MAYBE Problem: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(f(X,g(X),Y)) -> f#(Y,Y,Y) active#(g(X)) -> active#(X) active#(g(X)) -> g#(active(X)) g#(mark(X)) -> g#(X) proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> proper#(X2) proper#(f(X1,X2,X3)) -> proper#(X1) proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) proper#(g(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) 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(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(f(X,g(X),Y)) -> f#(Y,Y,Y) active#(g(X)) -> active#(X) active#(g(X)) -> g#(active(X)) g#(mark(X)) -> g#(X) proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> proper#(X2) proper#(f(X1,X2,X3)) -> proper#(X1) proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) proper#(g(X)) -> proper#(X) proper#(g(X)) -> g#(proper(X)) f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) 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(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) 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,g(X),Y)) -> f#(Y,Y,Y) 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#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> proper#(X3) -> proper#(g(X)) -> g#(proper(X)) proper#(f(X1,X2,X3)) -> proper#(X3) -> proper#(g(X)) -> proper#(X) proper#(f(X1,X2,X3)) -> proper#(X3) -> proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) proper#(f(X1,X2,X3)) -> proper#(X3) -> proper#(f(X1,X2,X3)) -> proper#(X1) proper#(f(X1,X2,X3)) -> proper#(X3) -> proper#(f(X1,X2,X3)) -> proper#(X2) proper#(f(X1,X2,X3)) -> proper#(X3) -> proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> proper#(X2) -> proper#(g(X)) -> g#(proper(X)) proper#(f(X1,X2,X3)) -> proper#(X2) -> proper#(g(X)) -> proper#(X) proper#(f(X1,X2,X3)) -> proper#(X2) -> proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) proper#(f(X1,X2,X3)) -> proper#(X2) -> proper#(f(X1,X2,X3)) -> proper#(X1) proper#(f(X1,X2,X3)) -> proper#(X2) -> proper#(f(X1,X2,X3)) -> proper#(X2) proper#(f(X1,X2,X3)) -> proper#(X2) -> proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> proper#(X1) -> proper#(g(X)) -> g#(proper(X)) proper#(f(X1,X2,X3)) -> proper#(X1) -> proper#(g(X)) -> proper#(X) proper#(f(X1,X2,X3)) -> proper#(X1) -> proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) proper#(f(X1,X2,X3)) -> proper#(X1) -> proper#(f(X1,X2,X3)) -> proper#(X1) proper#(f(X1,X2,X3)) -> proper#(X1) -> proper#(f(X1,X2,X3)) -> proper#(X2) proper#(f(X1,X2,X3)) -> proper#(X1) -> proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) -> f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) 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#(f(X1,X2,X3)) -> f#(proper(X1),proper(X2),proper(X3)) proper#(g(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X1) proper#(g(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X2) proper#(g(X)) -> proper#(X) -> proper#(f(X1,X2,X3)) -> proper#(X3) proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X) proper#(g(X)) -> g#(proper(X)) -> g#(mark(X)) -> g#(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) f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) -> f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) active#(f(X,g(X),Y)) -> f#(Y,Y,Y) -> f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) 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,g(X),Y)) -> f#(Y,Y,Y) SCC Processor: #sccs: 5 #rules: 10 #arcs: 55/256 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) CDG Processor: DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) 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)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) Open DPs: active#(g(X)) -> active#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(active#) = 0 problem: DPs: TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(f(X1,X2,X3)) -> proper#(X3) proper#(f(X1,X2,X3)) -> proper#(X2) proper#(f(X1,X2,X3)) -> proper#(X1) proper#(g(X)) -> proper#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 problem: DPs: TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: g#(mark(X)) -> g#(X) g#(ok(X)) -> g#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(g#) = 0 problem: DPs: TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: f#(ok(X1),ok(X2),ok(X3)) -> f#(X1,X2,X3) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(f#) = 2 problem: DPs: TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) proper(g(X)) -> g(proper(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed