MAYBE * Step 1: WeightGap MAYBE + Considered Problem: - Strict TRS: 2nd(cons(X,X1)) -> 2nd(cons1(X,X1)) 2nd(cons1(X,cons(Y,Z))) -> Y from(X) -> cons(X,from(s(X))) - Signature: {2nd/1,from/1} / {cons/2,cons1/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,from} and constructors {cons,cons1,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(cons) = {2} Following symbols are considered usable: all TcT has computed the following interpretation: p(2nd) = [1] x1 + [3] p(cons) = [1] x1 + [1] x2 + [11] p(cons1) = [1] x2 + [1] p(from) = [8] x1 + [0] p(s) = [1] Following rules are strictly oriented: 2nd(cons(X,X1)) = [1] X + [1] X1 + [14] > [1] X1 + [4] = 2nd(cons1(X,X1)) 2nd(cons1(X,cons(Y,Z))) = [1] Y + [1] Z + [15] > [1] Y + [0] = Y Following rules are (at-least) weakly oriented: from(X) = [8] X + [0] >= [1] X + [19] = cons(X,from(s(X))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: Failure MAYBE + Considered Problem: - Strict TRS: from(X) -> cons(X,from(s(X))) - Weak TRS: 2nd(cons(X,X1)) -> 2nd(cons1(X,X1)) 2nd(cons1(X,cons(Y,Z))) -> Y - Signature: {2nd/1,from/1} / {cons/2,cons1/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,from} and constructors {cons,cons1,s} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE