YES Input TRS: 1: dbl(0()) -> 0() 2: dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 3: dbls(nil()) -> nil() 4: dbls(cons(X,Y)) -> cons(n__dbl(activate(X)),n__dbls(activate(Y))) 5: sel(0(),cons(X,Y)) -> activate(X) 6: sel(s(X),cons(Y,Z)) -> sel(activate(X),activate(Z)) 7: indx(nil(),X) -> nil() 8: indx(cons(X,Y),Z) -> cons(n__sel(activate(X),activate(Z)),n__indx(activate(Y),activate(Z))) 9: from(X) -> cons(activate(X),n__from(n__s(activate(X)))) 10: dbl1(0()) -> 01() 11: dbl1(s(X)) -> s1(s1(dbl1(activate(X)))) 12: sel1(0(),cons(X,Y)) -> activate(X) 13: sel1(s(X),cons(Y,Z)) -> sel1(activate(X),activate(Z)) 14: quote(0()) -> 01() 15: quote(s(X)) -> s1(quote(activate(X))) 16: quote(dbl(X)) -> dbl1(X) 17: quote(sel(X,Y)) -> sel1(X,Y) 18: s(X) -> n__s(X) 19: dbl(X) -> n__dbl(X) 20: dbls(X) -> n__dbls(X) 21: sel(X1,X2) -> n__sel(X1,X2) 22: indx(X1,X2) -> n__indx(X1,X2) 23: from(X) -> n__from(X) 24: activate(n__s(X)) -> s(X) 25: activate(n__dbl(X)) -> dbl(activate(X)) 26: activate(n__dbls(X)) -> dbls(activate(X)) 27: activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2)) 28: activate(n__indx(X1,X2)) -> indx(activate(X1),X2) 29: activate(n__from(X)) -> from(X) 30: activate(X) -> X Number of strict rules: 30 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #dbl(s(X)) -> #s(n__s(n__dbl(activate(X)))) #2: #dbl(s(X)) -> #activate(X) #3: #activate(n__from(X)) -> #from(X) #4: #sel(s(X),cons(Y,Z)) -> #sel(activate(X),activate(Z)) #5: #sel(s(X),cons(Y,Z)) -> #activate(X) #6: #sel(s(X),cons(Y,Z)) -> #activate(Z) #7: #sel1(s(X),cons(Y,Z)) -> #sel1(activate(X),activate(Z)) #8: #sel1(s(X),cons(Y,Z)) -> #activate(X) #9: #sel1(s(X),cons(Y,Z)) -> #activate(Z) #10: #from(X) -> #activate(X) #11: #from(X) -> #activate(X) #12: #dbl1(s(X)) -> #dbl1(activate(X)) #13: #dbl1(s(X)) -> #activate(X) #14: #activate(n__s(X)) -> #s(X) #15: #sel1(0(),cons(X,Y)) -> #activate(X) #16: #activate(n__dbl(X)) -> #dbl(activate(X)) #17: #activate(n__dbl(X)) -> #activate(X) #18: #sel(0(),cons(X,Y)) -> #activate(X) #19: #activate(n__indx(X1,X2)) -> #indx(activate(X1),X2) #20: #activate(n__indx(X1,X2)) -> #activate(X1) #21: #activate(n__sel(X1,X2)) -> #sel(activate(X1),activate(X2)) #22: #activate(n__sel(X1,X2)) -> #activate(X1) #23: #activate(n__sel(X1,X2)) -> #activate(X2) #24: #quote(sel(X,Y)) -> #sel1(X,Y) #25: #activate(n__dbls(X)) -> #dbls(activate(X)) #26: #activate(n__dbls(X)) -> #activate(X) #27: #quote(dbl(X)) -> #dbl1(X) #28: #indx(cons(X,Y),Z) -> #activate(X) #29: #indx(cons(X,Y),Z) -> #activate(Z) #30: #indx(cons(X,Y),Z) -> #activate(Y) #31: #indx(cons(X,Y),Z) -> #activate(Z) #32: #quote(s(X)) -> #quote(activate(X)) #33: #quote(s(X)) -> #activate(X) #34: #dbls(cons(X,Y)) -> #activate(X) #35: #dbls(cons(X,Y)) -> #activate(Y) Number of SCCs: 4, DPs: 26 SCC { #32 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #dbl1 s: 1 01 s: [] p: 0 w: 0 s s: [1] p: 2 w: x1 dbls s: [1] p: 1 w: x1 activate s: 1 dbl s: [1] p: 3 w: x1 indx s: [2] p: 1 w: x2 + 4 n__indx s: [2] p: 1 w: x2 + 4 n__from s: [] p: 0 w: x1 + 284 #dbl s: [] p: 0 w: 1 #activate s: [] p: 0 w: 1 #dbls s: 1 n__dbls s: [1] p: 1 w: x1 n__s s: [1] p: 2 w: x1 n__dbl s: [1] p: 3 w: x1 0 s: [] p: 0 w: 1 #sel s: [] p: 0 w: 1 #indx s: [2,1] p: 0 w: x1 + x2 + 1 sel s: [] p: 0 w: x2 + 1 from s: [] p: 0 w: x1 + 284 #s s: [] p: 0 w: 1 nil s: [] p: 1 w: 4 dbl1 s: [] p: 0 w: 1 #sel1 s: [] p: 0 w: x1 + 1 n__sel s: [] p: 0 w: x2 + 1 #from s: [] p: 0 w: 1 quote s: [] p: 0 w: 1 cons s: [] p: 0 w: max(x1 + 2, x2) #quote s: [1] p: 0 w: x1 + 1 sel1 s: 2 s1 s: [] p: 0 w: 1 USABLE RULES: { 1..9 18..30 } Removed DPs: #32 Number of SCCs: 3, DPs: 25 SCC { #12 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #dbl1 s: 1 01 s: [] p: 0 w: 0 s s: [1] p: 3 w: x1 dbls s: [1] p: 2 w: x1 activate s: 1 dbl s: [1] p: 4 w: x1 indx s: [] p: 3 w: x2 + 4 n__indx s: [] p: 3 w: x2 + 4 n__from s: [] p: 1 w: x1 + 3 #dbl s: [] p: 0 w: 1 #activate s: [] p: 0 w: 1 #dbls s: 1 n__dbls s: [1] p: 2 w: x1 n__s s: [1] p: 3 w: x1 n__dbl s: [1] p: 4 w: x1 0 s: [] p: 1 w: 1 #sel s: [] p: 0 w: 1 #indx s: [2,1] p: 0 w: x1 + x2 + 1 sel s: [] p: 0 w: x2 + 1 from s: [] p: 1 w: x1 + 3 #s s: [] p: 0 w: 1 nil s: [] p: 2 w: 3 dbl1 s: [] p: 0 w: 1 #sel1 s: [] p: 0 w: x1 + 1 n__sel s: [] p: 0 w: x2 + 1 #from s: [] p: 0 w: 1 quote s: [] p: 0 w: 1 cons s: [1] p: 0 w: max(x1 + 2, x2) #quote s: [1] p: 0 w: x1 + 1 sel1 s: 2 s1 s: [] p: 0 w: 1 USABLE RULES: { 1..9 18..30 } Removed DPs: #12 Number of SCCs: 2, DPs: 24 SCC { #7 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #dbl1 s: [] p: 0 w: 0 01 s: [] p: 0 w: 0 s s: [1] p: 3 w: x1 dbls s: [] p: 2 w: x1 activate