Input TRS: 1: active(g(X)) -> mark(h(X)) 2: active(c()) -> mark(d()) 3: active(h(d())) -> mark(g(c())) 4: mark(g(X)) -> active(g(X)) 5: mark(h(X)) -> active(h(X)) 6: mark(c()) -> active(c()) 7: mark(d()) -> active(d()) 8: g(mark(X)) -> g(X) 9: g(active(X)) -> g(X) 10: h(mark(X)) -> h(X) 11: h(active(X)) -> h(X) Number of strict rules: 11 Direct Order(PosReal,>,Poly) ... removes: 8 10 11 9 h(x1) weight: 10451 + x1 d() weight: 0 c() weight: 0 mark(x1) weight: 30614 + 2 * x1 active(x1) weight: 30614 + 2 * x1 g(x1) weight: 10451 + 2 * x1 Number of strict rules: 7 Direct Order(PosReal,>,Poly) ... failed. Freezing mark active 1: active❆1_g(X) -> mark❆1_h(X) 2: active❆1_c() -> mark❆1_d() 3: active❆1_h(d()) -> mark❆1_g(c()) 4: mark❆1_g(X) -> active❆1_g(X) 5: mark❆1_h(X) -> active❆1_h(X) 6: mark❆1_c() -> active❆1_c() 7: mark❆1_d() -> active❆1_d() 12: active(h(_1)) ->= active❆1_h(_1) 13: active(d()) ->= active❆1_d() 14: active(c()) ->= active❆1_c() 15: active(g(_1)) ->= active❆1_g(_1) 16: mark(h(_1)) ->= mark❆1_h(_1) 17: mark(d()) ->= mark❆1_d() 18: mark(c()) ->= mark❆1_c() 19: mark(g(_1)) ->= mark❆1_g(_1) Number of strict rules: 7 Direct Order(PosReal,>,Poly) ... removes: 18 15 16 19 17 14 12 13 h(x1) weight: (/ 153 4) + x1 active❆1_h(x1) weight: x1 d() weight: 0 mark❆1_c() weight: 0 c() weight: 0 mark(x1) weight: (/ 1 4) + 2 * x1 mark❆1_h(x1) weight: x1 active❆1_c() weight: 0 active(x1) weight: (/ 1 4) + 2 * x1 active❆1_g(x1) weight: x1 mark❆1_d() weight: 0 mark❆1_g(x1) weight: x1 active❆1_d() weight: 0 g(x1) weight: (/ 1 4) + x1 Number of strict rules: 7 Direct Order(PosReal,>,Poly) ... failed. Dependency Pairs: #1: #active❆1_c() -> #mark❆1_d() #2: #mark❆1_c() -> #active❆1_c() #3: #mark❆1_h(X) -> #active❆1_h(X) #4: #active❆1_h(d()) -> #mark❆1_g(c()) #5: #active❆1_g(X) -> #mark❆1_h(X) #6: #mark❆1_g(X) -> #active❆1_g(X) Number of SCCs: 1, DPs: 4, edges: 4 SCC { #3..6 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded. h(x1) weight: 0 active❆1_h(x1) weight: 0 d() weight: (/ 5 4) #mark❆1_d() weight: 0 mark❆1_c() weight: 0 #active❆1_h(x1) weight: x1 c() weight: (/ 1 4) #active❆1_g(x1) weight: (/ 1 2) + x1 #mark❆1_h(x1) weight: (/ 1 4) + x1 #mark❆1_g(x1) weight: (/ 3 4) + x1 mark(x1) weight: 0 mark❆1_h(x1) weight: 0 active❆1_c() weight: 0 active(x1) weight: 0 active❆1_g(x1) weight: 0 mark❆1_d() weight: 0 mark❆1_g(x1) weight: 0 active❆1_d() weight: 0 #active❆1_c() weight: 0 g(x1) weight: 0 #mark❆1_c() weight: 0 Usable rules: { } Removed DPs: #3..6 Number of SCCs: 0, DPs: 0, edges: 0 YES