YES Input TRS: 1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) 2: active(__(X,nil())) -> mark(X) 3: active(__(nil(),X)) -> mark(X) 4: active(U11(tt())) -> mark(U12(tt())) 5: active(U12(tt())) -> mark(tt()) 6: active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) 7: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) 8: mark(nil()) -> active(nil()) 9: mark(U11(X)) -> active(U11(mark(X))) 10: mark(tt()) -> active(tt()) 11: mark(U12(X)) -> active(U12(mark(X))) 12: mark(isNePal(X)) -> active(isNePal(mark(X))) 13: __(mark(X1),X2) -> __(X1,X2) 14: __(X1,mark(X2)) -> __(X1,X2) 15: __(active(X1),X2) -> __(X1,X2) 16: __(X1,active(X2)) -> __(X1,X2) 17: U11(mark(X)) -> U11(X) 18: U11(active(X)) -> U11(X) 19: U12(mark(X)) -> U12(X) 20: U12(active(X)) -> U12(X) 21: isNePal(mark(X)) -> isNePal(X) 22: isNePal(active(X)) -> isNePal(X) Number of strict rules: 22 Direct POLO(bPol) ... removes: 4 3 5 6 2 U11 w: x1 + 13507 isNePal w: x1 + 19474 U12 w: x1 + 1 nil w: 29405 mark w: x1 active w: x1 tt w: 7630 __ w: x1 + x2 + 832 Number of strict rules: 17 Direct POLO(bPol) ... removes: 1 U11 w: 2 * x1 + 1 isNePal w: 2 * x1 + 6812 U12 w: x1 + 1 nil w: 1 mark w: x1 active w: x1 tt w: 1 __ w: 2 * x1 + x2 + 1 Number of strict rules: 16 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #__(mark(X1),X2) -> #__(X1,X2) #2: #mark(U11(X)) -> #U11(mark(X)) #3: #mark(U11(X)) -> #mark(X) #4: #mark(U12(X)) -> #U12(mark(X)) #5: #mark(U12(X)) -> #mark(X) #6: #mark(isNePal(X)) -> #isNePal(mark(X)) #7: #mark(isNePal(X)) -> #mark(X) #8: #__(X1,mark(X2)) -> #__(X1,X2) #9: #U12(active(X)) -> #U12(X) #10: #mark(__(X1,X2)) -> #__(mark(X1),mark(X2)) #11: #mark(__(X1,X2)) -> #mark(X1) #12: #mark(__(X1,X2)) -> #mark(X2) #13: #isNePal(active(X)) -> #isNePal(X) #14: #U11(mark(X)) -> #U11(X) #15: #U12(mark(X)) -> #U12(X) #16: #isNePal(mark(X)) -> #isNePal(X) #17: #__(X1,active(X2)) -> #__(X1,X2) #18: #__(active(X1),X2) -> #__(X1,X2) #19: #U11(active(X)) -> #U11(X) Number of SCCs: 5, DPs: 15 SCC { #9 #15 } POLO(Sum)... succeeded. U11 w: 0 #__ w: 0 isNePal w: 0 U12 w: 0 #U12 w: x1 #mark w: 0 #isNePal w: 0 nil w: 0 mark w: x1 + 1 #U11 w: 0 active w: x1 + 1 tt w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #9 #15 Number of SCCs: 4, DPs: 13 SCC { #13 #16 } POLO(Sum)... succeeded. U11 w: 0 #__ w: 0 isNePal w: 0 U12 w: 0 #U12 w: 0 #mark w: 0 #isNePal w: x1 nil w: 0 mark w: x1 + 1 #U11 w: 0 active w: x1 + 1 tt w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #13 #16 Number of SCCs: 3, DPs: 11 SCC { #14 #19 } POLO(Sum)... succeeded. U11 w: 0 #__ w: 0 isNePal w: 0 U12 w: 0 #U12 w: 0 #mark w: 0 #isNePal w: 0 nil w: 0 mark w: x1 + 1 #U11 w: x1 active w: x1 + 1 tt w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #14 #19 Number of SCCs: 2, DPs: 9 SCC { #3 #5 #7 #11 #12 } POLO(Sum)... succeeded. U11 w: x1 + 1 #__ w: 0 isNePal w: x1 + 1 U12 w: x1 + 1 #U12 w: 0 #mark w: x1 #isNePal w: 0 nil w: 0 mark w: 1 #U11 w: 0 active w: 1 tt w: 0 __ w: x1 + x2 + 1 USABLE RULES: { } Removed DPs: #3 #5 #7 #11 #12 Number of SCCs: 1, DPs: 4 SCC { #1 #8 #17 #18 } POLO(Sum)... succeeded. U11 w: 1 #__ w: x1 + x2 isNePal w: 1 U12 w: 1 #U12 w: 0 #mark w: 0 #isNePal w: 0 nil w: 0 mark w: x1 + 1 #U11 w: 0 active w: x1 + 1 tt w: 0 __ w: 1 USABLE RULES: { } Removed DPs: #1 #8 #17 #18 Number of SCCs: 0, DPs: 0