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: active(__(X1,X2)) -> __(active(X1),X2) 8: active(__(X1,X2)) -> __(X1,active(X2)) 9: active(U11(X)) -> U11(active(X)) 10: active(U12(X)) -> U12(active(X)) 11: active(isNePal(X)) -> isNePal(active(X)) 12: __(mark(X1),X2) -> mark(__(X1,X2)) 13: __(X1,mark(X2)) -> mark(__(X1,X2)) 14: U11(mark(X)) -> mark(U11(X)) 15: U12(mark(X)) -> mark(U12(X)) 16: isNePal(mark(X)) -> mark(isNePal(X)) 17: proper(__(X1,X2)) -> __(proper(X1),proper(X2)) 18: proper(nil()) -> ok(nil()) 19: proper(U11(X)) -> U11(proper(X)) 20: proper(tt()) -> ok(tt()) 21: proper(U12(X)) -> U12(proper(X)) 22: proper(isNePal(X)) -> isNePal(proper(X)) 23: __(ok(X1),ok(X2)) -> ok(__(X1,X2)) 24: U11(ok(X)) -> ok(U11(X)) 25: U12(ok(X)) -> ok(U12(X)) 26: isNePal(ok(X)) -> ok(isNePal(X)) 27: top(mark(X)) -> top(proper(X)) 28: top(ok(X)) -> top(active(X)) Number of strict rules: 28 Direct POLO(bPol) ... removes: 5 U11 w: x1 + 18748 top w: x1 + 26050 isNePal w: x1 + 38369 U12 w: x1 + 18748 proper w: x1 ok w: x1 nil w: 0 mark w: x1 active w: x1 tt w: 19621 __ w: x1 + x2 Number of strict rules: 27 Direct POLO(bPol) ... removes: 4 6 U11 w: x1 + 2 top w: x1 + 26050 isNePal w: x1 + 38369 U12 w: x1 + 1 proper w: x1 ok w: x1 nil w: 0 mark w: x1 active w: x1 tt w: 1 __ w: x1 + x2 Number of strict rules: 25 Direct POLO(bPol) ... removes: 3 2 U11 w: x1 + 1 top w: x1 + 38197 isNePal w: x1 + 1 U12 w: x1 + 1 proper w: x1 ok w: x1 nil w: 9123 mark w: x1 active w: x1 tt w: 0 __ w: x1 + x2 Number of strict rules: 23 Direct POLO(bPol) ... removes: 1 27 12 U11 w: x1 + 4 top w: 2 * x1 + 70495 isNePal w: x1 + 25783 U12 w: x1 + 2 proper w: x1 ok w: x1 nil w: 7036 mark w: x1 + 2 active w: x1 tt w: 1 __ w: 2 * x1 + x2 + 3 Number of strict rules: 20 Direct POLO(bPol) ... removes: 14 U11 w: 2 * x1 + 1149 top w: x1 + 87182 isNePal w: x1 + 2690 U12 w: x1 + 2200 proper w: x1 ok w: x1 nil w: 12341 mark w: x1 + 1 active w: x1 tt w: 1052 __ w: 2 * x1 + x2 + 282 Number of strict rules: 19 Direct POLO(bPol) ... removes: 15 U11 w: x1 + 1889 top w: x1 + 108473 isNePal w: x1 + 2690 U12 w: 2 * x1 + 1179 proper w: x1 ok w: x1 nil w: 12341 mark w: x1 + 1 active w: x1 tt w: 257 __ w: 2 * x1 + x2 + 1 Number of strict rules: 18 Direct POLO(bPol) ... removes: 16 U11 w: x1 + 29007 top w: x1 + 116146 isNePal w: 2 * x1 + 15078 U12 w: x1 + 1 proper w: x1 ok w: x1 nil w: 29350 mark w: x1 + 1 active w: x1 tt w: 1 __ w: 2 * x1 + x2 + 18418 Number of strict rules: 17 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #__(X1,mark(X2)) -> #__(X1,X2) #2: #active(U11(X)) -> #U11(active(X)) #3: #active(U11(X)) -> #active(X) #4: #active(isNePal(X)) -> #isNePal(active(X)) #5: #active(isNePal(X)) -> #active(X) #6: #U11(ok(X)) -> #U11(X) #7: #__(ok(X1),ok(X2)) -> #__(X1,X2) #8: #U12(ok(X)) -> #U12(X) #9: #active(__(X1,X2)) -> #__(active(X1),X2) #10: #active(__(X1,X2)) -> #active(X1) #11: #active(U12(X)) -> #U12(active(X)) #12: #active(U12(X)) -> #active(X) #13: #top(ok(X)) -> #top(active(X)) #14: #top(ok(X)) -> #active(X) #15: #proper(isNePal(X)) -> #isNePal(proper(X)) #16: #proper(isNePal(X)) -> #proper(X) #17: #proper(__(X1,X2)) -> #__(proper(X1),proper(X2)) #18: #proper(__(X1,X2)) -> #proper(X1) #19: #proper(__(X1,X2)) -> #proper(X2) #20: #proper(U11(X)) -> #U11(proper(X)) #21: #proper(U11(X)) -> #proper(X) #22: #isNePal(ok(X)) -> #isNePal(X) #23: #proper(U12(X)) -> #U12(proper(X)) #24: #proper(U12(X)) -> #proper(X) #25: #active(__(X1,X2)) -> #__(X1,active(X2)) #26: #active(__(X1,X2)) -> #active(X2) Number of SCCs: 7, DPs: 16 SCC { #22 } POLO(Sum)... succeeded. U11 w: 0 top w: 0 #top w: 0 #__ w: 0 isNePal w: 0 U12 w: 0 #U12 w: 0 proper w: 0 ok w: x1 + 1 #isNePal w: x1 nil w: 0 mark w: 0 #proper w: 0 #U11 w: 0 active w: 0 #active w: 0 tt w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #22 Number of SCCs: 6, DPs: 15 SCC { #8 } POLO(Sum)... succeeded. U11 w: 0 top w: 0 #top w: 0 #__ w: 0 isNePal w: 0 U12 w: 0 #U12 w: x1 proper w: 0 ok w: x1 + 1 #isNePal w: 0 nil w: 0 mark w: 0 #proper w: 0 #U11 w: 0 active w: 0 #active w: 0 tt w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #8 Number of SCCs: 5, DPs: 14 SCC { #6 } POLO(Sum)... succeeded. U11 w: 0 top w: 0 #top w: 0 #__ w: 0 isNePal w: 0 U12 w: 0 #U12 w: 0 proper w: 0 ok w: x1 + 1 #isNePal w: 0 nil w: 0 mark w: 0 #proper w: 0 #U11 w: x1 active w: 0 #active w: 0 tt w: 0 __ w: 0 USABLE RULES: { } Removed DPs: #6 Number of SCCs: 4, DPs: 13 SCC { #13 } POLO(Sum)... succeeded. U11 w: x1 + 1 top w: 0 #top w: x1 #__ w: 0 isNePal w: x1 + 60386 U12 w: x1 + 16304 #U12 w: 0 proper w: 0 ok w: x1 + 2 #isNePal w: 0 nil w: 0 mark w: x1 + 31755 #proper w: 0 #U11 w: 0 active w: x1 + 1 #active w: 0 tt w: 0 __ w: x2 + 1 USABLE RULES: { 7..11 13 23..26 } Removed DPs: #13 Number of SCCs: 3, DPs: 12 SCC { #1 #7 } POLO(Sum)... succeeded. U11 w: x1 + 1 top w: 0 #top w: x1 #__ w: x1 + x2 isNePal w: x1 + 60386 U12 w: x1 + 16304 #U12 w: 0 proper w: 0 ok w: x1 + 47262 #isNePal w: 0 nil w: 0 mark w: x1 + 31755 #proper w: 0 #U11 w: 0 active w: x1 + 17678 #active w: 0 tt w: 0 __ w: x2 + 1 USABLE RULES: { 7..11 13 23..26 } Removed DPs: #1 #7 Number of SCCs: 2, DPs: 10 SCC { #16 #18 #19 #21 #24 } POLO(Sum)... succeeded. U11 w: x1 + 1 top w: 0 #top w: x1 #__ w: 0 isNePal w: x1 + 1 U12 w: x1 + 18458 #U12 w: 0 proper w: 0 ok w: x1 + 47262 #isNePal w: 0 nil w: 0 mark w: x1 + 30205 #proper w: x1 #U11 w: 0 active w: x1 #active w: 0 tt w: 0 __ w: x1 + x2 + 1 USABLE RULES: { 7..11 13 23..26 } Removed DPs: #16 #18 #19 #21 #24 Number of SCCs: 1, DPs: 5 SCC { #3 #5 #10 #12 #26 } POLO(Sum)... succeeded. U11 w: x1 + 1 top w: 0 #top w: x1 #__ w: 0 isNePal w: x1 + 33119 U12 w: x1 + 1 #U12 w: 0 proper w: 0 ok w: x1 + 21034 #isNePal w: 0 nil w: 0 mark w: x1 + 17498 #proper w: 0 #U11 w: 0 active w: x1 #active w: x1 tt w: 0 __ w: x1 + x2 + 1 USABLE RULES: { 7..11 13 23..26 } Removed DPs: #3 #5 #10 #12 #26 Number of SCCs: 0, DPs: 0