s: 1 dbl s: [1] p: 4 w: x1 indx s: [] p: 2 w: x2 + 31603 n__indx s: [] p: 2 w: x2 + 31603 n__from s: [] p: 1 w: x1 + 4 #dbl s: [] p: 0 w: 1 #activate s: [] p: 0 w: 1 #dbls s: 1 n__dbls s: [] p: 2 w: x1 n__s s: [1] p: 3 w: x1 n__dbl s: [1] p: 4 w: x1 0 s: [] p: 1 w: 1 #sel s: [] p: 0 w: 1 #indx s: [2,1] p: 0 w: x1 + x2 + 1 sel s: [] p: 0 w: x2 + 1 from s: [] p: 1 w: x1 + 4 #s s: [] p: 0 w: 1 nil s: [] p: 2 w: 20585 dbl1 s: [] p: 0 w: 1 #sel1 s: 1 n__sel s: [] p: 0 w: x2 + 1 #from s: [] p: 0 w: 1 quote s: [] p: 0 w: 1 cons s: [] p: 0 w: max(x1 + 3, x2) #quote s: [] p: 0 w: 1 sel1 s: 2 s1 s: [] p: 0 w: 1 USABLE RULES: { 1..9 18..30 } Removed DPs: #7 Number of SCCs: 1, DPs: 23 SCC { #2..6 #10 #11 #16..23 #25 #26 #28..31 #34 #35 } POLO(Sum)... POLO(max)... succeeded. #dbl1 w: 0 01 w: 0 s w: x1 dbls w: x1 + 2 activate w: x1 dbl w: x1 + 2 indx w: max(x1 + 67291, x2 + 67293) n__indx w: max(x1 + 67291, x2 + 67293) n__from w: x1 + 31893 #dbl w: x1 + 10424 #activate w: x1 + 10423 #dbls w: x1 + 10424 n__dbls w: x1 + 2 n__s w: x1 n__dbl w: x1 + 2 0 w: 1 #sel w: max(x1 + 10425, x2 + 10424) #indx w: max(x1 + 18458, x2 + 77715) sel w: max(x1 + 45634, x2 + 20979) from w: x1 + 31893 #s w: 0 nil w: 67294 dbl1 w: 0 #sel1 w: 0 n__sel w: max(x1 + 45634, x2 + 20979) #from w: x1 + 10424 quote w: 0 cons w: max(x1 + 21657, x2) #quote w: 0 sel1 w: 0 s1 w: 0 USABLE RULES: { 1..9 18..30 } Removed DPs: #2 #3 #5 #6 #10 #11 #16..23 #25 #26 #28..31 #34 #35 Number of SCCs: 1, DPs: 1 SCC { #4 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. #dbl1 s: [] p: 0 w: 0 01 s: [] p: 0 w: 0 s s: [1] p: 3 w: x1 dbls s: [] p: 2 w: x1 activate s: 1 dbl s: [1] p: 4 w: x1 indx s: [] p: 2 w: x2 + 31603 n__indx s: [] p: 2 w: x2 + 31603 n__from s: [] p: 1 w: x1 + 491 #dbl s: [] p: 0 w: 1 #activate s: [] p: 0 w: 1 #dbls s: 1 n__dbls s: [] p: 2 w: x1 n__s s: [1] p: 3 w: x1 n__dbl s: [1] p: 4 w: x1 0 s: [] p: 1 w: 1 #sel s: 1 #indx s: [2,1] p: 0 w: x1 + x2 + 1 sel s: [] p: 0 w: x2 + 1 from s: [] p: 1 w: x1 + 491 #s s: [] p: 0 w: 1 nil s: [] p: 2 w: 7579 dbl1 s: [] p: 0 w: 1 #sel1 s: 1 n__sel s: [] p: 0 w: x2 + 1 #from s: [] p: 0 w: 1 quote s: [] p: 0 w: 1 cons s: [] p: 0 w: max(x1 + 490, x2) #quote s: [] p: 0 w: 1 sel1 s: 2 s1 s: [] p: 0 w: 1 USABLE RULES: { 1..9 18..30 } Removed DPs: #4 Number of SCCs: 0, DPs: 0