MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(a(), b(), X) -> a__f(mark(X), X, mark(X)) , mark(a()) -> a() , mark(b()) -> b() , mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) , mark(c()) -> a__c() , a__c() -> a() , a__c() -> b() , a__c() -> c() } 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__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X))) , mark^#(a()) -> c_3() , mark^#(b()) -> c_4() , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3))) , mark^#(c()) -> c_6(a__c^#()) , a__c^#() -> c_7() , a__c^#() -> c_8() , a__c^#() -> c_9() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X))) , mark^#(a()) -> c_3() , mark^#(b()) -> c_4() , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3))) , mark^#(c()) -> c_6(a__c^#()) , a__c^#() -> c_7() , a__c^#() -> c_8() , a__c^#() -> c_9() } Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(a(), b(), X) -> a__f(mark(X), X, mark(X)) , mark(a()) -> a() , mark(b()) -> b() , mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) , mark(c()) -> a__c() , a__c() -> a() , a__c() -> b() , a__c() -> c() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,4,7,8,9} by applications of Pre({3,4,7,8,9}) = {1,6}. Here rules are labeled as follows: DPs: { 1: a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , 2: a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X))) , 3: mark^#(a()) -> c_3() , 4: mark^#(b()) -> c_4() , 5: mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3))) , 6: mark^#(c()) -> c_6(a__c^#()) , 7: a__c^#() -> c_7() , 8: a__c^#() -> c_8() , 9: a__c^#() -> c_9() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X))) , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3))) , mark^#(c()) -> c_6(a__c^#()) } Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(a(), b(), X) -> a__f(mark(X), X, mark(X)) , mark(a()) -> a() , mark(b()) -> b() , mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) , mark(c()) -> a__c() , a__c() -> a() , a__c() -> b() , a__c() -> c() } Weak DPs: { mark^#(a()) -> c_3() , mark^#(b()) -> c_4() , a__c^#() -> c_7() , a__c^#() -> c_8() , a__c^#() -> c_9() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {4} by applications of Pre({4}) = {1}. Here rules are labeled as follows: DPs: { 1: a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , 2: a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X))) , 3: mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3))) , 4: mark^#(c()) -> c_6(a__c^#()) , 5: mark^#(a()) -> c_3() , 6: mark^#(b()) -> c_4() , 7: a__c^#() -> c_7() , 8: a__c^#() -> c_8() , 9: a__c^#() -> c_9() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X))) , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3))) } Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(a(), b(), X) -> a__f(mark(X), X, mark(X)) , mark(a()) -> a() , mark(b()) -> b() , mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) , mark(c()) -> a__c() , a__c() -> a() , a__c() -> b() , a__c() -> c() } Weak DPs: { mark^#(a()) -> c_3() , mark^#(b()) -> c_4() , mark^#(c()) -> c_6(a__c^#()) , a__c^#() -> c_7() , a__c^#() -> c_8() , a__c^#() -> c_9() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..