MAYBE 1184.50/297.29 MAYBE 1184.50/297.29 1184.50/297.29 We are left with following problem, upon which TcT provides the 1184.50/297.29 certificate MAYBE. 1184.50/297.29 1184.50/297.29 Strict Trs: 1184.50/297.29 { terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) 1184.50/297.29 , terms(X) -> n__terms(X) 1184.50/297.29 , sqr(0()) -> 0() 1184.50/297.29 , sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1184.50/297.29 , s(X) -> n__s(X) 1184.50/297.29 , add(0(), X) -> X 1184.50/297.29 , add(s(X), Y) -> s(add(X, Y)) 1184.50/297.29 , dbl(0()) -> 0() 1184.50/297.29 , dbl(s(X)) -> s(s(dbl(X))) 1184.50/297.29 , first(X1, X2) -> n__first(X1, X2) 1184.50/297.29 , first(0(), X) -> nil() 1184.50/297.29 , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 1184.50/297.29 , activate(X) -> X 1184.50/297.29 , activate(n__terms(X)) -> terms(activate(X)) 1184.50/297.29 , activate(n__s(X)) -> s(activate(X)) 1184.50/297.29 , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) 1184.50/297.29 , half(0()) -> 0() 1184.50/297.29 , half(s(0())) -> 0() 1184.50/297.29 , half(s(s(X))) -> s(half(X)) 1184.50/297.29 , half(dbl(X)) -> X } 1184.50/297.29 Obligation: 1184.50/297.29 runtime complexity 1184.50/297.29 Answer: 1184.50/297.29 MAYBE 1184.50/297.29 1184.50/297.29 None of the processors succeeded. 1184.50/297.29 1184.50/297.29 Details of failed attempt(s): 1184.50/297.29 ----------------------------- 1184.50/297.29 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.50/297.29 following reason: 1184.50/297.29 1184.50/297.29 Computation stopped due to timeout after 297.0 seconds. 1184.50/297.29 1184.50/297.29 2) 'Best' failed due to the following reason: 1184.50/297.29 1184.50/297.29 None of the processors succeeded. 1184.50/297.29 1184.50/297.29 Details of failed attempt(s): 1184.50/297.29 ----------------------------- 1184.50/297.29 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.50/297.29 seconds)' failed due to the following reason: 1184.50/297.29 1184.50/297.29 Computation stopped due to timeout after 148.0 seconds. 1184.50/297.29 1184.50/297.29 2) 'Best' failed due to the following reason: 1184.50/297.29 1184.50/297.29 None of the processors succeeded. 1184.50/297.29 1184.50/297.29 Details of failed attempt(s): 1184.50/297.29 ----------------------------- 1184.50/297.29 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.50/297.29 to the following reason: 1184.50/297.29 1184.50/297.29 The processor is inapplicable, reason: 1184.50/297.29 Processor only applicable for innermost runtime complexity analysis 1184.50/297.29 1184.50/297.29 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.50/297.29 following reason: 1184.50/297.29 1184.50/297.29 The processor is inapplicable, reason: 1184.50/297.29 Processor only applicable for innermost runtime complexity analysis 1184.50/297.29 1184.50/297.29 1184.50/297.29 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.50/297.29 failed due to the following reason: 1184.50/297.29 1184.50/297.29 None of the processors succeeded. 1184.50/297.29 1184.50/297.29 Details of failed attempt(s): 1184.50/297.29 ----------------------------- 1184.50/297.29 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.50/297.29 failed due to the following reason: 1184.50/297.29 1184.50/297.29 match-boundness of the problem could not be verified. 1184.50/297.29 1184.50/297.29 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.50/297.29 failed due to the following reason: 1184.50/297.29 1184.50/297.29 match-boundness of the problem could not be verified. 1184.50/297.29 1184.50/297.29 1184.50/297.29 1184.50/297.29 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.50/297.29 the following reason: 1184.50/297.29 1184.50/297.29 We add the following weak dependency pairs: 1184.50/297.29 1184.50/297.29 Strict DPs: 1184.50/297.29 { terms^#(N) -> c_1(sqr^#(N), N) 1184.50/297.29 , terms^#(X) -> c_2(X) 1184.50/297.29 , sqr^#(0()) -> c_3() 1184.50/297.29 , sqr^#(s(X)) -> c_4(s^#(add(sqr(X), dbl(X)))) 1184.50/297.29 , s^#(X) -> c_5(X) 1184.50/297.29 , add^#(0(), X) -> c_6(X) 1184.50/297.29 , add^#(s(X), Y) -> c_7(s^#(add(X, Y))) 1184.50/297.29 , dbl^#(0()) -> c_8() 1184.50/297.29 , dbl^#(s(X)) -> c_9(s^#(s(dbl(X)))) 1184.50/297.29 , first^#(X1, X2) -> c_10(X1, X2) 1184.50/297.29 , first^#(0(), X) -> c_11() 1184.50/297.29 , first^#(s(X), cons(Y, Z)) -> c_12(Y, X, activate^#(Z)) 1184.50/297.29 , activate^#(X) -> c_13(X) 1184.50/297.29 , activate^#(n__terms(X)) -> c_14(terms^#(activate(X))) 1184.50/297.29 , activate^#(n__s(X)) -> c_15(s^#(activate(X))) 1184.50/297.29 , activate^#(n__first(X1, X2)) -> 1184.50/297.29 c_16(first^#(activate(X1), activate(X2))) 1184.50/297.29 , half^#(0()) -> c_17() 1184.50/297.29 , half^#(s(0())) -> c_18() 1184.50/297.29 , half^#(s(s(X))) -> c_19(s^#(half(X))) 1184.50/297.29 , half^#(dbl(X)) -> c_20(X) } 1184.50/297.29 1184.50/297.29 and mark the set of starting terms. 1184.50/297.29 1184.50/297.29 We are left with following problem, upon which TcT provides the 1184.50/297.29 certificate MAYBE. 1184.50/297.29 1184.50/297.29 Strict DPs: 1184.50/297.29 { terms^#(N) -> c_1(sqr^#(N), N) 1184.50/297.29 , terms^#(X) -> c_2(X) 1184.50/297.29 , sqr^#(0()) -> c_3() 1184.50/297.29 , sqr^#(s(X)) -> c_4(s^#(add(sqr(X), dbl(X)))) 1184.50/297.29 , s^#(X) -> c_5(X) 1184.50/297.29 , add^#(0(), X) -> c_6(X) 1184.50/297.29 , add^#(s(X), Y) -> c_7(s^#(add(X, Y))) 1184.50/297.29 , dbl^#(0()) -> c_8() 1184.50/297.29 , dbl^#(s(X)) -> c_9(s^#(s(dbl(X)))) 1184.50/297.29 , first^#(X1, X2) -> c_10(X1, X2) 1184.50/297.29 , first^#(0(), X) -> c_11() 1184.50/297.29 , first^#(s(X), cons(Y, Z)) -> c_12(Y, X, activate^#(Z)) 1184.50/297.29 , activate^#(X) -> c_13(X) 1184.50/297.29 , activate^#(n__terms(X)) -> c_14(terms^#(activate(X))) 1184.50/297.29 , activate^#(n__s(X)) -> c_15(s^#(activate(X))) 1184.50/297.29 , activate^#(n__first(X1, X2)) -> 1184.50/297.29 c_16(first^#(activate(X1), activate(X2))) 1184.50/297.29 , half^#(0()) -> c_17() 1184.50/297.29 , half^#(s(0())) -> c_18() 1184.50/297.29 , half^#(s(s(X))) -> c_19(s^#(half(X))) 1184.50/297.29 , half^#(dbl(X)) -> c_20(X) } 1184.50/297.29 Strict Trs: 1184.50/297.29 { terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) 1184.50/297.29 , terms(X) -> n__terms(X) 1184.50/297.29 , sqr(0()) -> 0() 1184.50/297.29 , sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1184.50/297.29 , s(X) -> n__s(X) 1184.50/297.29 , add(0(), X) -> X 1184.50/297.29 , add(s(X), Y) -> s(add(X, Y)) 1184.50/297.29 , dbl(0()) -> 0() 1184.50/297.29 , dbl(s(X)) -> s(s(dbl(X))) 1184.50/297.29 , first(X1, X2) -> n__first(X1, X2) 1184.50/297.29 , first(0(), X) -> nil() 1184.50/297.29 , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 1184.50/297.29 , activate(X) -> X 1184.50/297.29 , activate(n__terms(X)) -> terms(activate(X)) 1184.50/297.29 , activate(n__s(X)) -> s(activate(X)) 1184.50/297.29 , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) 1184.50/297.29 , half(0()) -> 0() 1184.50/297.29 , half(s(0())) -> 0() 1184.50/297.29 , half(s(s(X))) -> s(half(X)) 1184.50/297.29 , half(dbl(X)) -> X } 1184.50/297.29 Obligation: 1184.50/297.29 runtime complexity 1184.50/297.29 Answer: 1184.50/297.29 MAYBE 1184.50/297.29 1184.50/297.29 We estimate the number of application of {3,8,11,17,18} by 1184.50/297.29 applications of Pre({3,8,11,17,18}) = {1,2,5,6,10,12,13,16,20}. 