MAYBE 1185.47/297.30 MAYBE 1185.47/297.30 1185.47/297.30 We are left with following problem, upon which TcT provides the 1185.47/297.30 certificate MAYBE. 1185.47/297.30 1185.47/297.30 Strict Trs: 1185.47/297.30 { terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) 1185.47/297.30 , terms(X) -> n__terms(X) 1185.47/297.30 , sqr(X) -> n__sqr(X) 1185.47/297.30 , sqr(0()) -> 0() 1185.47/297.30 , sqr(s(X)) -> s(n__add(n__sqr(activate(X)), n__dbl(activate(X)))) 1185.47/297.30 , s(X) -> n__s(X) 1185.47/297.30 , activate(X) -> X 1185.47/297.30 , activate(n__terms(X)) -> terms(activate(X)) 1185.47/297.30 , activate(n__s(X)) -> s(X) 1185.47/297.30 , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) 1185.47/297.30 , activate(n__sqr(X)) -> sqr(activate(X)) 1185.47/297.30 , activate(n__dbl(X)) -> dbl(activate(X)) 1185.47/297.30 , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) 1185.47/297.30 , dbl(X) -> n__dbl(X) 1185.47/297.30 , dbl(0()) -> 0() 1185.47/297.30 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 1185.47/297.30 , add(X1, X2) -> n__add(X1, X2) 1185.47/297.30 , add(0(), X) -> X 1185.47/297.30 , add(s(X), Y) -> s(n__add(activate(X), Y)) 1185.47/297.30 , first(X1, X2) -> n__first(X1, X2) 1185.47/297.30 , first(0(), X) -> nil() 1185.47/297.30 , first(s(X), cons(Y, Z)) -> 1185.47/297.30 cons(Y, n__first(activate(X), activate(Z))) } 1185.47/297.30 Obligation: 1185.47/297.30 runtime complexity 1185.47/297.30 Answer: 1185.47/297.30 MAYBE 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1185.47/297.30 following reason: 1185.47/297.30 1185.47/297.30 Computation stopped due to timeout after 297.0 seconds. 1185.47/297.30 1185.47/297.30 2) 'Best' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1185.47/297.30 seconds)' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'empty' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 2) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'empty' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 2) 'Fastest' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'empty' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 2) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'empty' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 2) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'empty' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 2) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 1185.47/297.30 1185.47/297.30 1185.47/297.30 2) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'empty' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 2) 'With Problem ...' failed due to the following reason: 1185.47/297.30 1185.47/297.30 Empty strict component of the problem is NOT empty. 1185.47/297.30 1185.47/297.30 1185.47/297.30 1185.47/297.30 1185.47/297.30 1185.47/297.30 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1185.47/297.30 failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1185.47/297.30 failed due to the following reason: 1185.47/297.30 1185.47/297.30 match-boundness of the problem could not be verified. 1185.47/297.30 1185.47/297.30 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 1185.47/297.30 failed due to the following reason: 1185.47/297.30 1185.47/297.30 match-boundness of the problem could not be verified. 