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: innermost runtime complexity Answer: MAYBE We add following dependency tuples: Strict DPs: { a__f^#(X1, X2, X3) -> c_1() , a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(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^#(X1), 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() , a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(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^#(X1), mark^#(X3)) , mark^#(c()) -> c_6(a__c^#()) , a__c^#() -> c_7() , a__c^#() -> c_8() , a__c^#() -> c_9() } Weak 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: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1,3,4,7,8,9} by applications of Pre({1,3,4,7,8,9}) = {2,5,6}. Here rules are labeled as follows: DPs: { 1: a__f^#(X1, X2, X3) -> c_1() , 2: a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(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)), mark^#(X1), 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^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(X), mark^#(X)) , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3)), mark^#(X1), mark^#(X3)) , mark^#(c()) -> c_6(a__c^#()) } Weak DPs: { a__f^#(X1, X2, X3) -> c_1() , mark^#(a()) -> c_3() , mark^#(b()) -> c_4() , a__c^#() -> c_7() , a__c^#() -> c_8() , a__c^#() -> c_9() } Weak 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: innermost runtime complexity Answer: MAYBE We estimate the number of application of {3} by applications of Pre({3}) = {1,2}. Here rules are labeled as follows: DPs: { 1: a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(X), mark^#(X)) , 2: mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3)), mark^#(X1), mark^#(X3)) , 3: mark^#(c()) -> c_6(a__c^#()) , 4: a__f^#(X1, X2, X3) -> c_1() , 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^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(X), mark^#(X)) , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3)), mark^#(X1), mark^#(X3)) } Weak DPs: { a__f^#(X1, X2, X3) -> c_1() , 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() } Weak 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: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { a__f^#(X1, X2, X3) -> c_1() , 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() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { a__f^#(a(), b(), X) -> c_2(a__f^#(mark(X), X, mark(X)), mark^#(X), mark^#(X)) , mark^#(f(X1, X2, X3)) -> c_5(a__f^#(mark(X1), X2, mark(X3)), mark^#(X1), mark^#(X3)) } Weak 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: innermost runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrices' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'matrix interpretation of dimension 4' failed due to the following reason: The input cannot be shown compatible 2) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 3) 'matrix interpretation of dimension 3' failed due to the following reason: The input cannot be shown compatible 4) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 5) 'matrix interpretation of dimension 2' failed due to the following reason: The input cannot be shown compatible 6) 'matrix interpretation of dimension 1' failed due to the following reason: The input cannot be shown compatible 2) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. Arrrr..