1184.50/297.29 Here rules are labeled as follows: 1184.50/297.29 1184.50/297.29 DPs: 1184.50/297.29 { 1: terms^#(N) -> c_1(sqr^#(N), N) 1184.50/297.29 , 2: terms^#(X) -> c_2(X) 1184.50/297.29 , 3: sqr^#(0()) -> c_3() 1184.50/297.29 , 4: sqr^#(s(X)) -> c_4(s^#(add(sqr(X), dbl(X)))) 1184.50/297.29 , 5: s^#(X) -> c_5(X) 1184.50/297.29 , 6: add^#(0(), X) -> c_6(X) 1184.50/297.29 , 7: add^#(s(X), Y) -> c_7(s^#(add(X, Y))) 1184.50/297.29 , 8: dbl^#(0()) -> c_8() 1184.50/297.29 , 9: dbl^#(s(X)) -> c_9(s^#(s(dbl(X)))) 1184.50/297.29 , 10: first^#(X1, X2) -> c_10(X1, X2) 1184.50/297.29 , 11: first^#(0(), X) -> c_11() 1184.50/297.29 , 12: first^#(s(X), cons(Y, Z)) -> c_12(Y, X, activate^#(Z)) 1184.50/297.29 , 13: activate^#(X) -> c_13(X) 1184.50/297.29 , 14: activate^#(n__terms(X)) -> c_14(terms^#(activate(X))) 1184.50/297.29 , 15: activate^#(n__s(X)) -> c_15(s^#(activate(X))) 1184.50/297.29 , 16: activate^#(n__first(X1, X2)) -> 1184.50/297.29 c_16(first^#(activate(X1), activate(X2))) 1184.50/297.29 , 17: half^#(0()) -> c_17() 1184.50/297.29 , 18: half^#(s(0())) -> c_18() 1184.50/297.29 , 19: half^#(s(s(X))) -> c_19(s^#(half(X))) 1184.50/297.29 , 20: half^#(dbl(X)) -> c_20(X) } 1184.50/297.29 1184.50/297.29 We are left with following problem, upon which TcT provides the 1184.50/297.29 certificate MAYBE. 1184.50/297.29 1184.50/297.29 Strict DPs: 1184.50/297.29 { terms^#(N) -> c_1(sqr^#(N), N) 1184.50/297.29 , terms^#(X) -> c_2(X) 1184.50/297.29 , sqr^#(s(X)) -> c_4(s^#(add(sqr(X), dbl(X)))) 1184.50/297.29 , s^#(X) -> c_5(X) 1184.50/297.29 , add^#(0(), X) -> c_6(X) 1184.50/297.29 , add^#(s(X), Y) -> c_7(s^#(add(X, Y))) 1184.50/297.29 , dbl^#(s(X)) -> c_9(s^#(s(dbl(X)))) 1184.50/297.29 , first^#(X1, X2) -> c_10(X1, X2) 1184.50/297.29 , first^#(s(X), cons(Y, Z)) -> c_12(Y, X, activate^#(Z)) 1184.50/297.29 , activate^#(X) -> c_13(X) 1184.50/297.29 , activate^#(n__terms(X)) -> c_14(terms^#(activate(X))) 1184.50/297.29 , activate^#(n__s(X)) -> c_15(s^#(activate(X))) 1184.50/297.29 , activate^#(n__first(X1, X2)) -> 1184.50/297.29 c_16(first^#(activate(X1), activate(X2))) 1184.50/297.29 , half^#(s(s(X))) -> c_19(s^#(half(X))) 1184.50/297.29 , half^#(dbl(X)) -> c_20(X) } 1184.50/297.29 Strict Trs: 1184.50/297.29 { terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) 1184.50/297.29 , terms(X) -> n__terms(X) 1184.50/297.29 , sqr(0()) -> 0() 1184.50/297.29 , sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1184.50/297.29 , s(X) -> n__s(X) 1184.50/297.29 , add(0(), X) -> X 1184.50/297.29 , add(s(X), Y) -> s(add(X, Y)) 1184.50/297.29 , dbl(0()) -> 0() 1184.50/297.29 , dbl(s(X)) -> s(s(dbl(X))) 1184.50/297.29 , first(X1, X2) -> n__first(X1, X2) 1184.50/297.29 , first(0(), X) -> nil() 1184.50/297.29 , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 1184.50/297.29 , activate(X) -> X 1184.50/297.29 , activate(n__terms(X)) -> terms(activate(X)) 1184.50/297.29 , activate(n__s(X)) -> s(activate(X)) 1184.50/297.29 , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) 1184.50/297.29 , half(0()) -> 0() 1184.50/297.29 , half(s(0())) -> 0() 1184.89/297.31 , half(s(s(X))) -> s(half(X)) 1184.89/297.31 , half(dbl(X)) -> X } 1184.89/297.31 Weak DPs: 1184.89/297.31 { sqr^#(0()) -> c_3() 1184.89/297.31 , dbl^#(0()) -> c_8() 1184.89/297.31 , first^#(0(), X) -> c_11() 1184.89/297.31 , half^#(0()) -> c_17() 1184.89/297.31 , half^#(s(0())) -> c_18() } 1184.89/297.31 Obligation: 1184.89/297.31 runtime complexity 1184.89/297.31 Answer: 1184.89/297.31 MAYBE 1184.89/297.31 1184.89/297.31 Empty strict component of the problem is NOT empty. 1184.89/297.31 1184.89/297.31 1184.89/297.31 Arrrr.. 1185.74/298.14 EOF