok(d(X)), h(mark(X)) -> mark(h(X)), h(ok(X)) -> ok(h(X)), proper(c(X)) -> c(proper(X)), proper(f(X)) -> f(proper(X)), proper(g(X)) -> g(proper(X)), proper(d(X)) -> d(proper(X)), proper(h(X)) -> h(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(c#) = 0 Strict: {} Qed