1185.47/297.30 1185.47/297.30 1185.47/297.30 3) 'Best' failed due to the following reason: 1185.47/297.30 1185.47/297.30 None of the processors succeeded. 1185.47/297.30 1185.47/297.30 Details of failed attempt(s): 1185.47/297.30 ----------------------------- 1185.47/297.30 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1185.47/297.30 to the following reason: 1185.47/297.30 1185.47/297.30 The processor is inapplicable, reason: 1185.47/297.30 Processor only applicable for innermost runtime complexity analysis 1185.47/297.30 1185.47/297.30 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1185.47/297.30 following reason: 1185.47/297.30 1185.47/297.30 The processor is inapplicable, reason: 1185.47/297.30 Processor only applicable for innermost runtime complexity analysis 1185.47/297.30 1185.47/297.30 1185.47/297.30 1185.47/297.30 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1185.47/297.30 the following reason: 1185.47/297.30 1185.47/297.30 We add the following weak dependency pairs: 1185.47/297.30 1185.47/297.30 Strict DPs: 1185.47/297.30 { terms^#(N) -> c_1(sqr^#(N), N) 1185.47/297.30 , terms^#(X) -> c_2(X) 1185.47/297.30 , sqr^#(X) -> c_3(X) 1185.47/297.30 , sqr^#(0()) -> c_4() 1185.47/297.30 , sqr^#(s(X)) -> 1185.47/297.30 c_5(s^#(n__add(n__sqr(activate(X)), n__dbl(activate(X))))) 1185.47/297.30 , s^#(X) -> c_6(X) 1185.47/297.30 , activate^#(X) -> c_7(X) 1185.47/297.30 , activate^#(n__terms(X)) -> c_8(terms^#(activate(X))) 1185.47/297.30 , activate^#(n__s(X)) -> c_9(s^#(X)) 1185.47/297.30 , activate^#(n__add(X1, X2)) -> 1185.47/297.30 c_10(add^#(activate(X1), activate(X2))) 1185.47/297.30 , activate^#(n__sqr(X)) -> c_11(sqr^#(activate(X))) 1185.47/297.30 , activate^#(n__dbl(X)) -> c_12(dbl^#(activate(X))) 1185.47/297.30 , activate^#(n__first(X1, X2)) -> 1185.47/297.30 c_13(first^#(activate(X1), activate(X2))) 1185.47/297.30 , add^#(X1, X2) -> c_17(X1, X2) 1185.47/297.30 , add^#(0(), X) -> c_18(X) 1185.47/297.30 , add^#(s(X), Y) -> c_19(s^#(n__add(activate(X), Y))) 1185.47/297.30 , dbl^#(X) -> c_14(X) 1185.47/297.30 , dbl^#(0()) -> c_15() 1185.47/297.30 , dbl^#(s(X)) -> c_16(s^#(n__s(n__dbl(activate(X))))) 1185.47/297.30 , first^#(X1, X2) -> c_20(X1, X2) 1185.47/297.30 , first^#(0(), X) -> c_21() 1185.47/297.30 , first^#(s(X), cons(Y, Z)) -> 1185.47/297.30 c_22(Y, activate^#(X), activate^#(Z)) } 1185.47/297.30 1185.47/297.30 and mark the set of starting terms. 1185.47/297.30 1185.47/297.30 We are left with following problem, upon which TcT provides the 1185.47/297.30 certificate MAYBE. 1185.47/297.30 1185.47/297.30 Strict DPs: 1185.47/297.30 { terms^#(N) -> c_1(sqr^#(N), N) 1185.47/297.30 , terms^#(X) -> c_2(X) 1185.47/297.30 , sqr^#(X) -> c_3(X) 1185.47/297.30 , sqr^#(0()) -> c_4() 1185.47/297.30 , sqr^#(s(X)) -> 1185.47/297.30 c_5(s^#(n__add(n__sqr(activate(X)), n__dbl(activate(X))))) 1185.47/297.30 , s^#(X) -> c_6(X) 1185.47/297.30 , activate^#(X) -> c_7(X) 1185.47/297.30 , activate^#(n__terms(X)) -> c_8(terms^#(activate(X))) 1185.47/297.30 , activate^#(n__s(X)) -> c_9(s^#(X)) 1185.47/297.30 , activate^#(n__add(X1, X2)) -> 1185.47/297.30 c_10(add^#(activate(X1), activate(X2))) 1185.47/297.30 , activate^#(n__sqr(X)) -> c_11(sqr^#(activate(X))) 1185.47/297.30 , activate^#(n__dbl(X)) -> c_12(dbl^#(activate(X))) 1185.47/297.30 , activate^#(n__first(X1, X2)) -> 1185.47/297.30 c_13(first^#(activate(X1), activate(X2))) 1185.47/297.30 , add^#(X1, X2) -> c_17(X1, X2) 1185.47/297.30 , add^#(0(), X) -> c_18(X) 1185.47/297.30 , add^#(s(X), Y) -> c_19(s^#(n__add(activate(X), Y))) 1185.47/297.30 , dbl^#(X) -> c_14(X) 1185.47/297.30 , dbl^#(0()) -> c_15() 1185.47/297.30 , dbl^#(s(X)) -> c_16(s^#(n__s(n__dbl(activate(X))))) 1185.47/297.31 , first^#(X1, X2) -> c_20(X1, X2) 1185.47/297.31 , first^#(0(), X) -> c_21() 1185.47/297.31 , first^#(s(X), cons(Y, Z)) -> 1185.47/297.31 c_22(Y, activate^#(X), activate^#(Z)) } 1185.47/297.31 Strict Trs: 1185.47/297.31 { terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) 1185.47/297.31 , terms(X) -> n__terms(X) 1185.47/297.31 , sqr(X) -> n__sqr(X) 1185.47/297.31 , sqr(0()) -> 0() 1185.47/297.31 , sqr(s(X)) -> s(n__add(n__sqr(activate(X)), n__dbl(activate(X)))) 1185.47/297.31 , s(X) -> n__s(X) 1185.47/297.31 , activate(X) -> X 1185.47/297.31 , activate(n__terms(X)) -> terms(activate(X)) 1185.47/297.31 , activate(n__s(X)) -> s(X) 1185.47/297.31 , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) 1185.47/297.31 , activate(n__sqr(X)) -> sqr(activate(X)) 1185.47/297.31 , activate(n__dbl(X)) -> dbl(activate(X)) 1185.47/297.31 , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) 1185.47/297.31 , dbl(X) -> n__dbl(X) 1185.47/297.31 , dbl(0()) -> 0() 1185.47/297.31 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 1185.47/297.31 , add(X1, X2) -> n__add(X1, X2) 1185.47/297.31 , add(0(), X) -> X 1185.47/297.31 , add(s(X), Y) -> s(n__add(activate(X), Y)) 1185.47/297.31 , first(X1, X2) -> n__first(X1, X2) 1185.47/297.31 , first(0(), X) -> nil() 1185.47/297.31 , first(s(X), cons(Y, Z)) -> 1185.47/297.31 cons(Y, n__first(activate(X), activate(Z))) } 1185.47/297.31 Obligation: 1185.47/297.31 runtime complexity 1185.47/297.31 Answer: 1185.47/297.31 MAYBE 1185.47/297.31 1185.47/297.31 We estimate the number of application of {4,18,21} by applications 1185.47/297.31 of Pre({4,18,21}) = {1,2,3,6,7,11,12,13,14,15,17,20,22}. Here rules 1185.47/297.31 are labeled as follows: 1185.47/297.31 1185.47/297.31 DPs: 1185.47/297.31 { 1: terms^#(N) -> c_1(sqr^#(N), N) 1185.47/297.31 , 2: terms^#(X) -> c_2(X) 1185.47/297.31 , 3: sqr^#(X) -> c_3(X) 1185.47/297.31 , 4: sqr^#(0()) -> c_4() 1185.47/297.31 , 5: sqr^#(s(X)) -> 1185.47/297.31 c_5(s^#(n__add(n__sqr(activate(X)), n__dbl(activate(X))))) 1185.47/297.31 , 6: s^#(X) -> c_6(X) 1185.47/297.31 , 7: activate^#(X) -> c_7(X) 1185.47/297.31 , 8: activate^#(n__terms(X)) -> c_8(terms^#(activate(X))) 1185.47/297.31 , 9: activate^#(n__s(X)) -> c_9(s^#(X)) 1185.47/297.31 , 10: activate^#(n__add(X1, X2)) -> 1185.47/297.31 c_10(add^#(activate(X1), activate(X2))) 1185.47/297.31 , 11: activate^#(n__sqr(X)) -> c_11(sqr^#(activate(X))) 1185.47/297.31 , 12: activate^#(n__dbl(X)) -> c_12(dbl^#(activate(X))) 1185.47/297.31 , 13: activate^#(n__first(X1, X2)) -> 1185.47/297.31 c_13(first^#(activate(X1), activate(X2))) 1185.47/297.31 , 14: add^#(X1, X2) -> c_17(X1, X2) 1185.47/297.31 , 15: add^#(0(), X) -> c_18(X) 1185.47/297.31 , 16: add^#(s(X), Y) -> c_19(s^#(n__add(activate(X), Y))) 1185.47/297.31 , 17: dbl^#(X) -> c_14(X) 1185.47/297.31 , 18: dbl^#(0()) -> c_15() 1185.47/297.31 , 19: dbl^#(s(X)) -> c_16(s^#(n__s(n__dbl(activate(X))))) 1185.47/297.31 , 20: first^#(X1, X2) -> c_20(X1, X2) 1185.47/297.31 , 21: first^#(0(), X) -> c_21() 1185.47/297.31 , 22: first^#(s(X), cons(Y, Z)) -> 1185.47/297.31 c_22(Y, activate^#(X), activate^#(Z)) } 1185.47/297.31 1185.47/297.31 We are left with following problem, upon which TcT provides the 1185.47/297.31 certificate MAYBE. 1185.47/297.31 1185.47/297.31 Strict DPs: 1185.47/297.31 { terms^#(N) -> c_1(sqr^#(N), N) 1185.47/297.31 , terms^#(X) -> c_2(X) 1185.47/297.31 , sqr^#(X) -> c_3(X) 1185.47/297.31 , sqr^#(s(X)) -> 1185.47/297.31 c_5(s^#(n__add(n__sqr(activate(X)), n__dbl(activate(X))))) 1185.47/297.31 , s^#(X) -> c_6(X) 1185.47/297.31 , activate^#(X) -> c_7(X) 1185.47/297.31 , activate^#(n__terms(X)) -> c_8(terms^#(activate(X))) 1185.47/297.31 , activate^#(n__s(X)) -> c_9(s^#(X)) 1185.47/297.31 , activate^#(n__add(X1, X2)) -> 1185.47/297.31 c_10(add^#(activate(X1), activate(X2))) 1185.47/297.31 , activate^#(n__sqr(X)) -> c_11(sqr^#(activate(X))) 1185.47/297.31 , activate^#(n__dbl(X)) -> c_12(dbl^#(activate(X))) 1185.47/297.31 , activate^#(n__first(X1, X2)) -> 1185.47/297.31 c_13(first^#(activate(X1), activate(X2))) 1185.47/297.31 , add^#(X1, X2) -> c_17(X1, X2) 1185.47/297.31 , add^#(0(), X) -> c_18(X) 1185.47/297.31 , add^#(s(X), Y) -> c_19(s^#(n__add(activate(X), Y))) 1185.47/297.31 , dbl^#(X) -> c_14(X) 1185.47/297.31 , dbl^#(s(X)) -> c_16(s^#(n__s(n__dbl(activate(X))))) 1185.47/297.31 , first^#(X1, X2) -> c_20(X1, X2) 1185.47/297.31 , first^#(s(X), cons(Y, Z)) -> 1185.47/297.31 c_22(Y, activate^#(X), activate^#(Z)) } 1185.47/297.31 Strict Trs: 1185.47/297.31 { terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) 1185.47/297.31 , terms(X) -> n__terms(X) 1185.47/297.31 , sqr(X) -> n__sqr(X) 1185.47/297.31 , sqr(0()) -> 0() 1185.47/297.31 , sqr(s(X)) -> s(n__add(n__sqr(activate(X)), n__dbl(activate(X)))) 1185.47/297.31 , s(X) -> n__s(X) 1185.47/297.31 , activate(X) -> X 1185.47/297.31 , activate(n__terms(X)) -> terms(activate(X)) 1185.47/297.31 , activate(n__s(X)) -> s(X) 1185.47/297.31 , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) 1185.47/297.31 , activate(n__sqr(X)) -> sqr(activate(X)) 1185.47/297.31 , activate(n__dbl(X)) -> dbl(activate(X)) 1185.47/297.31 , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) 1185.47/297.31 , dbl(X) -> n__dbl(X) 1185.47/297.31 , dbl(0()) -> 0() 1185.47/297.31 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 1185.47/297.31 , add(X1, X2) -> n__add(X1, X2) 1185.47/297.31 , add(0(), X) -> X 1185.47/297.31 , add(s(X), Y) -> s(n__add(activate(X), Y)) 1185.47/297.31 , first(X1, X2) -> n__first(X1, X2) 1185.47/297.31 , first(0(), X) -> nil() 1185.47/297.31 , first(s(X), cons(Y, Z)) -> 1185.47/297.31 cons(Y, n__first(activate(X), activate(Z))) } 1185.47/297.31 Weak DPs: 1185.47/297.31 { sqr^#(0()) -> c_4() 1185.47/297.31 , dbl^#(0()) -> c_15() 1185.47/297.31 , first^#(0(), X) -> c_21() } 1185.47/297.31 Obligation: 1185.47/297.31 runtime complexity 1185.47/297.31 Answer: 1185.47/297.31 MAYBE 1185.47/297.31 1185.47/297.31 Empty strict component of the problem is NOT empty. 1185.47/297.31 1185.47/297.31 1185.47/297.31 Arrrr.. 1186.38/298.14 EOF