MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__h(X) -> a__g(mark(X), X) , a__h(X) -> h(X) , a__g(X1, X2) -> g(X1, X2) , a__g(a(), X) -> a__f(b(), X) , mark(a()) -> a__a() , mark(b()) -> b() , mark(h(X)) -> a__h(mark(X)) , mark(g(X1, X2)) -> a__g(mark(X1), X2) , mark(f(X1, X2)) -> a__f(mark(X1), X2) , a__f(X, X) -> a__h(a__a()) , a__f(X1, X2) -> f(X1, X2) , a__a() -> a() , a__a() -> b() } 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: 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) '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) '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: { a__h^#(X) -> c_1(a__g^#(mark(X), X)) , a__h^#(X) -> c_2(X) , a__g^#(X1, X2) -> c_3(X1, X2) , a__g^#(a(), X) -> c_4(a__f^#(b(), X)) , a__f^#(X, X) -> c_10(a__h^#(a__a())) , a__f^#(X1, X2) -> c_11(X1, X2) , mark^#(a()) -> c_5(a__a^#()) , mark^#(b()) -> c_6() , mark^#(h(X)) -> c_7(a__h^#(mark(X))) , mark^#(g(X1, X2)) -> c_8(a__g^#(mark(X1), X2)) , mark^#(f(X1, X2)) -> c_9(a__f^#(mark(X1), X2)) , a__a^#() -> c_12() , a__a^#() -> c_13() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__h^#(X) -> c_1(a__g^#(mark(X), X)) , a__h^#(X) -> c_2(X) , a__g^#(X1, X2) -> c_3(X1, X2) , a__g^#(a(), X) -> c_4(a__f^#(b(), X)) , a__f^#(X, X) -> c_10(a__h^#(a__a())) , a__f^#(X1, X2) -> c_11(X1, X2) , mark^#(a()) -> c_5(a__a^#()) , mark^#(b()) -> c_6() , mark^#(h(X)) -> c_7(a__h^#(mark(X))) , mark^#(g(X1, X2)) -> c_8(a__g^#(mark(X1), X2)) , mark^#(f(X1, X2)) -> c_9(a__f^#(mark(X1), X2)) , a__a^#() -> c_12() , a__a^#() -> c_13() } Strict Trs: { a__h(X) -> a__g(mark(X), X) , a__h(X) -> h(X) , a__g(X1, X2) -> g(X1, X2) , a__g(a(), X) -> a__f(b(), X) , mark(a()) -> a__a() , mark(b()) -> b() , mark(h(X)) -> a__h(mark(X)) , mark(g(X1, X2)) -> a__g(mark(X1), X2) , mark(f(X1, X2)) -> a__f(mark(X1), X2) , a__f(X, X) -> a__h(a__a()) , a__f(X1, X2) -> f(X1, X2) , a__a() -> a() , a__a() -> b() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {8,12,13} by applications of Pre({8,12,13}) = {2,3,6,7}. Here rules are labeled as follows: DPs: { 1: a__h^#(X) -> c_1(a__g^#(mark(X), X)) , 2: a__h^#(X) -> c_2(X) , 3: a__g^#(X1, X2) -> c_3(X1, X2) , 4: a__g^#(a(), X) -> c_4(a__f^#(b(), X)) , 5: a__f^#(X, X) -> c_10(a__h^#(a__a())) , 6: a__f^#(X1, X2) -> c_11(X1, X2) , 7: mark^#(a()) -> c_5(a__a^#()) , 8: mark^#(b()) -> c_6() , 9: mark^#(h(X)) -> c_7(a__h^#(mark(X))) , 10: mark^#(g(X1, X2)) -> c_8(a__g^#(mark(X1), X2)) , 11: mark^#(f(X1, X2)) -> c_9(a__f^#(mark(X1), X2)) , 12: a__a^#() -> c_12() , 13: a__a^#() -> c_13() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__h^#(X) -> c_1(a__g^#(mark(X), X)) , a__h^#(X) -> c_2(X) , a__g^#(X1, X2) -> c_3(X1, X2) , a__g^#(a(), X) -> c_4(a__f^#(b(), X)) , a__f^#(X, X) -> c_10(a__h^#(a__a())) , a__f^#(X1, X2) -> c_11(X1, X2) , mark^#(a()) -> c_5(a__a^#()) , mark^#(h(X)) -> c_7(a__h^#(mark(X))) , mark^#(g(X1, X2)) -> c_8(a__g^#(mark(X1), X2)) , mark^#(f(X1, X2)) -> c_9(a__f^#(mark(X1), X2)) } Strict Trs: { a__h(X) -> a__g(mark(X), X) , a__h(X) -> h(X) , a__g(X1, X2) -> g(X1, X2) , a__g(a(), X) -> a__f(b(), X) , mark(a()) -> a__a() , mark(b()) -> b() , mark(h(X)) -> a__h(mark(X)) , mark(g(X1, X2)) -> a__g(mark(X1), X2) , mark(f(X1, X2)) -> a__f(mark(X1), X2) , a__f(X, X) -> a__h(a__a()) , a__f(X1, X2) -> f(X1, X2) , a__a() -> a() , a__a() -> b() } Weak DPs: { mark^#(b()) -> c_6() , a__a^#() -> c_12() , a__a^#() -> c_13() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {7} by applications of Pre({7}) = {2,3,6}. Here rules are labeled as follows: DPs: { 1: a__h^#(X) -> c_1(a__g^#(mark(X), X)) , 2: a__h^#(X) -> c_2(X) , 3: a__g^#(X1, X2) -> c_3(X1, X2) , 4: a__g^#(a(), X) -> c_4(a__f^#(b(), X)) , 5: a__f^#(X, X) -> c_10(a__h^#(a__a())) , 6: a__f^#(X1, X2) -> c_11(X1, X2) , 7: mark^#(a()) -> c_5(a__a^#()) , 8: mark^#(h(X)) -> c_7(a__h^#(mark(X))) , 9: mark^#(g(X1, X2)) -> c_8(a__g^#(mark(X1), X2)) , 10: mark^#(f(X1, X2)) -> c_9(a__f^#(mark(X1), X2)) , 11: mark^#(b()) -> c_6() , 12: a__a^#() -> c_12() , 13: a__a^#() -> c_13() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__h^#(X) -> c_1(a__g^#(mark(X), X)) , a__h^#(X) -> c_2(X) , a__g^#(X1, X2) -> c_3(X1, X2) , a__g^#(a(), X) -> c_4(a__f^#(b(), X)) , a__f^#(X, X) -> c_10(a__h^#(a__a())) , a__f^#(X1, X2) -> c_11(X1, X2) , mark^#(h(X)) -> c_7(a__h^#(mark(X))) , mark^#(g(X1, X2)) -> c_8(a__g^#(mark(X1), X2)) , mark^#(f(X1, X2)) -> c_9(a__f^#(mark(X1), X2)) } Strict Trs: { a__h(X) -> a__g(mark(X), X) , a__h(X) -> h(X) , a__g(X1, X2) -> g(X1, X2) , a__g(a(), X) -> a__f(b(), X) , mark(a()) -> a__a() , mark(b()) -> b() , mark(h(X)) -> a__h(mark(X)) , mark(g(X1, X2)) -> a__g(mark(X1), X2) , mark(f(X1, X2)) -> a__f(mark(X1), X2) , a__f(X, X) -> a__h(a__a()) , a__f(X1, X2) -> f(X1, X2) , a__a() -> a() , a__a() -> b() } Weak DPs: { mark^#(a()) -> c_5(a__a^#()) , mark^#(b()) -> c_6() , a__a^#() -> c_12() , a__a^#() -> c_13() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..