Input TRS: 1: f_0(x) -> a() 2: f_1(x) -> g_1(x,x) 3: g_1(s(x),y) -> b(f_0(y),g_1(x,y)) 4: f_2(x) -> g_2(x,x) 5: g_2(s(x),y) -> b(f_1(y),g_2(x,y)) 6: f_3(x) -> g_3(x,x) 7: g_3(s(x),y) -> b(f_2(y),g_3(x,y)) 8: f_4(x) -> g_4(x,x) 9: g_4(s(x),y) -> b(f_3(y),g_4(x,y)) 10: f_5(x) -> g_5(x,x) 11: g_5(s(x),y) -> b(f_4(y),g_5(x,y)) 12: f_6(x) -> g_6(x,x) 13: g_6(s(x),y) -> b(f_5(y),g_6(x,y)) 14: f_7(x) -> g_7(x,x) 15: g_7(s(x),y) -> b(f_6(y),g_7(x,y)) 16: f_8(x) -> g_8(x,x) 17: g_8(s(x),y) -> b(f_7(y),g_8(x,y)) 18: f_9(x) -> g_9(x,x) 19: g_9(s(x),y) -> b(f_8(y),g_9(x,y)) 20: f_10(x) -> g_10(x,x) 21: g_10(s(x),y) -> b(f_9(y),g_10(x,y)) Number of strict rules: 21 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #f_1(x) -> #g_1(x,x) #2: #f_3(x) -> #g_3(x,x) #3: #g_6(s(x),y) -> #f_5(y) #4: #g_6(s(x),y) -> #g_6(x,y) #5: #g_4(s(x),y) -> #f_3(y) #6: #g_4(s(x),y) -> #g_4(x,y) #7: #g_5(s(x),y) -> #f_4(y) #8: #g_5(s(x),y) -> #g_5(x,y) #9: #f_6(x) -> #g_6(x,x) #10: #f_7(x) -> #g_7(x,x) #11: #f_10(x) -> #g_10(x,x) #12: #g_3(s(x),y) -> #f_2(y) #13: #g_3(s(x),y) -> #g_3(x,y) #14: #f_5(x) -> #g_5(x,x) #15: #g_2(s(x),y) -> #f_1(y) #16: #g_2(s(x),y) -> #g_2(x,y) #17: #g_8(s(x),y) -> #f_7(y) #18: #g_8(s(x),y) -> #g_8(x,y) #19: #g_9(s(x),y) -> #f_8(y) #20: #g_9(s(x),y) -> #g_9(x,y) #21: #g_10(s(x),y) -> #f_9(y) #22: #g_10(s(x),y) -> #g_10(x,y) #23: #f_8(x) -> #g_8(x,x) #24: #g_1(s(x),y) -> #f_0(y) #25: #g_1(s(x),y) -> #g_1(x,y) #26: #f_4(x) -> #g_4(x,x) #27: #g_7(s(x),y) -> #f_6(y) #28: #g_7(s(x),y) -> #g_7(x,y) #29: #f_2(x) -> #g_2(x,x) #30: #f_9(x) -> #g_9(x,x) Number of SCCs: 10, DPs: 10, edges: 10 SCC { #25 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: x1 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #25 Number of SCCs: 9, DPs: 9, edges: 9 SCC { #16 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: x1 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #16 Number of SCCs: 8, DPs: 8, edges: 8 SCC { #13 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: x1 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #13 Number of SCCs: 7, DPs: 7, edges: 7 SCC { #6 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: x1 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #6 Number of SCCs: 6, DPs: 6, edges: 6 SCC { #8 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: x1 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #8 Number of SCCs: 5, DPs: 5, edges: 5 SCC { #4 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: x1 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #4 Number of SCCs: 4, DPs: 4, edges: 4 SCC { #28 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: x1 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #28 Number of SCCs: 3, DPs: 3, edges: 3 SCC { #18 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: x1 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #18 Number of SCCs: 2, DPs: 2, edges: 2 SCC { #20 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: 0 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: x1 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #20 Number of SCCs: 1, DPs: 1, edges: 1 SCC { #22 } Removing DPs: Order(PosReal,>,Sum)... succeeded. a() weight: 0 f_9(x1) weight: 0 g_5(x1,x2) weight: 0 f_6(x1) weight: 0 f_7(x1) weight: 0 #g_1(x1,x2) weight: 0 #f_6(x1) weight: 0 s(x1) weight: (/ 1 2) + x1 #g_4(x1,x2) weight: 0 g_9(x1,x2) weight: 0 #f_4(x1) weight: 0 b(x1,x2) weight: 0 g_3(x1,x2) weight: 0 #f_8(x1) weight: 0 #f_10(x1) weight: 0 g_8(x1,x2) weight: 0 #g_6(x1,x2) weight: 0 f_5(x1) weight: 0 f_2(x1) weight: 0 g_10(x1,x2) weight: 0 #g_3(x1,x2) weight: 0 g_7(x1,x2) weight: 0 #f_2(x1) weight: 0 g_1(x1,x2) weight: 0 g_2(x1,x2) weight: 0 #g_2(x1,x2) weight: 0 #f_9(x1) weight: 0 f_1(x1) weight: 0 #f_7(x1) weight: 0 #g_5(x1,x2) weight: 0 g_6(x1,x2) weight: 0 f_8(x1) weight: 0 g_4(x1,x2) weight: 0 #f_0(x1) weight: 0 #g_10(x1,x2) weight: x1 f_0(x1) weight: 0 f_10(x1) weight: 0 #f_3(x1) weight: 0 f_4(x1) weight: 0 #f_1(x1) weight: 0 #g_7(x1,x2) weight: 0 #g_8(x1,x2) weight: 0 #f_5(x1) weight: 0 #g_9(x1,x2) weight: 0 f_3(x1) weight: 0 Usable rules: { } Removed DPs: #22 Number of SCCs: 0, DPs: 0, edges: 0 YES