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(b(), X, c()) -> a__f(X, a__c(), X) , a__c() -> b() , a__c() -> c() , mark(b()) -> b() , mark(c()) -> a__c() , mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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. 2) '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^#(b(), X, c()) -> c_2(a__f^#(X, a__c(), X)) , a__c^#() -> c_3() , a__c^#() -> c_4() , mark^#(b()) -> c_5() , mark^#(c()) -> c_6(a__c^#()) , mark^#(f(X1, X2, X3)) -> c_7(a__f^#(X1, mark(X2), X3)) } 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^#(b(), X, c()) -> c_2(a__f^#(X, a__c(), X)) , a__c^#() -> c_3() , a__c^#() -> c_4() , mark^#(b()) -> c_5() , mark^#(c()) -> c_6(a__c^#()) , mark^#(f(X1, X2, X3)) -> c_7(a__f^#(X1, mark(X2), X3)) } Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(b(), X, c()) -> a__f(X, a__c(), X) , a__c() -> b() , a__c() -> c() , mark(b()) -> b() , mark(c()) -> a__c() , mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,4,5} by applications of Pre({3,4,5}) = {1,6}. Here rules are labeled as follows: DPs: { 1: a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , 2: a__f^#(b(), X, c()) -> c_2(a__f^#(X, a__c(), X)) , 3: a__c^#() -> c_3() , 4: a__c^#() -> c_4() , 5: mark^#(b()) -> c_5() , 6: mark^#(c()) -> c_6(a__c^#()) , 7: mark^#(f(X1, X2, X3)) -> c_7(a__f^#(X1, mark(X2), X3)) } 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^#(b(), X, c()) -> c_2(a__f^#(X, a__c(), X)) , mark^#(c()) -> c_6(a__c^#()) , mark^#(f(X1, X2, X3)) -> c_7(a__f^#(X1, mark(X2), X3)) } Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(b(), X, c()) -> a__f(X, a__c(), X) , a__c() -> b() , a__c() -> c() , mark(b()) -> b() , mark(c()) -> a__c() , mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) } Weak DPs: { a__c^#() -> c_3() , a__c^#() -> c_4() , mark^#(b()) -> c_5() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {1}. Here rules are labeled as follows: DPs: { 1: a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) , 2: a__f^#(b(), X, c()) -> c_2(a__f^#(X, a__c(), X)) , 3: mark^#(c()) -> c_6(a__c^#()) , 4: mark^#(f(X1, X2, X3)) -> c_7(a__f^#(X1, mark(X2), X3)) , 5: a__c^#() -> c_3() , 6: a__c^#() -> c_4() , 7: mark^#(b()) -> c_5() } 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^#(b(), X, c()) -> c_2(a__f^#(X, a__c(), X)) , mark^#(f(X1, X2, X3)) -> c_7(a__f^#(X1, mark(X2), X3)) } Strict Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3) , a__f(b(), X, c()) -> a__f(X, a__c(), X) , a__c() -> b() , a__c() -> c() , mark(b()) -> b() , mark(c()) -> a__c() , mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) } Weak DPs: { a__c^#() -> c_3() , a__c^#() -> c_4() , mark^#(b()) -> c_5() , mark^#(c()) -> c_6(a__c^#()) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..