MAYBE 1184.30/297.19 MAYBE 1184.30/297.19 1184.30/297.19 We are left with following problem, upon which TcT provides the 1184.30/297.19 certificate MAYBE. 1184.30/297.19 1184.30/297.19 Strict Trs: 1184.30/297.19 { dbl(X) -> n__dbl(X) 1184.30/297.19 , dbl(0()) -> 0() 1184.30/297.19 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 1184.30/297.19 , s(X) -> n__s(X) 1184.30/297.19 , activate(X) -> X 1184.30/297.19 , activate(n__s(X)) -> s(X) 1184.30/297.19 , activate(n__dbl(X)) -> dbl(X) 1184.30/297.19 , activate(n__dbls(X)) -> dbls(X) 1184.30/297.19 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1184.30/297.19 , activate(n__indx(X1, X2)) -> indx(X1, X2) 1184.30/297.19 , activate(n__from(X)) -> from(X) 1184.30/297.19 , dbls(X) -> n__dbls(X) 1184.30/297.19 , dbls(nil()) -> nil() 1184.30/297.19 , dbls(cons(X, Y)) -> 1184.30/297.19 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 1184.30/297.19 , sel(X1, X2) -> n__sel(X1, X2) 1184.30/297.19 , sel(0(), cons(X, Y)) -> activate(X) 1184.30/297.19 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) 1184.30/297.19 , indx(X1, X2) -> n__indx(X1, X2) 1184.30/297.19 , indx(nil(), X) -> nil() 1184.30/297.19 , indx(cons(X, Y), Z) -> 1184.30/297.19 cons(n__sel(activate(X), activate(Z)), 1184.30/297.19 n__indx(activate(Y), activate(Z))) 1184.30/297.19 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 1184.30/297.19 , from(X) -> n__from(X) } 1184.30/297.19 Obligation: 1184.30/297.19 runtime complexity 1184.30/297.19 Answer: 1184.30/297.19 MAYBE 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.30/297.19 following reason: 1184.30/297.19 1184.30/297.19 Computation stopped due to timeout after 297.0 seconds. 1184.30/297.19 1184.30/297.19 2) 'Best' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.30/297.19 seconds)' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'empty' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 2) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'empty' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 2) 'Fastest' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'empty' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 2) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'empty' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 2) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'empty' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 2) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 1184.30/297.19 1184.30/297.19 1184.30/297.19 2) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'empty' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 2) 'With Problem ...' failed due to the following reason: 1184.30/297.19 1184.30/297.19 Empty strict component of the problem is NOT empty. 1184.30/297.19 1184.30/297.19 1184.30/297.19 1184.30/297.19 1184.30/297.19 1184.30/297.19 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.30/297.19 failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.30/297.19 failed due to the following reason: 1184.30/297.19 1184.30/297.19 match-boundness of the problem could not be verified. 1184.30/297.19 1184.30/297.19 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.30/297.19 failed due to the following reason: 1184.30/297.19 1184.30/297.19 match-boundness of the problem could not be verified. 1184.30/297.19 1184.30/297.19 1184.30/297.19 3) 'Best' failed due to the following reason: 1184.30/297.19 1184.30/297.19 None of the processors succeeded. 1184.30/297.19 1184.30/297.19 Details of failed attempt(s): 1184.30/297.19 ----------------------------- 1184.30/297.19 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.30/297.19 following reason: 1184.30/297.19 1184.30/297.19 The processor is inapplicable, reason: 1184.30/297.19 Processor only applicable for innermost runtime complexity analysis 1184.30/297.19 1184.30/297.19 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.30/297.19 to the following reason: 1184.30/297.19 1184.30/297.19 The processor is inapplicable, reason: 1184.30/297.19 Processor only applicable for innermost runtime complexity analysis 1184.30/297.19 1184.30/297.19 1184.30/297.19 1184.30/297.19 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.30/297.19 the following reason: 1184.30/297.19 1184.30/297.19 We add the following weak dependency pairs: 1184.30/297.19 1184.30/297.19 Strict DPs: 1184.30/297.19 { dbl^#(X) -> c_1(X) 1184.30/297.19 , dbl^#(0()) -> c_2() 1184.30/297.19 , dbl^#(s(X)) -> c_3(s^#(n__s(n__dbl(activate(X))))) 1184.30/297.19 , s^#(X) -> c_4(X) 1184.30/297.19 , activate^#(X) -> c_5(X) 1184.30/297.19 , activate^#(n__s(X)) -> c_6(s^#(X)) 1184.30/297.19 , activate^#(n__dbl(X)) -> c_7(dbl^#(X)) 1184.30/297.19 , activate^#(n__dbls(X)) -> c_8(dbls^#(X)) 1184.30/297.19 , activate^#(n__sel(X1, X2)) -> c_9(sel^#(X1, X2)) 1184.30/297.19 , activate^#(n__indx(X1, X2)) -> c_10(indx^#(X1, X2)) 1184.30/297.19 , activate^#(n__from(X)) -> c_11(from^#(X)) 1184.30/297.19 , dbls^#(X) -> c_12(X) 1184.30/297.19 , dbls^#(nil()) -> c_13() 1184.30/297.19 , dbls^#(cons(X, Y)) -> c_14(activate^#(X), activate^#(Y)) 1184.30/297.19 , sel^#(X1, X2) -> c_15(X1, X2) 1184.30/297.19 , sel^#(0(), cons(X, Y)) -> c_16(activate^#(X)) 1184.30/297.19 , sel^#(s(X), cons(Y, Z)) -> c_17(sel^#(activate(X), activate(Z))) 1184.30/297.19 , indx^#(X1, X2) -> c_18(X1, X2) 1184.30/297.19 , indx^#(nil(), X) -> c_19() 1184.30/297.19 , indx^#(cons(X, Y), Z) -> 1184.30/297.19 c_20(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 1184.30/297.19 , from^#(X) -> c_21(activate^#(X), activate^#(X)) 1184.30/297.19 , from^#(X) -> c_22(X) } 1184.30/297.19 1184.30/297.19 and mark the set of starting terms. 1184.30/297.19 1184.30/297.19 We are left with following problem, upon which TcT provides the 1184.30/297.19 certificate MAYBE. 1184.30/297.19 1184.30/297.19 Strict DPs: 1184.30/297.19 { dbl^#(X) -> c_1(X) 1184.30/297.19 , dbl^#(0()) -> c_2() 1184.30/297.19 , dbl^#(s(X)) -> c_3(s^#(n__s(n__dbl(activate(X))))) 1184.30/297.19 , s^#(X) -> c_4(X) 1184.30/297.19 , activate^#(X) -> c_5(X) 1184.30/297.19 , activate^#(n__s(X)) -> c_6(s^#(X)) 1184.30/297.19 , activate^#(n__dbl(X)) -> c_7(dbl^#(X)) 1184.30/297.19 , activate^#(n__dbls(X)) -> c_8(dbls^#(X)) 1184.30/297.19 , activate^#(n__sel(X1, X2)) -> c_9(sel^#(X1, X2)) 1184.30/297.19 , activate^#(n__indx(X1, X2)) -> c_10(indx^#(X1, X2)) 1184.30/297.19 , activate^#(n__from(X)) -> c_11(from^#(X)) 1184.30/297.19 , dbls^#(X) -> c_12(X) 1184.30/297.19 , dbls^#(nil()) -> c_13() 1184.30/297.19 , dbls^#(cons(X, Y)) -> c_14(activate^#(X), activate^#(Y)) 1184.30/297.19 , sel^#(X1, X2) -> c_15(X1, X2) 1184.30/297.19 , sel^#(0(), cons(X, Y)) -> c_16(activate^#(X)) 1184.30/297.19 , sel^#(s(X), cons(Y, Z)) -> c_17(sel^#(activate(X), activate(Z))) 1184.30/297.19 , indx^#(X1, X2) -> c_18(X1, X2) 1184.30/297.19 , indx^#(nil(), X) -> c_19() 1184.30/297.19 , indx^#(cons(X, Y), Z) -> 1184.30/297.19 c_20(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 1184.69/297.22 , from^#(X) -> c_21(activate^#(X), activate^#(X)) 1184.69/297.22 , from^#(X) -> c_22(X) } 1184.69/297.22 Strict Trs: 1184.69/297.22 { dbl(X) -> n__dbl(X) 1184.69/297.22 , dbl(0()) -> 0() 1184.69/297.22 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 1184.69/297.22 , s(X) -> n__s(X) 1184.69/297.22 , activate(X) -> X 1184.69/297.22 , activate(n__s(X)) -> s(X) 1184.69/297.22 , activate(n__dbl(X)) -> dbl(X) 1184.69/297.22 , activate(n__dbls(X)) -> dbls(X) 1184.69/297.22 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1184.69/297.22 , activate(n__indx(X1, X2)) -> indx(X1, X2) 1184.69/297.22 , activate(n__from(X)) -> from(X) 1184.69/297.22 , dbls(X) -> n__dbls(X) 1184.69/297.22 , dbls(nil()) -> nil() 1184.69/297.22 , dbls(cons(X, Y)) -> 1184.69/297.22 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 1184.69/297.22 , sel(X1, X2) -> n__sel(X1, X2) 1184.69/297.22 , sel(0(), cons(X, Y)) -> activate(X) 1184.69/297.22 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) 1184.69/297.22 , indx(X1, X2) -> n__indx(X1, X2) 1184.69/297.22 , indx(nil(), X) -> nil() 1184.69/297.22 , indx(cons(X, Y), Z) -> 1184.69/297.22 cons(n__sel(activate(X), activate(Z)), 1184.69/297.22 n__indx(activate(Y), activate(Z))) 1184.69/297.22 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 1184.69/297.22 , from(X) -> n__from(X) } 1184.69/297.22 Obligation: 1184.69/297.22 runtime complexity 1184.69/297.22 Answer: 1184.69/297.22 MAYBE 1184.69/297.22 1184.69/297.22 We estimate the number of application of {2,13,19} by applications 1184.69/297.22 of Pre({2,13,19}) = {1,4,5,7,8,10,12,15,18,22}. Here rules are 1184.69/297.22 labeled as follows: 1184.69/297.22 1184.69/297.22 DPs: 1184.69/297.22 { 1: dbl^#(X) -> c_1(X) 1184.69/297.22 , 2: dbl^#(0()) -> c_2() 1184.69/297.22 , 3: dbl^#(s(X)) -> c_3(s^#(n__s(n__dbl(activate(X))))) 1184.69/297.22 , 4: s^#(X) -> c_4(X) 1184.69/297.22 , 5: activate^#(X) -> c_5(X) 1184.69/297.22 , 6: activate^#(n__s(X)) -> c_6(s^#(X)) 1184.69/297.22 , 7: activate^#(n__dbl(X)) -> c_7(dbl^#(X)) 1184.69/297.22 , 8: activate^#(n__dbls(X)) -> c_8(dbls^#(X)) 1184.69/297.22 , 9: activate^#(n__sel(X1, X2)) -> c_9(sel^#(X1, X2)) 1184.69/297.22 , 10: activate^#(n__indx(X1, X2)) -> c_10(indx^#(X1, X2)) 1184.69/297.22 , 11: activate^#(n__from(X)) -> c_11(from^#(X)) 1184.69/297.22 , 12: dbls^#(X) -> c_12(X) 1184.69/297.22 , 13: dbls^#(nil()) -> c_13() 1184.69/297.22 , 14: dbls^#(cons(X, Y)) -> c_14(activate^#(X), activate^#(Y)) 1184.69/297.22 , 15: sel^#(X1, X2) -> c_15(X1, X2) 1184.69/297.22 , 16: sel^#(0(), cons(X, Y)) -> c_16(activate^#(X)) 1184.69/297.22 , 17: sel^#(s(X), cons(Y, Z)) -> 1184.69/297.22 c_17(sel^#(activate(X), activate(Z))) 1184.69/297.22 , 18: indx^#(X1, X2) -> c_18(X1, X2) 1184.69/297.22 , 19: indx^#(nil(), X) -> c_19() 1184.69/297.22 , 20: indx^#(cons(X, Y), Z) -> 1184.69/297.22 c_20(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 1184.69/297.22 , 21: from^#(X) -> c_21(activate^#(X), activate^#(X)) 1184.69/297.22 , 22: from^#(X) -> c_22(X) } 1184.69/297.22 1184.69/297.22 We are left with following problem, upon which TcT provides the 1184.69/297.22 certificate MAYBE. 