MAYBE * Step 1: WeightGap MAYBE + Considered Problem: - Strict TRS: cons(x,cons(y,z)) -> big() inf(x) -> cons(x,inf(s(x))) - Signature: {cons/2,inf/1} / {big/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {cons,inf} and constructors {big,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(big) = [1] p(cons) = [1] x2 + [1] p(inf) = [4] x1 + [0] p(s) = [1] x1 + [4] Following rules are strictly oriented: cons(x,cons(y,z)) = [1] z + [2] > [1] = big() Following rules are (at-least) weakly oriented: inf(x) = [4] x + [0] >= [4] x + [17] = cons(x,inf(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: inf(x) -> cons(x,inf(s(x))) - Weak TRS: cons(x,cons(y,z)) -> big() - Signature: {cons/2,inf/1} / {big/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {cons,inf} and constructors {big,s} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE