MAYBE 757.98/297.14 MAYBE 757.98/297.14 757.98/297.14 We are left with following problem, upon which TcT provides the 757.98/297.14 certificate MAYBE. 757.98/297.14 757.98/297.14 Strict Trs: 757.98/297.14 { active(terms(X)) -> terms(active(X)) 757.98/297.14 , active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N)))) 757.98/297.14 , active(cons(X1, X2)) -> cons(active(X1), X2) 757.98/297.14 , active(recip(X)) -> recip(active(X)) 757.98/297.14 , active(sqr(X)) -> sqr(active(X)) 757.98/297.14 , active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X)))) 757.98/297.14 , active(sqr(0())) -> mark(0()) 757.98/297.14 , active(s(X)) -> s(active(X)) 757.98/297.14 , active(add(X1, X2)) -> add(X1, active(X2)) 757.98/297.14 , active(add(X1, X2)) -> add(active(X1), X2) 757.98/297.14 , active(add(s(X), Y)) -> mark(s(add(X, Y))) 757.98/297.14 , active(add(0(), X)) -> mark(X) 757.98/297.14 , active(dbl(X)) -> dbl(active(X)) 757.98/297.14 , active(dbl(s(X))) -> mark(s(s(dbl(X)))) 757.98/297.14 , active(dbl(0())) -> mark(0()) 757.98/297.14 , active(first(X1, X2)) -> first(X1, active(X2)) 757.98/297.14 , active(first(X1, X2)) -> first(active(X1), X2) 757.98/297.14 , active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) 757.98/297.14 , active(first(0(), X)) -> mark(nil()) 757.98/297.14 , active(half(X)) -> half(active(X)) 757.98/297.14 , active(half(s(s(X)))) -> mark(s(half(X))) 757.98/297.14 , active(half(s(0()))) -> mark(0()) 757.98/297.14 , active(half(0())) -> mark(0()) 757.98/297.14 , active(half(dbl(X))) -> mark(X) 757.98/297.14 , terms(mark(X)) -> mark(terms(X)) 757.98/297.14 , terms(ok(X)) -> ok(terms(X)) 757.98/297.14 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 757.98/297.14 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 757.98/297.14 , recip(mark(X)) -> mark(recip(X)) 757.98/297.14 , recip(ok(X)) -> ok(recip(X)) 757.98/297.14 , sqr(mark(X)) -> mark(sqr(X)) 757.98/297.14 , sqr(ok(X)) -> ok(sqr(X)) 757.98/297.14 , s(mark(X)) -> mark(s(X)) 757.98/297.14 , s(ok(X)) -> ok(s(X)) 757.98/297.14 , add(X1, mark(X2)) -> mark(add(X1, X2)) 757.98/297.14 , add(mark(X1), X2) -> mark(add(X1, X2)) 757.98/297.14 , add(ok(X1), ok(X2)) -> ok(add(X1, X2)) 757.98/297.14 , dbl(mark(X)) -> mark(dbl(X)) 757.98/297.14 , dbl(ok(X)) -> ok(dbl(X)) 757.98/297.14 , first(X1, mark(X2)) -> mark(first(X1, X2)) 757.98/297.14 , first(mark(X1), X2) -> mark(first(X1, X2)) 757.98/297.14 , first(ok(X1), ok(X2)) -> ok(first(X1, X2)) 757.98/297.14 , half(mark(X)) -> mark(half(X)) 757.98/297.14 , half(ok(X)) -> ok(half(X)) 757.98/297.14 , proper(terms(X)) -> terms(proper(X)) 757.98/297.14 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 757.98/297.14 , proper(recip(X)) -> recip(proper(X)) 757.98/297.14 , proper(sqr(X)) -> sqr(proper(X)) 757.98/297.14 , proper(s(X)) -> s(proper(X)) 757.98/297.14 , proper(0()) -> ok(0()) 757.98/297.14 , proper(add(X1, X2)) -> add(proper(X1), proper(X2)) 757.98/297.14 , proper(dbl(X)) -> dbl(proper(X)) 757.98/297.14 , proper(first(X1, X2)) -> first(proper(X1), proper(X2)) 757.98/297.14 , proper(nil()) -> ok(nil()) 757.98/297.14 , proper(half(X)) -> half(proper(X)) 757.98/297.14 , top(mark(X)) -> top(proper(X)) 757.98/297.14 , top(ok(X)) -> top(active(X)) } 757.98/297.14 Obligation: 757.98/297.14 innermost runtime complexity 757.98/297.14 Answer: 757.98/297.14 MAYBE 757.98/297.14 757.98/297.14 None of the processors succeeded. 757.98/297.14 757.98/297.14 Details of failed attempt(s): 757.98/297.14 ----------------------------- 757.98/297.14 1) 'empty' failed due to the following reason: 757.98/297.14 757.98/297.14 Empty strict component of the problem is NOT empty. 757.98/297.14 757.98/297.14 2) 'Best' failed due to the following reason: 757.98/297.14 757.98/297.14 None of the processors succeeded. 757.98/297.14 757.98/297.14 Details of failed attempt(s): 757.98/297.14 ----------------------------- 757.98/297.14 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 757.98/297.14 following reason: 757.98/297.14 757.98/297.14 Computation stopped due to timeout after 297.0 seconds. 757.98/297.14 757.98/297.14 2) 'Best' failed due to the following reason: 757.98/297.14 757.98/297.14 None of the processors succeeded. 757.98/297.14 757.98/297.14 Details of failed attempt(s): 757.98/297.14 ----------------------------- 757.98/297.14 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 757.98/297.14 seconds)' failed due to the following reason: 757.98/297.14 757.98/297.14 Computation stopped due to timeout after 148.0 seconds. 757.98/297.14 757.98/297.14 2) 'Best' failed due to the following reason: 757.98/297.14 757.98/297.14 None of the processors succeeded. 757.98/297.14 757.98/297.14 Details of failed attempt(s): 757.98/297.14 ----------------------------- 757.98/297.14 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 757.98/297.14 following reason: 757.98/297.14 757.98/297.14 The input cannot be shown compatible 757.98/297.14 757.98/297.14 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 757.98/297.14 to the following reason: 757.98/297.14 757.98/297.14 The input cannot be shown compatible 757.98/297.14 757.98/297.14 757.98/297.14 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 757.98/297.14 failed due to the following reason: 757.98/297.14 757.98/297.14 None of the processors succeeded. 757.98/297.14 757.98/297.14 Details of failed attempt(s): 757.98/297.14 ----------------------------- 757.98/297.14 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 757.98/297.14 failed due to the following reason: 757.98/297.14 757.98/297.14 match-boundness of the problem could not be verified. 757.98/297.14 757.98/297.14 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 757.98/297.14 failed due to the following reason: 757.98/297.14 757.98/297.14 match-boundness of the problem could not be verified. 757.98/297.14 757.98/297.14 757.98/297.14 757.98/297.14 757.98/297.14 757.98/297.14 Arrrr.. 758.30/297.46 EOF