1184.69/297.22 1184.69/297.22 Strict DPs: 1184.69/297.22 { dbl^#(X) -> c_1(X) 1184.69/297.22 , dbl^#(s(X)) -> c_3(s^#(n__s(n__dbl(activate(X))))) 1184.69/297.22 , s^#(X) -> c_4(X) 1184.69/297.22 , activate^#(X) -> c_5(X) 1184.69/297.22 , activate^#(n__s(X)) -> c_6(s^#(X)) 1184.69/297.22 , activate^#(n__dbl(X)) -> c_7(dbl^#(X)) 1184.69/297.22 , activate^#(n__dbls(X)) -> c_8(dbls^#(X)) 1184.69/297.22 , activate^#(n__sel(X1, X2)) -> c_9(sel^#(X1, X2)) 1184.69/297.22 , activate^#(n__indx(X1, X2)) -> c_10(indx^#(X1, X2)) 1184.69/297.22 , activate^#(n__from(X)) -> c_11(from^#(X)) 1184.69/297.22 , dbls^#(X) -> c_12(X) 1184.69/297.22 , dbls^#(cons(X, Y)) -> c_14(activate^#(X), activate^#(Y)) 1184.69/297.22 , sel^#(X1, X2) -> c_15(X1, X2) 1184.69/297.22 , sel^#(0(), cons(X, Y)) -> c_16(activate^#(X)) 1184.69/297.22 , sel^#(s(X), cons(Y, Z)) -> c_17(sel^#(activate(X), activate(Z))) 1184.69/297.22 , indx^#(X1, X2) -> c_18(X1, X2) 1184.69/297.22 , indx^#(cons(X, Y), Z) -> 1184.69/297.22 c_20(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 1184.69/297.22 , from^#(X) -> c_21(activate^#(X), activate^#(X)) 1184.69/297.22 , from^#(X) -> c_22(X) } 1184.69/297.22 Strict Trs: 1184.69/297.22 { dbl(X) -> n__dbl(X) 1184.69/297.22 , dbl(0()) -> 0() 1184.69/297.22 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 1184.69/297.22 , s(X) -> n__s(X) 1184.69/297.22 , activate(X) -> X 1184.69/297.22 , activate(n__s(X)) -> s(X) 1184.69/297.22 , activate(n__dbl(X)) -> dbl(X) 1184.69/297.22 , activate(n__dbls(X)) -> dbls(X) 1184.69/297.22 , activate(n__sel(X1, X2)) -> sel(X1, X2) 1184.69/297.22 , activate(n__indx(X1, X2)) -> indx(X1, X2) 1184.69/297.22 , activate(n__from(X)) -> from(X) 1184.69/297.22 , dbls(X) -> n__dbls(X) 1184.69/297.22 , dbls(nil()) -> nil() 1184.69/297.22 , dbls(cons(X, Y)) -> 1184.69/297.22 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 1184.69/297.22 , sel(X1, X2) -> n__sel(X1, X2) 1184.69/297.22 , sel(0(), cons(X, Y)) -> activate(X) 1184.69/297.22 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) 1184.69/297.22 , indx(X1, X2) -> n__indx(X1, X2) 1184.69/297.22 , indx(nil(), X) -> nil() 1184.69/297.22 , indx(cons(X, Y), Z) -> 1184.69/297.22 cons(n__sel(activate(X), activate(Z)), 1184.69/297.22 n__indx(activate(Y), activate(Z))) 1184.69/297.22 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 1184.69/297.22 , from(X) -> n__from(X) } 1184.69/297.22 Weak DPs: 1184.69/297.22 { dbl^#(0()) -> c_2() 1184.69/297.22 , dbls^#(nil()) -> c_13() 1184.69/297.22 , indx^#(nil(), X) -> c_19() } 1184.69/297.22 Obligation: 1184.69/297.22 runtime complexity 1184.69/297.22 Answer: 1184.69/297.22 MAYBE 1184.69/297.22 1184.69/297.22 Empty strict component of the problem is NOT empty. 1184.69/297.22 1184.69/297.22 1184.69/297.22 Arrrr.. 1185.56/298.04 EOF