MAYBE * Step 1: WeightGap MAYBE + Considered Problem: - Strict TRS: from(X) -> cons(X,from(s(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,Z) - Signature: {from/1,sel/2} / {0/0,cons/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {from,sel} and constructors {0,cons,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(0) = [0] p(cons) = [1] x1 + [1] x2 + [1] p(from) = [1] x1 + [15] p(s) = [4] p(sel) = [1] x2 + [0] Following rules are strictly oriented: sel(0(),cons(X,Y)) = [1] X + [1] Y + [1] > [1] X + [0] = X sel(s(X),cons(Y,Z)) = [1] Y + [1] Z + [1] > [1] Z + [0] = sel(X,Z) Following rules are (at-least) weakly oriented: from(X) = [1] X + [15] >= [1] X + [20] = 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: sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,Z) - Signature: {from/1,sel/2} / {0/0,cons/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {from,sel} and constructors {0,cons,s} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE