MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(X) -> h(activate(X)) , h(n__d()) -> g(n__c()) , activate(X) -> X , activate(n__d()) -> d() , activate(n__c()) -> c() , c() -> d() , c() -> n__c() , d() -> n__d() } Obligation: innermost runtime complexity Answer: MAYBE We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. Trs: { activate(X) -> X , activate(n__d()) -> d() , c() -> n__c() } The induced complexity on above rules (modulo remaining rules) is YES(?,O(n^1)) . These rules are moved into the corresponding weak component(s). Sub-proof: ---------- TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [g](x1) = [2] x1 + [2] [h](x1) = [2] x1 + [0] [activate](x1) = [1] x1 + [1] [c] = [2] [d] = [2] [n__d] = [2] [n__c] = [1] This order satisfies the following ordering constraints: [g(X)] = [2] X + [2] >= [2] X + [2] = [h(activate(X))] [h(n__d())] = [4] >= [4] = [g(n__c())] [activate(X)] = [1] X + [1] > [1] X + [0] = [X] [activate(n__d())] = [3] > [2] = [d()] [activate(n__c())] = [2] >= [2] = [c()] [c()] = [2] >= [2] = [d()] [c()] = [2] > [1] = [n__c()] [d()] = [2] >= [2] = [n__d()] We return to the main proof. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(X) -> h(activate(X)) , h(n__d()) -> g(n__c()) , activate(n__c()) -> c() , c() -> d() , d() -> n__d() } Weak Trs: { activate(X) -> X , activate(n__d()) -> d() , c() -> n__c() } Obligation: innermost runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..