MAYBE Problem: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Proof: DP Processor: DPs: active#(f(X,g(X),Y)) -> f#(Y,Y,Y) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) active#(g(b())) -> mark#(c()) active#(b()) -> mark#(c()) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) mark#(g(X)) -> mark#(X) mark#(g(X)) -> g#(mark(X)) mark#(g(X)) -> active#(g(mark(X))) mark#(b()) -> active#(b()) mark#(c()) -> active#(c()) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) EDG Processor: DPs: active#(f(X,g(X),Y)) -> f#(Y,Y,Y) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) active#(g(b())) -> mark#(c()) active#(b()) -> mark#(c()) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) mark#(g(X)) -> mark#(X) mark#(g(X)) -> g#(mark(X)) mark#(g(X)) -> active#(g(mark(X))) mark#(b()) -> active#(b()) mark#(c()) -> active#(c()) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) graph: g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X) g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X) g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X) mark#(b()) -> active#(b()) -> active#(b()) -> mark#(c()) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) -> active#(f(X,g(X),Y)) -> f#(Y,Y,Y) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) -> active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) mark#(g(X)) -> g#(mark(X)) -> g#(mark(X)) -> g#(X) mark#(g(X)) -> g#(mark(X)) -> g#(active(X)) -> g#(X) mark#(g(X)) -> mark#(X) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X) mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> g#(mark(X)) mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(mark(X))) mark#(g(X)) -> mark#(X) -> mark#(b()) -> active#(b()) mark#(g(X)) -> mark#(X) -> mark#(c()) -> active#(c()) mark#(g(X)) -> active#(g(mark(X))) -> active#(f(X,g(X),Y)) -> f#(Y,Y,Y) mark#(g(X)) -> active#(g(mark(X))) -> active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) mark#(g(X)) -> active#(g(mark(X))) -> active#(g(b())) -> mark#(c()) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(mark(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(X1,mark(X2),X3) -> f#(X1,X2,X3) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) active#(b()) -> mark#(c()) -> mark#(c()) -> active#(c()) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) -> mark#(g(X)) -> mark#(X) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) -> mark#(g(X)) -> g#(mark(X)) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) -> mark#(g(X)) -> active#(g(mark(X))) active#(g(b())) -> mark#(c()) -> mark#(c()) -> active#(c()) SCC Processor: #sccs: 3 #rules: 12 #arcs: 60/324 DPs: f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) f#(X1,active(X2),X3) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) f#(X1,mark(X2),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()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dimension: 1 interpretation: [f#](x0, x1, x2) = x0 + x1 + x2 + 1, [c] = 1, [b] = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [f](x0, x1, x2) = 1, [g](x0) = 1 orientation: f#(mark(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 1 = f#(X1,X2,X3) f#(X1,X2,active(X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 1 = f#(X1,X2,X3) f#(X1,active(X2),X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 1 = f#(X1,X2,X3) f#(active(X1),X2,X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 1 = f#(X1,X2,X3) f#(X1,X2,mark(X3)) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 1 = f#(X1,X2,X3) f#(X1,mark(X2),X3) = X1 + X2 + X3 + 2 >= X1 + X2 + X3 + 1 = f#(X1,X2,X3) active(f(X,g(X),Y)) = 2 >= 2 = mark(f(Y,Y,Y)) active(g(b())) = 2 >= 2 = mark(c()) active(b()) = 2 >= 2 = mark(c()) mark(f(X1,X2,X3)) = 2 >= 2 = active(f(X1,X2,X3)) mark(g(X)) = 2 >= 2 = active(g(mark(X))) mark(b()) = 2 >= 2 = active(b()) mark(c()) = 2 >= 2 = active(c()) f(mark(X1),X2,X3) = 1 >= 1 = f(X1,X2,X3) f(X1,mark(X2),X3) = 1 >= 1 = f(X1,X2,X3) f(X1,X2,mark(X3)) = 1 >= 1 = f(X1,X2,X3) f(active(X1),X2,X3) = 1 >= 1 = f(X1,X2,X3) f(X1,active(X2),X3) = 1 >= 1 = f(X1,X2,X3) f(X1,X2,active(X3)) = 1 >= 1 = f(X1,X2,X3) g(mark(X)) = 1 >= 1 = g(X) g(active(X)) = 1 >= 1 = g(X) problem: DPs: TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Qed DPs: mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) mark#(g(X)) -> active#(g(mark(X))) mark#(g(X)) -> mark#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [c] = 0, [b] = 0, [mark](x0) = x0, [active](x0) = x0, [f](x0, x1, x2) = 0, [g](x0) = x0 + 1 orientation: mark#(f(X1,X2,X3)) = 0 >= 0 = active#(f(X1,X2,X3)) active#(f(X,g(X),Y)) = 0 >= 0 = mark#(f(Y,Y,Y)) mark#(g(X)) = X + 1 >= X + 1 = active#(g(mark(X))) mark#(g(X)) = X + 1 >= X = mark#(X) active(f(X,g(X),Y)) = 0 >= 0 = mark(f(Y,Y,Y)) active(g(b())) = 1 >= 0 = mark(c()) active(b()) = 0 >= 0 = mark(c()) mark(f(X1,X2,X3)) = 0 >= 0 = active(f(X1,X2,X3)) mark(g(X)) = X + 1 >= X + 1 = active(g(mark(X))) mark(b()) = 0 >= 0 = active(b()) mark(c()) = 0 >= 0 = active(c()) f(mark(X1),X2,X3) = 0 >= 0 = f(X1,X2,X3) f(X1,mark(X2),X3) = 0 >= 0 = f(X1,X2,X3) f(X1,X2,mark(X3)) = 0 >= 0 = f(X1,X2,X3) f(active(X1),X2,X3) = 0 >= 0 = f(X1,X2,X3) f(X1,active(X2),X3) = 0 >= 0 = f(X1,X2,X3) f(X1,X2,active(X3)) = 0 >= 0 = f(X1,X2,X3) g(mark(X)) = X + 1 >= X + 1 = g(X) g(active(X)) = X + 1 >= X + 1 = g(X) problem: DPs: mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) mark#(g(X)) -> active#(g(mark(X))) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [c] = 0, [b] = 0, [mark](x0) = 0, [active](x0) = 0, [f](x0, x1, x2) = 0, [g](x0) = 1 orientation: mark#(f(X1,X2,X3)) = 0 >= 0 = active#(f(X1,X2,X3)) active#(f(X,g(X),Y)) = 0 >= 0 = mark#(f(Y,Y,Y)) mark#(g(X)) = 1 >= 0 = active#(g(mark(X))) 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()) mark(f(X1,X2,X3)) = 0 >= 0 = active(f(X1,X2,X3)) mark(g(X)) = 0 >= 0 = active(g(mark(X))) mark(b()) = 0 >= 0 = active(b()) mark(c()) = 0 >= 0 = active(c()) f(mark(X1),X2,X3) = 0 >= 0 = f(X1,X2,X3) f(X1,mark(X2),X3) = 0 >= 0 = f(X1,X2,X3) f(X1,X2,mark(X3)) = 0 >= 0 = f(X1,X2,X3) f(active(X1),X2,X3) = 0 >= 0 = f(X1,X2,X3) f(X1,active(X2),X3) = 0 >= 0 = f(X1,X2,X3) f(X1,X2,active(X3)) = 0 >= 0 = f(X1,X2,X3) g(mark(X)) = 1 >= 1 = g(X) g(active(X)) = 1 >= 1 = g(X) problem: DPs: mark#(f(X1,X2,X3)) -> active#(f(X1,X2,X3)) active#(f(X,g(X),Y)) -> mark#(f(Y,Y,Y)) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Open DPs: g#(mark(X)) -> g#(X) g#(active(X)) -> g#(X) TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Matrix Interpretation Processor: dimension: 1 interpretation: [g#](x0) = x0 + 1, [c] = 0, [b] = 0, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [f](x0, x1, x2) = x2, [g](x0) = 0 orientation: g#(mark(X)) = X + 2 >= X + 1 = g#(X) g#(active(X)) = X + 2 >= X + 1 = g#(X) active(f(X,g(X),Y)) = Y + 1 >= Y + 1 = mark(f(Y,Y,Y)) active(g(b())) = 1 >= 1 = mark(c()) active(b()) = 1 >= 1 = mark(c()) mark(f(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(f(X1,X2,X3)) mark(g(X)) = 1 >= 1 = active(g(mark(X))) mark(b()) = 1 >= 1 = active(b()) mark(c()) = 1 >= 1 = active(c()) f(mark(X1),X2,X3) = X3 >= X3 = f(X1,X2,X3) f(X1,mark(X2),X3) = X3 >= X3 = f(X1,X2,X3) f(X1,X2,mark(X3)) = X3 + 1 >= X3 = f(X1,X2,X3) f(active(X1),X2,X3) = X3 >= X3 = f(X1,X2,X3) f(X1,active(X2),X3) = X3 >= X3 = f(X1,X2,X3) f(X1,X2,active(X3)) = X3 + 1 >= X3 = f(X1,X2,X3) g(mark(X)) = 0 >= 0 = g(X) g(active(X)) = 0 >= 0 = g(X) problem: DPs: TRS: active(f(X,g(X),Y)) -> mark(f(Y,Y,Y)) active(g(b())) -> mark(c()) active(b()) -> mark(c()) mark(f(X1,X2,X3)) -> active(f(X1,X2,X3)) mark(g(X)) -> active(g(mark(X))) mark(b()) -> active(b()) mark(c()) -> active(c()) f(mark(X1),X2,X3) -> f(X1,X2,X3) f(X1,mark(X2),X3) -> f(X1,X2,X3) f(X1,X2,mark(X3)) -> f(X1,X2,X3) f(active(X1),X2,X3) -> f(X1,X2,X3) f(X1,active(X2),X3) -> f(X1,X2,X3) f(X1,X2,active(X3)) -> f(X1,X2,X3) g(mark(X)) -> g(X) g(active(X)) -> g(X) Qed