MAYBE 1185.15/297.42 MAYBE 1185.15/297.42 1185.15/297.42 We are left with following problem, upon which TcT provides the 1185.15/297.42 certificate MAYBE. 1185.15/297.42 1185.15/297.42 Strict Trs: 1185.15/297.42 { a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) 1185.15/297.42 , a__terms(X) -> terms(X) 1185.15/297.42 , a__sqr(X) -> sqr(X) 1185.15/297.42 , a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1185.15/297.42 , a__sqr(0()) -> 0() 1185.15/297.42 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1185.15/297.42 , mark(recip(X)) -> recip(mark(X)) 1185.15/297.42 , mark(terms(X)) -> a__terms(mark(X)) 1185.15/297.42 , mark(s(X)) -> s(X) 1185.15/297.42 , mark(0()) -> 0() 1185.15/297.42 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1185.15/297.42 , mark(sqr(X)) -> a__sqr(mark(X)) 1185.15/297.42 , mark(dbl(X)) -> a__dbl(mark(X)) 1185.15/297.42 , mark(nil()) -> nil() 1185.15/297.42 , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) 1185.15/297.42 , a__dbl(X) -> dbl(X) 1185.15/297.42 , a__dbl(s(X)) -> s(s(dbl(X))) 1185.15/297.42 , a__dbl(0()) -> 0() 1185.15/297.42 , a__add(X1, X2) -> add(X1, X2) 1185.15/297.42 , a__add(s(X), Y) -> s(add(X, Y)) 1185.15/297.42 , a__add(0(), X) -> mark(X) 1185.15/297.42 , a__first(X1, X2) -> first(X1, X2) 1185.15/297.42 , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) 1185.15/297.42 , a__first(0(), X) -> nil() } 1185.15/297.42 Obligation: 1185.15/297.42 runtime complexity 1185.15/297.42 Answer: 1185.15/297.42 MAYBE 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1185.15/297.42 following reason: 1185.15/297.42 1185.15/297.42 Computation stopped due to timeout after 297.0 seconds. 1185.15/297.42 1185.15/297.42 2) 'Best' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1185.15/297.42 seconds)' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'empty' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 2) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'empty' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 2) 'Fastest' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'empty' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 2) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'empty' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 2) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'empty' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 2) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 1185.15/297.42 1185.15/297.42 1185.15/297.42 2) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'empty' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 2) 'With Problem ...' failed due to the following reason: 1185.15/297.42 1185.15/297.42 Empty strict component of the problem is NOT empty. 1185.15/297.42 1185.15/297.42 1185.15/297.42 1185.15/297.42 1185.15/297.42 1185.15/297.42 2) 'Best' failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1185.15/297.42 following reason: 1185.15/297.42 1185.15/297.42 The processor is inapplicable, reason: 1185.15/297.42 Processor only applicable for innermost runtime complexity analysis 1185.15/297.42 1185.15/297.42 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1185.15/297.42 to the following reason: 1185.15/297.42 1185.15/297.42 The processor is inapplicable, reason: 1185.15/297.42 Processor only applicable for innermost runtime complexity analysis 1185.15/297.42 1185.15/297.42 1185.15/297.42 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1185.15/297.42 failed due to the following reason: 1185.15/297.42 1185.15/297.42 None of the processors succeeded. 1185.15/297.42 1185.15/297.42 Details of failed attempt(s): 1185.15/297.42 ----------------------------- 1185.15/297.42 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1185.15/297.42 failed due to the following reason: 1185.15/297.42 1185.15/297.42 match-boundness of the problem could not be verified. 1185.15/297.42 1185.15/297.42 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1185.15/297.42 failed due to the following reason: 1185.15/297.42 1185.15/297.42 match-boundness of the problem could not be verified. 1185.15/297.42 1185.15/297.42 1185.15/297.42 1185.15/297.42 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1185.15/297.42 the following reason: 1185.15/297.42 1185.15/297.42 We add the following weak dependency pairs: 1185.15/297.42 1185.15/297.42 Strict DPs: 1185.15/297.42 { a__terms^#(N) -> c_1(a__sqr^#(mark(N)), N) 1185.15/297.42 , a__terms^#(X) -> c_2(X) 1185.15/297.42 , a__sqr^#(X) -> c_3(X) 1185.15/297.42 , a__sqr^#(s(X)) -> c_4(X, X) 1185.15/297.42 , a__sqr^#(0()) -> c_5() 1185.15/297.42 , mark^#(cons(X1, X2)) -> c_6(mark^#(X1), X2) 1185.15/297.42 , mark^#(recip(X)) -> c_7(mark^#(X)) 1185.15/297.42 , mark^#(terms(X)) -> c_8(a__terms^#(mark(X))) 1185.15/297.42 , mark^#(s(X)) -> c_9(X) 1185.15/297.42 , mark^#(0()) -> c_10() 1185.15/297.42 , mark^#(add(X1, X2)) -> c_11(a__add^#(mark(X1), mark(X2))) 1185.15/297.42 , mark^#(sqr(X)) -> c_12(a__sqr^#(mark(X))) 1185.15/297.42 , mark^#(dbl(X)) -> c_13(a__dbl^#(mark(X))) 1185.15/297.42 , mark^#(nil()) -> c_14() 1185.15/297.42 , mark^#(first(X1, X2)) -> c_15(a__first^#(mark(X1), mark(X2))) 1185.15/297.42 , a__add^#(X1, X2) -> c_19(X1, X2) 1185.15/297.42 , a__add^#(s(X), Y) -> c_20(X, Y) 1185.15/297.42 , a__add^#(0(), X) -> c_21(mark^#(X)) 1185.15/297.42 , a__dbl^#(X) -> c_16(X) 1185.15/297.42 , a__dbl^#(s(X)) -> c_17(X) 1185.15/297.42 , a__dbl^#(0()) -> c_18() 1185.15/297.42 , a__first^#(X1, X2) -> c_22(X1, X2) 1185.15/297.42 , a__first^#(s(X), cons(Y, Z)) -> c_23(mark^#(Y), X, Z) 1185.15/297.42 , a__first^#(0(), X) -> c_24() } 1185.15/297.42 1185.15/297.42 and mark the set of starting terms. 1185.15/297.42 1185.15/297.42 We are left with following problem, upon which TcT provides the 1185.15/297.42 certificate MAYBE. 1185.15/297.42 1185.15/297.42 Strict DPs: 1185.15/297.42 { a__terms^#(N) -> c_1(a__sqr^#(mark(N)), N) 1185.15/297.42 , a__terms^#(X) -> c_2(X) 1185.15/297.42 , a__sqr^#(X) -> c_3(X) 1185.15/297.42 , a__sqr^#(s(X)) -> c_4(X, X) 1185.15/297.42 , a__sqr^#(0()) -> c_5() 1185.15/297.42 , mark^#(cons(X1, X2)) -> c_6(mark^#(X1), X2) 1185.15/297.42 , mark^#(recip(X)) -> c_7(mark^#(X)) 1185.15/297.42 , mark^#(terms(X)) -> c_8(a__terms^#(mark(X))) 1185.15/297.42 , mark^#(s(X)) -> c_9(X) 1185.15/297.42 , mark^#(0()) -> c_10() 1185.15/297.42 , mark^#(add(X1, X2)) -> c_11(a__add^#(mark(X1), mark(X2))) 1185.15/297.42 , mark^#(sqr(X)) -> c_12(a__sqr^#(mark(X))) 1185.15/297.42 , mark^#(dbl(X)) -> c_13(a__dbl^#(mark(X))) 1185.15/297.42 , mark^#(nil()) -> c_14() 1185.15/297.42 , mark^#(first(X1, X2)) -> c_15(a__first^#(mark(X1), mark(X2))) 1185.15/297.42 , a__add^#(X1, X2) -> c_19(X1, X2) 1185.15/297.42 , a__add^#(s(X), Y) -> c_20(X, Y) 1185.15/297.42 , a__add^#(0(), X) -> c_21(mark^#(X)) 1185.15/297.42 , a__dbl^#(X) -> c_16(X) 1185.15/297.42 , a__dbl^#(s(X)) -> c_17(X) 1185.15/297.42 , a__dbl^#(0()) -> c_18() 1185.15/297.42 , a__first^#(X1, X2) -> c_22(X1, X2) 1185.15/297.42 , a__first^#(s(X), cons(Y, Z)) -> c_23(mark^#(Y), X, Z) 1185.15/297.44 , a__first^#(0(), X) -> c_24() } 1185.15/297.44 Strict Trs: 1185.15/297.44 { a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) 1185.15/297.44 , a__terms(X) -> terms(X) 1185.15/297.44 , a__sqr(X) -> sqr(X) 1185.15/297.44 , a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1185.15/297.44 , a__sqr(0()) -> 0() 1185.15/297.44 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1185.15/297.44 , mark(recip(X)) -> recip(mark(X)) 1185.15/297.44 , mark(terms(X)) -> a__terms(mark(X)) 1185.15/297.44 , mark(s(X)) -> s(X) 1185.15/297.44 , mark(0()) -> 0() 1185.15/297.44 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1185.15/297.44 , mark(sqr(X)) -> a__sqr(mark(X)) 1185.15/297.44 , mark(dbl(X)) -> a__dbl(mark(X)) 1185.15/297.44 , mark(nil()) -> nil() 1185.15/297.44 , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) 1185.15/297.44 , a__dbl(X) -> dbl(X) 1185.15/297.44 , a__dbl(s(X)) -> s(s(dbl(X))) 1185.15/297.44 , a__dbl(0()) -> 0() 1185.15/297.44 , a__add(X1, X2) -> add(X1, X2) 1185.15/297.44 , a__add(s(X), Y) -> s(add(X, Y)) 1185.15/297.44 , a__add(0(), X) -> mark(X) 1185.15/297.44 , a__first(X1, X2) -> first(X1, X2) 1185.15/297.44 , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) 1185.15/297.44 , a__first(0(), X) -> nil() } 1185.15/297.44 Obligation: 1185.15/297.44 runtime complexity 1185.15/297.44 Answer: 1185.15/297.44 MAYBE 1185.15/297.44 1185.15/297.44 We estimate the number of application of {5,10,14,21,24} by 1185.15/297.44 applications of Pre({5,10,14,21,24}) = 1185.15/297.44 {1,2,3,4,6,7,9,12,13,15,16,17,18,19,20,22,23}. Here rules are 1185.15/297.44 labeled as follows: 1185.15/297.44 1185.15/297.44 DPs: 1185.15/297.44 { 1: a__terms^#(N) -> c_1(a__sqr^#(mark(N)), N) 1185.15/297.44 , 2: a__terms^#(X) -> c_2(X) 1185.15/297.44 , 3: a__sqr^#(X) -> c_3(X) 1185.15/297.44 , 4: a__sqr^#(s(X)) -> c_4(X, X) 1185.15/297.44 , 5: a__sqr^#(0()) -> c_5() 1185.15/297.44 , 6: mark^#(cons(X1, X2)) -> c_6(mark^#(X1), X2) 1185.15/297.44 , 7: mark^#(recip(X)) -> c_7(mark^#(X)) 1185.15/297.44 , 8: mark^#(terms(X)) -> c_8(a__terms^#(mark(X))) 1185.15/297.44 , 9: mark^#(s(X)) -> c_9(X) 1185.15/297.44 , 10: mark^#(0()) -> c_10() 1185.15/297.44 , 11: mark^#(add(X1, X2)) -> c_11(a__add^#(mark(X1), mark(X2))) 1185.15/297.44 , 12: mark^#(sqr(X)) -> c_12(a__sqr^#(mark(X))) 1185.15/297.44 , 13: mark^#(dbl(X)) -> c_13(a__dbl^#(mark(X))) 1185.15/297.44 , 14: mark^#(nil()) -> c_14() 1185.15/297.44 , 15: mark^#(first(X1, X2)) -> c_15(a__first^#(mark(X1), mark(X2))) 1185.15/297.44 , 16: a__add^#(X1, X2) -> c_19(X1, X2) 1185.15/297.44 , 17: a__add^#(s(X), Y) -> c_20(X, Y) 1185.15/297.44 , 18: a__add^#(0(), X) -> c_21(mark^#(X)) 1185.15/297.44 , 19: a__dbl^#(X) -> c_16(X) 1185.15/297.44 , 20: a__dbl^#(s(X)) -> c_17(X) 1185.15/297.44 , 21: a__dbl^#(0()) -> c_18() 1185.15/297.44 , 22: a__first^#(X1, X2) -> c_22(X1, X2) 1185.15/297.44 , 23: a__first^#(s(X), cons(Y, Z)) -> c_23(mark^#(Y), X, Z) 1185.15/297.44 , 24: a__first^#(0(), X) -> c_24() } 1185.15/297.44 1185.15/297.44 We are left with following problem, upon which TcT provides the 1185.15/297.44 certificate MAYBE. 