MAYBE Problem: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Proof: DP Processor: DPs: active#(f(a(),b(),X)) -> f#(X,X,X) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) active#(c()) -> mark#(a()) active#(c()) -> mark#(b()) mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) mark#(a()) -> active#(a()) 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) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) TDG Processor: DPs: active#(f(a(),b(),X)) -> f#(X,X,X) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) active#(c()) -> mark#(a()) active#(c()) -> mark#(b()) mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) mark#(a()) -> active#(a()) 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) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) graph: mark#(c()) -> active#(c()) -> active#(c()) -> mark#(b()) mark#(c()) -> active#(c()) -> active#(c()) -> mark#(a()) mark#(c()) -> active#(c()) -> active#(f(a(),b(),X)) -> mark#(f(X,X,X)) mark#(c()) -> active#(c()) -> active#(f(a(),b(),X)) -> f#(X,X,X) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(c()) -> active#(c()) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(b()) -> active#(b()) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(a()) -> active#(a()) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) -> active#(c()) -> mark#(b()) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) -> active#(c()) -> mark#(a()) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) -> active#(f(a(),b(),X)) -> mark#(f(X,X,X)) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) -> active#(f(a(),b(),X)) -> f#(X,X,X) mark#(b()) -> active#(b()) -> active#(c()) -> mark#(b()) mark#(b()) -> active#(b()) -> active#(c()) -> mark#(a()) mark#(b()) -> active#(b()) -> active#(f(a(),b(),X)) -> mark#(f(X,X,X)) mark#(b()) -> active#(b()) -> active#(f(a(),b(),X)) -> f#(X,X,X) mark#(a()) -> active#(a()) -> active#(c()) -> mark#(b()) mark#(a()) -> active#(a()) -> active#(c()) -> mark#(a()) mark#(a()) -> active#(a()) -> active#(f(a(),b(),X)) -> mark#(f(X,X,X)) mark#(a()) -> active#(a()) -> active#(f(a(),b(),X)) -> f#(X,X,X) f#(mark(X1),X2,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,active(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#(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#(X1,mark(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#(active(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#(X1,active(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#(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#(X1,mark(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,mark(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,active(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,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#(X1,mark(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,active(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,active(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,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#(X1,mark(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,mark(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,active(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,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#(X1,mark(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#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(X1,X2,active(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#(active(X1),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#(X1,mark(X2),X3) -> f#(X1,X2,X3) f#(X1,X2,active(X3)) -> f#(X1,X2,X3) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) active#(c()) -> mark#(b()) -> mark#(c()) -> active#(c()) active#(c()) -> mark#(b()) -> mark#(b()) -> active#(b()) active#(c()) -> mark#(b()) -> mark#(a()) -> active#(a()) active#(c()) -> mark#(b()) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(c()) -> mark#(b()) -> mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) active#(c()) -> mark#(b()) -> mark#(f(X1,X2,X3)) -> mark#(X3) active#(c()) -> mark#(a()) -> mark#(c()) -> active#(c()) active#(c()) -> mark#(a()) -> mark#(b()) -> active#(b()) active#(c()) -> mark#(a()) -> mark#(a()) -> active#(a()) active#(c()) -> mark#(a()) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(c()) -> mark#(a()