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(and(tt(),X)) -> mark(X) 5: active(isNePal(__(I,__(P,I)))) -> mark(tt()) 6: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) 7: mark(nil()) -> active(nil()) 8: mark(and(X1,X2)) -> active(and(mark(X1),X2)) 9: mark(tt()) -> active(tt()) 10: mark(isNePal(X)) -> active(isNePal(mark(X))) 11: __(mark(X1),X2) -> __(X1,X2) 12: __(X1,mark(X2)) -> __(X1,X2) 13: __(active(X1),X2) -> __(X1,X2) 14: __(X1,active(X2)) -> __(X1,X2) 15: and(mark(X1),X2) -> and(X1,X2) 16: and(X1,mark(X2)) -> and(X1,X2) 17: and(active(X1),X2) -> and(X1,X2) 18: and(X1,active(X2)) -> and(X1,X2) 19: isNePal(mark(X)) -> isNePal(X) 20: isNePal(active(X)) -> isNePal(X) Number of strict rules: 20 Direct POLO(bPol) ... removes: 4 3 5 2 and w: x1 + x2 + 1 isNePal w: x1 + 2 nil w: 32286 mark w: x1 active w: x1 tt w: 1 __ w: x1 + x2 + 2 Number of strict rules: 16 Direct POLO(bPol) ... removes: 1 and w: x1 + x2 + 1 isNePal w: 2 * x1 + 18588 nil w: 1 mark w: x1 active w: x1 tt w: 1 __ w: 2 * x1 + x2 + 1 Number of strict rules: 15 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #mark(__(X1,X2)) -> #__(mark(X1),mark(X2)) #2: #mark(__(X1,X2)) -> #mark(X1) #3: #mark(__(X1,X2)) -> #mark(X2) #4: #__(active(X1),X2) -> #__(X1,X2) #5: #__(mark(X1),X2) -> #__(X1,X2) #6: #__(X1,mark(X2)) -> #__(X1,X2) #7: #__(X1,active(X2)) -> #__(X1,X2) #8: #isNePal(active(X)) -> #isNePal(X) #9: #mark(isNePal(X)) -> #isNePal(mark(X)) #10: #mark(isNePal(X)) -> #mark(X) #11: #and(active(X1),X2) -> #and(X1,X2) #12: #isNePal(mark(X)) -> #isNePal(X) #13: #and(X1,mark(X2)) -> #and(X1,X2) #14: #mark(and(X1,X2)) -> #and(mark(X1),X2) #15: #mark(and(X1,X2)) -> #mark(X1) #16: #and(mark(X1),X2) -> #and(X1,X2) #17: #and(X1,active(X2)) -> #and(X1,X2) Number of SCCs: 4, DPs: 14 SCC { #8 #12 } POLO(Sum)... succeeded. and w: 0 #__ w: 0 isNePal w: 0 #mark w: 0 #isNePal w: x1 nil w: 0 mark w: x1 + 1 active w: x1 + 1 tt w: 0 #and w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #8 #12 Number of SCCs: 3, DPs: 12 SCC { #2 #3 #10 #15 } POLO(Sum)... succeeded. and w: x1 + 1 #__ w: 0 isNePal w: x1 + 1 #mark w: x1 #isNePal w: 0 nil w: 0 mark w: 1 active w: 1 tt w: 0 #and w: 0 __ w: x1 + x2 + 1 USABLE RULES: { } Removed DPs: #2 #3 #10 #15 Number of SCCs: 2, DPs: 8 SCC { #4..7 } POLO(Sum)... succeeded. and w: 1 #__ w: x1 + x2 isNePal w: 1 #mark w: 0 #isNePal w: 0 nil w: 0 mark w: x1 + 1 active w: x1 + 1 tt w: 0 #and w: 0 __ w: 1 USABLE RULES: { } Removed DPs: #4..7 Number of SCCs: 1, DPs: 4 SCC { #11 #13 #16 #17 } POLO(Sum)... succeeded. and w: 1 #__ w: 0 isNePal w: 1 #mark w: 0 #isNePal w: 0 nil w: 0 mark w: x1 + 1 active w: x1 + 1 tt w: 0 #and w: x1 + x2 __ w: 1 USABLE RULES: { } Removed DPs: #11 #13 #16 #17 Number of SCCs: 0, DPs: 0