1185.15/297.44 1185.15/297.44 Strict DPs: 1185.15/297.44 { a__terms^#(N) -> c_1(a__sqr^#(mark(N)), N) 1185.15/297.44 , a__terms^#(X) -> c_2(X) 1185.15/297.44 , a__sqr^#(X) -> c_3(X) 1185.15/297.44 , a__sqr^#(s(X)) -> c_4(X, X) 1185.15/297.44 , mark^#(cons(X1, X2)) -> c_6(mark^#(X1), X2) 1185.15/297.44 , mark^#(recip(X)) -> c_7(mark^#(X)) 1185.15/297.44 , mark^#(terms(X)) -> c_8(a__terms^#(mark(X))) 1185.15/297.44 , mark^#(s(X)) -> c_9(X) 1185.15/297.44 , mark^#(add(X1, X2)) -> c_11(a__add^#(mark(X1), mark(X2))) 1185.15/297.44 , mark^#(sqr(X)) -> c_12(a__sqr^#(mark(X))) 1185.15/297.44 , mark^#(dbl(X)) -> c_13(a__dbl^#(mark(X))) 1185.15/297.44 , mark^#(first(X1, X2)) -> c_15(a__first^#(mark(X1), mark(X2))) 1185.15/297.44 , a__add^#(X1, X2) -> c_19(X1, X2) 1185.15/297.44 , a__add^#(s(X), Y) -> c_20(X, Y) 1185.15/297.44 , a__add^#(0(), X) -> c_21(mark^#(X)) 1185.15/297.44 , a__dbl^#(X) -> c_16(X) 1185.15/297.44 , a__dbl^#(s(X)) -> c_17(X) 1185.15/297.44 , a__first^#(X1, X2) -> c_22(X1, X2) 1185.15/297.44 , a__first^#(s(X), cons(Y, Z)) -> c_23(mark^#(Y), X, Z) } 1185.15/297.44 Strict Trs: 1185.15/297.44 { a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) 1185.15/297.44 , a__terms(X) -> terms(X) 1185.15/297.44 , a__sqr(X) -> sqr(X) 1185.15/297.44 , a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1185.15/297.44 , a__sqr(0()) -> 0() 1185.15/297.44 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1185.15/297.44 , mark(recip(X)) -> recip(mark(X)) 1185.15/297.44 , mark(terms(X)) -> a__terms(mark(X)) 1185.15/297.44 , mark(s(X)) -> s(X) 1185.15/297.44 , mark(0()) -> 0() 1185.15/297.44 , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) 1185.15/297.44 , mark(sqr(X)) -> a__sqr(mark(X)) 1185.15/297.44 , mark(dbl(X)) -> a__dbl(mark(X)) 1185.15/297.44 , mark(nil()) -> nil() 1185.15/297.44 , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) 1185.15/297.44 , a__dbl(X) -> dbl(X) 1185.15/297.44 , a__dbl(s(X)) -> s(s(dbl(X))) 1185.15/297.44 , a__dbl(0()) -> 0() 1185.15/297.44 , a__add(X1, X2) -> add(X1, X2) 1185.15/297.44 , a__add(s(X), Y) -> s(add(X, Y)) 1185.15/297.44 , a__add(0(), X) -> mark(X) 1185.15/297.44 , a__first(X1, X2) -> first(X1, X2) 1185.15/297.44 , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) 1185.15/297.44 , a__first(0(), X) -> nil() } 1185.15/297.44 Weak DPs: 1185.15/297.44 { a__sqr^#(0()) -> c_5() 1185.15/297.44 , mark^#(0()) -> c_10() 1185.15/297.44 , mark^#(nil()) -> c_14() 1185.15/297.44 , a__dbl^#(0()) -> c_18() 1185.15/297.44 , a__first^#(0(), X) -> c_24() } 1185.15/297.44 Obligation: 1185.15/297.44 runtime complexity 1185.15/297.44 Answer: 1185.15/297.44 MAYBE 1185.15/297.44 1185.15/297.44 Empty strict component of the problem is NOT empty. 1185.15/297.44 1185.15/297.44 1185.15/297.44 Arrrr.. 1185.70/297.88 EOF