) -> mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) active#(c()) -> mark#(a()) -> mark#(f(X1,X2,X3)) -> mark#(X3) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(c()) -> active#(c()) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(b()) -> active#(b()) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(a()) -> active#(a()) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(f(X1,X2,X3)) -> f#(X1,X2,mark(X3)) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(f(X1,X2,X3)) -> mark#(X3) active#(f(a(),b(),X)) -> f#(X,X,X) -> f#(X1,X2,active(X3)) -> f#(X1,X2,X3) active#(f(a(),b(),X)) -> f#(X,X,X) -> f#(X1,active(X2),X3) -> f#(X1,X2,X3) active#(f(a(),b(),X)) -> f#(X,X,X) -> f#(active(X1),X2,X3) -> f#(X1,X2,X3) active#(f(a(),b(),X)) -> f#(X,X,X) -> f#(X1,X2,mark(X3)) -> f#(X1,X2,X3) active#(f(a(),b(),X)) -> f#(X,X,X) -> f#(X1,mark(X2),X3) -> f#(X1,X2,X3) active#(f(a(),b(),X)) -> f#(X,X,X) -> f#(mark(X1),X2,X3) -> f#(X1,X2,X3) SCC Processor: #sccs: 2 #rules: 14 #arcs: 88/256 DPs: mark#(c()) -> active#(c()) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(c()) -> mark#(a()) mark#(a()) -> active#(a()) active#(c()) -> mark#(b()) mark#(b()) -> active#(b()) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) EDG Processor: DPs: mark#(c()) -> active#(c()) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(c()) -> mark#(a()) mark#(a()) -> active#(a()) active#(c()) -> mark#(b()) mark#(b()) -> active#(b()) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) graph: mark#(c()) -> active#(c()) -> active#(c()) -> mark#(a()) mark#(c()) -> active#(c()) -> active#(c()) -> mark#(b()) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(a()) -> active#(a()) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(b()) -> active#(b()) mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(c()) -> active#(c()) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) -> active#(f(a(),b(),X)) -> mark#(f(X,X,X)) active#(c()) -> mark#(b()) -> mark#(b()) -> active#(b()) active#(c()) -> mark#(a()) -> mark#(a()) -> active#(a()) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(f(X1,X2,X3)) -> mark#(X3) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) -> mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) SCC Processor: #sccs: 1 #rules: 3 #arcs: 12/64 DPs: mark#(f(X1,X2,X3)) -> mark#(X3) mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 5x0, [active#](x0) = 5x0 + 0, [c] = 0, [mark](x0) = x0, [active](x0) = x0, [f](x0, x1, x2) = 1x2 + 0, [b] = 0, [a] = 0 orientation: mark#(f(X1,X2,X3)) = 6X3 + 5 >= 5X3 = mark#(X3) mark#(f(X1,X2,X3)) = 6X3 + 5 >= 6X3 + 5 = active#(f(X1,X2,mark(X3))) active#(f(a(),b(),X)) = 6X + 5 >= 6X + 5 = mark#(f(X,X,X)) active(f(a(),b(),X)) = 1X + 0 >= 1X + 0 = mark(f(X,X,X)) active(c()) = 0 >= 0 = mark(a()) active(c()) = 0 >= 0 = mark(b()) mark(f(X1,X2,X3)) = 1X3 + 0 >= 1X3 + 0 = active(f(X1,X2,mark(X3))) mark(a()) = 0 >= 0 = active(a()) mark(b()) = 0 >= 0 = active(b()) mark(c()) = 0 >= 0 = active(c()) f(mark(X1),X2,X3) = 1X3 + 0 >= 1X3 + 0 = f(X1,X2,X3) f(X1,mark(X2),X3) = 1X3 + 0 >= 1X3 + 0 = f(X1,X2,X3) f(X1,X2,mark(X3)) = 1X3 + 0 >= 1X3 + 0 = f(X1,X2,X3) f(active(X1),X2,X3) = 1X3 + 0 >= 1X3 + 0 = f(X1,X2,X3) f(X1,active(X2),X3) = 1X3 + 0 >= 1X3 + 0 = f(X1,X2,X3) f(X1,X2,active(X3)) = 1X3 + 0 >= 1X3 + 0 = f(X1,X2,X3) problem: DPs: mark#(f(X1,X2,X3)) -> active#(f(X1,X2,mark(X3))) active#(f(a(),b(),X)) -> mark#(f(X,X,X)) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Open DPs: 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) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Subterm Criterion Processor: simple projection: pi(f#) = 2 problem: DPs: f#(mark(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,active(X2),X3) -> f#(X1,X2,X3) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Subterm Criterion Processor: simple projection: pi(f#) = 1 problem: DPs: f#(mark(X1),X2,X3) -> f#(X1,X2,X3) f#(active(X1),X2,X3) -> f#(X1,X2,X3) TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Subterm Criterion Processor: simple projection: pi(f#) = 0 problem: DPs: TRS: active(f(a(),b(),X)) -> mark(f(X,X,X)) active(c()) -> mark(a()) active(c()) -> mark(b()) mark(f(X1,X2,X3)) -> active(f(X1,X2,mark(X3))) mark(a()) -> active(a()) 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) Qed