MAYBE * Step 1: WeightGap MAYBE + Considered Problem: - Strict TRS: f(t(),x,y) -> f(g(x,y),x,s(y)) g(s(x),0()) -> t() g(s(x),s(y)) -> g(x,y) - Signature: {f/3,g/2} / {0/0,s/1,t/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s,t} + 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(f) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [8] p(f) = [1] x1 + [2] x2 + [1] x3 + [1] p(g) = [8] p(s) = [0] p(t) = [15] Following rules are strictly oriented: f(t(),x,y) = [2] x + [1] y + [16] > [2] x + [9] = f(g(x,y),x,s(y)) Following rules are (at-least) weakly oriented: g(s(x),0()) = [8] >= [15] = t() g(s(x),s(y)) = [8] >= [8] = g(x,y) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: Failure MAYBE + Considered Problem: - Strict TRS: g(s(x),0()) -> t() g(s(x),s(y)) -> g(x,y) - Weak TRS: f(t(),x,y) -> f(g(x,y),x,s(y)) - Signature: {f/3,g/2} / {0/0,s/1,t/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s,t} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE