MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { plus(0(), y) -> y , plus(s(x), y) -> s(plus(x, y)) , lt(x, 0()) -> false() , lt(0(), s(y)) -> true() , lt(s(x), s(y)) -> lt(x, y) , fib(x) -> fibiter(x, 0(), 0(), s(0())) , fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) , if(true(), b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) , if(false(), b, c, x, y) -> x } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { plus^#(0(), y) -> c_1(y) , plus^#(s(x), y) -> c_2(plus^#(x, y)) , lt^#(x, 0()) -> c_3() , lt^#(0(), s(y)) -> c_4() , lt^#(s(x), s(y)) -> c_5(lt^#(x, y)) , fib^#(x) -> c_6(fibiter^#(x, 0(), 0(), s(0()))) , fibiter^#(b, c, x, y) -> c_7(if^#(lt(c, b), b, c, x, y)) , if^#(true(), b, c, x, y) -> c_8(fibiter^#(b, s(c), y, plus(x, y))) , if^#(false(), b, c, x, y) -> c_9(x) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { plus^#(0(), y) -> c_1(y) , plus^#(s(x), y) -> c_2(plus^#(x, y)) , lt^#(x, 0()) -> c_3() , lt^#(0(), s(y)) -> c_4() , lt^#(s(x), s(y)) -> c_5(lt^#(x, y)) , fib^#(x) -> c_6(fibiter^#(x, 0(), 0(), s(0()))) , fibiter^#(b, c, x, y) -> c_7(if^#(lt(c, b), b, c, x, y)) , if^#(true(), b, c, x, y) -> c_8(fibiter^#(b, s(c), y, plus(x, y))) , if^#(false(), b, c, x, y) -> c_9(x) } Strict Trs: { plus(0(), y) -> y , plus(s(x), y) -> s(plus(x, y)) , lt(x, 0()) -> false() , lt(0(), s(y)) -> true() , lt(s(x), s(y)) -> lt(x, y) , fib(x) -> fibiter(x, 0(), 0(), s(0())) , fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) , if(true(), b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) , if(false(), b, c, x, y) -> x } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,4} by applications of Pre({3,4}) = {1,5,9}. Here rules are labeled as follows: DPs: { 1: plus^#(0(), y) -> c_1(y) , 2: plus^#(s(x), y) -> c_2(plus^#(x, y)) , 3: lt^#(x, 0()) -> c_3() , 4: lt^#(0(), s(y)) -> c_4() , 5: lt^#(s(x), s(y)) -> c_5(lt^#(x, y)) , 6: fib^#(x) -> c_6(fibiter^#(x, 0(), 0(), s(0()))) , 7: fibiter^#(b, c, x, y) -> c_7(if^#(lt(c, b), b, c, x, y)) , 8: if^#(true(), b, c, x, y) -> c_8(fibiter^#(b, s(c), y, plus(x, y))) , 9: if^#(false(), b, c, x, y) -> c_9(x) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { plus^#(0(), y) -> c_1(y) , plus^#(s(x), y) -> c_2(plus^#(x, y)) , lt^#(s(x), s(y)) -> c_5(lt^#(x, y)) , fib^#(x) -> c_6(fibiter^#(x, 0(), 0(), s(0()))) , fibiter^#(b, c, x, y) -> c_7(if^#(lt(c, b), b, c, x, y)) , if^#(true(), b, c, x, y) -> c_8(fibiter^#(b, s(c), y, plus(x, y))) , if^#(false(), b, c, x, y) -> c_9(x) } Strict Trs: { plus(0(), y) -> y , plus(s(x), y) -> s(plus(x, y)) , lt(x, 0()) -> false() , lt(0(), s(y)) -> true() , lt(s(x), s(y)) -> lt(x, y) , fib(x) -> fibiter(x, 0(), 0(), s(0())) , fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) , if(true(), b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) , if(false(), b, c, x, y) -> x } Weak DPs: { lt^#(x, 0()) -> c_3() , lt^#(0(), s(y)) -> c_4() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..