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)) 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)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [c] = 0, [b] = 1, [mark](x0) = 0, [active](x0) = x0, [f](x0, x1, x2) = 0, [g](x0) = x0 + 1 orientation: active#(g(X)) = X + 2 >= X + 1 = active#(X) active(f(X,g(X),Y)) = 0 >= 0 = mark(f(Y,Y,Y)) active(g(b())) = 2 >= 0 = mark(c()) active(b()) = 1 >= 0 = mark(c()) active(g(X)) = X + 1 >= X + 1 = g(active(X)) g(mark(X)) = 1 >= 0 = mark(g(X)) proper(f(X1,X2,X3)) = 0 >= 0 = f(proper(X1),proper(X2),proper(X3)) proper(g(X)) = X + 1 >= X + 1 = g(proper(X)) proper(b()) = 1 >= 1 = ok(b()) proper(c()) = 0 >= 0 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(f(X1,X2,X3)) g(ok(X)) = X + 1 >= X + 1 = ok(g(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) 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)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [c] = 0, [b] = 0, [mark](x0) = 1, [active](x0) = x0 + 1, [f](x0, x1, x2) = x0 + x1 + x2 + 1, [g](x0) = x0 orientation: proper#(f(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3) proper#(f(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2) proper#(f(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1) proper#(g(X)) = X + 1 >= X + 1 = proper#(X) active(f(X,g(X),Y)) = 2X + Y + 2 >= 1 = mark(f(Y,Y,Y)) active(g(b())) = 1 >= 1 = mark(c()) active(b()) = 1 >= 1 = mark(c()) active(g(X)) = X + 1 >= X + 1 = g(active(X)) g(mark(X)) = 1 >= 1 = mark(g(X)) proper(f(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = f(proper(X1),proper(X2),proper(X3)) proper(g(X)) = X >= X = g(proper(X)) proper(b()) = 0 >= 0 = ok(b()) proper(c()) = 0 >= 0 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(f(X1,X2,X3)) g(ok(X)) = 0 >= 0 = ok(g(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: 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)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [c] = 0, [b] = 1, [mark](x0) = 0, [active](x0) = x0, [f](x0, x1, x2) = 0, [g](x0) = x0 + 1 orientation: proper#(g(X)) = X + 2 >= X + 1 = proper#(X) active(f(X,g(X),Y)) = 0 >= 0 = mark(f(Y,Y,Y)) active(g(b())) = 2 >= 0 = mark(c()) active(b()) = 1 >= 0 = mark(c()) active(g(X)) = X + 1 >= X + 1 = g(active(X)) g(mark(X)) = 1 >= 0 = mark(g(X)) proper(f(X1,X2,X3)) = 0 >= 0 = f(proper(X1),proper(X2),proper(X3)) proper(g(X)) = X + 1 >= X + 1 = g(proper(X)) proper(b()) = 1 >= 1 = ok(b()) proper(c()) = 0 >= 0 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(f(X1,X2,X3)) g(ok(X)) = X + 1 >= X + 1 = ok(g(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) 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)) Matrix Interpretation Processor: dimension: 1 interpretation: [g#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [c] = 0, [b] = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [f](x0, x1, x2) = x2, [g](x0) = x0 orientation: g#(mark(X)) = X + 1 >= X + 1 = g#(X) g#(ok(X)) = X + 2 >= X + 1 = g#(X) active(f(X,g(X),Y)) = Y + 1 >= Y = mark(f(Y,Y,Y)) active(g(b())) = 1 >= 0 = mark(c()) active(b()) = 1 >= 0 = mark(c()) active(g(X)) = X + 1 >= X + 1 = g(active(X)) g(mark(X)) = X >= X = mark(g(X)) proper(f(X1,X2,X3)) = 1 >= 1 = f(proper(X1),proper(X2),proper(X3)) proper(g(X)) = 1 >= 1 = g(proper(X)) proper(b()) = 1 >= 1 = ok(b()) proper(c()) = 1 >= 1 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(f(X1,X2,X3)) g(ok(X)) = X + 1 >= X + 1 = ok(g(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: g#(mark(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)) Matrix Interpretation Processor: dimension: 1 interpretation: [g#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = 0, [c] = 0, [b] = 0, [mark](x0) = x0 + 1, [active](x0) = 1, [f](x0, x1, x2) = 0, [g](x0) = x0 orientation: g#(mark(X)) = X + 2 >= X + 1 = g#(X) active(f(X,g(X),Y)) = 1 >= 1 = mark(f(Y,Y,Y)) active(g(b())) = 1 >= 1 = mark(c()) active(b()) = 1 >= 1 = mark(c()) active(g(X)) = 1 >= 1 = g(active(X)) g(mark(X)) = X + 1 >= X + 1 = mark(g(X)) proper(f(X1,X2,X3)) = 0 >= 0 = f(proper(X1),proper(X2),proper(X3)) proper(g(X)) = 0 >= 0 = g(proper(X)) proper(b()) = 0 >= 0 = ok(b()) proper(c()) = 0 >= 0 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = 0 >= 0 = ok(f(X1,X2,X3)) g(ok(X)) = 0 >= 0 = ok(g(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) 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)) Matrix Interpretation Processor: dimension: 1 interpretation: [f#](x0, x1, x2) = x2 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [c] = 0, [b] = 0, [mark](x0) = 0, [active](x0) = 0, [f](x0, x1, x2) = x2, [g](x0) = x0 orientation: f#(ok(X1),ok(X2),ok(X3)) = X3 + 2 >= X3 + 1 = f#(X1,X2,X3) active(f(X,g(X),Y)) = 0 >= 0 = mark(f(Y,Y,Y)) active(g(b())) = 0 >= 0 = mark(c()) active(b()) = 0 >= 0 = mark(c()) active(g(X)) = 0 >= 0 = g(active(X)) g(mark(X)) = 0 >= 0 = mark(g(X)) proper(f(X1,X2,X3)) = 1 >= 1 = f(proper(X1),proper(X2),proper(X3)) proper(g(X)) = 1 >= 1 = g(proper(X)) proper(b()) = 1 >= 1 = ok(b()) proper(c()) = 1 >= 1 = ok(c()) f(ok(X1),ok(X2),ok(X3)) = X3 + 1 >= X3 + 1 = ok(f(X1,X2,X3)) g(ok(X)) = X + 1 >= X + 1 = ok(g(X)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) 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