MAYBE * Step 1: WeightGap MAYBE + Considered Problem: - Strict TRS: cond(true(),x,y) -> cond(gr(x,y),p(x),y) gr(0(),x) -> false() gr(s(x),0()) -> true() gr(s(x),s(y)) -> gr(x,y) p(0()) -> 0() p(s(x)) -> x - Signature: {cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond,gr,p} and constructors {0,false,s,true} + 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(cond) = {1,2} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [4] p(cond) = [1] x1 + [1] x2 + [11] x3 + [0] p(false) = [2] p(gr) = [10] p(p) = [1] x1 + [3] p(s) = [1] x1 + [0] p(true) = [0] Following rules are strictly oriented: gr(0(),x) = [10] > [2] = false() gr(s(x),0()) = [10] > [0] = true() p(0()) = [7] > [4] = 0() p(s(x)) = [1] x + [3] > [1] x + [0] = x Following rules are (at-least) weakly oriented: cond(true(),x,y) = [1] x + [11] y + [0] >= [1] x + [11] y + [13] = cond(gr(x,y),p(x),y) gr(s(x),s(y)) = [10] >= [10] = gr(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: cond(true(),x,y) -> cond(gr(x,y),p(x),y) gr(s(x),s(y)) -> gr(x,y) - Weak TRS: gr(0(),x) -> false() gr(s(x),0()) -> true() p(0()) -> 0() p(s(x)) -> x - Signature: {cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond,gr,p} and constructors {0,false,s,true} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE