Input TRS: 1: a__2nd(cons1(X,cons(Y,Z))) -> mark(Y) 2: a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) 3: a__from(X) -> cons(mark(X),from(s(X))) 4: mark(2nd(X)) -> a__2nd(mark(X)) 5: mark(from(X)) -> a__from(mark(X)) 6: mark(cons(X1,X2)) -> cons(mark(X1),X2) 7: mark(s(X)) -> s(mark(X)) 8: mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) 9: a__2nd(X) -> 2nd(X) 10: a__from(X) -> from(X) Number of strict rules: 10 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #a__2nd(cons(X,X1)) -> #a__2nd(cons1(mark(X),mark(X1))) #2: #a__2nd(cons(X,X1)) -> #mark(X) #3: #a__2nd(cons(X,X1)) -> #mark(X1) #4: #mark(cons(X1,X2)) -> #mark(X1) #5: #mark(s(X)) -> #mark(X) #6: #mark(from(X)) -> #a__from(mark(X)) #7: #mark(from(X)) -> #mark(X) #8: #a__from(X) -> #mark(X) #9: #a__2nd(cons1(X,cons(Y,Z))) -> #mark(Y) #10: #mark(cons1(X1,X2)) -> #mark(X1) #11: #mark(cons1(X1,X2)) -> #mark(X2) #12: #mark(2nd(X)) -> #a__2nd(mark(X)) #13: #mark(2nd(X)) -> #mark(X) Number of SCCs: 1, DPs: 13, edges: 86 SCC { #1..13 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded. s(x1) weight: x1 #a__from(x1) weight: (/ 1 4) + x1 a__from(x1) weight: (/ 1 2) + x1 2nd(x1) weight: (/ 1 2) + x1 a__2nd(x1) weight: (/ 1 2) + x1 #a__2nd(x1) weight: (/ 1 4) + x1 cons1(x1,x2) weight: max{x2, (/ 1 4) + x1} #mark(x1) weight: x1 from(x1) weight: (/ 1 2) + x1 mark(x1) weight: x1 cons(x1,x2) weight: max{x2, (/ 1 4) + x1} Usable rules: { 1..10 } Removed DPs: #2..4 #6..10 #12 #13 Number of SCCs: 1, DPs: 2, edges: 4 SCC { #5 #11 } Removing DPs: Order(PosReal,>,Sum)... succeeded. s(x1) weight: (/ 1 2) + x1 #a__from(x1) weight: 0 a__from(x1) weight: (/ 3 2) 2nd(x1) weight: (/ 1 2) + x1 a__2nd(x1) weight: x1 #a__2nd(x1) weight: 0 cons1(x1,x2) weight: 2 + x2 #mark(x1) weight: x1 from(x1) weight: (/ 1 2) mark(x1) weight: (/ 1 2) + x1 cons(x1,x2) weight: 2 Usable rules: { } Removed DPs: #5 #11 Number of SCCs: 0, DPs: 0, edges: 0 YES