MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> 0() } 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: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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 2) '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 3) '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 perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { f^#(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> c_1(f^#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> c_2(f^#(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> c_3(f^#(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> c_4(f^#(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> c_5(f^#(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> c_6(f^#(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> c_7(f^#(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> c_8(f^#(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> c_9(f^#(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> c_10(f^#(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> c_11() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> c_1(f^#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> c_2(f^#(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> c_3(f^#(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> c_4(f^#(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> c_5(f^#(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> c_6(f^#(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> c_7(f^#(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> c_8(f^#(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> c_9(f^#(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> c_10(f^#(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> c_11() } Strict Trs: { f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> 0() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {11} by applications of Pre({11}) = {1,2,3,4,5,6,7,8,9,10}. Here rules are labeled as follows: DPs: { 1: f^#(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> c_1(f^#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , 2: f^#(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> c_2(f^#(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , 3: f^#(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> c_3(f^#(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10)) , 4: f^#(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> c_4(f^#(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10)) , 5: f^#(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> c_5(f^#(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10)) , 6: f^#(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> c_6(f^#(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10)) , 7: f^#(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> c_7(f^#(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10)) , 8: f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> c_8(f^#(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10)) , 9: f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> c_9(f^#(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10)) , 10: f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> c_10(f^#(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10)) , 11: f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> c_11() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> c_1(f^#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> c_2(f^#(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> c_3(f^#(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> c_4(f^#(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> c_5(f^#(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> c_6(f^#(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> c_7(f^#(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> c_8(f^#(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> c_9(f^#(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10)) , f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> c_10(f^#(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10)) } Strict Trs: { f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> 0() } Weak DPs: { f^#(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> c_11() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..