* Step 1: Sum WORST_CASE(NON_POLY,?) + Considered Problem: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) f(0()) -> 0() f(s(0())) -> s(0()) f(s(s(x))) -> +(p(g(x)),q(g(x))) f(s(s(x))) -> p(h(g(x))) g(0()) -> pair(s(0()),s(0())) g(s(x)) -> h(g(x)) g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x))) h(x) -> pair(+(p(x),q(x)),p(x)) p(pair(x,y)) -> x q(pair(x,y)) -> y - Signature: {+/2,f/1,g/1,h/1,p/1,q/1} / {0/0,pair/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,f,g,h,p,q} and constructors {0,pair,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(NON_POLY,?) + Considered Problem: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) f(0()) -> 0() f(s(0())) -> s(0()) f(s(s(x))) -> +(p(g(x)),q(g(x))) f(s(s(x))) -> p(h(g(x))) g(0()) -> pair(s(0()),s(0())) g(s(x)) -> h(g(x)) g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x))) h(x) -> pair(+(p(x),q(x)),p(x)) p(pair(x,y)) -> x q(pair(x,y)) -> y - Signature: {+/2,f/1,g/1,h/1,p/1,q/1} / {0/0,pair/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,f,g,h,p,q} and constructors {0,pair,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: g(x){x -> s(x)} = g(s(x)) ->^+ pair(+(p(g(x)),q(g(x))),p(g(x))) = C[g(x) = g(x){}] g(x){x -> s(x)} = g(s(x)) ->^+ pair(+(p(g(x)),q(g(x))),p(g(x))) = C[g(x) = g(x){}] WORST_CASE(NON_POLY,?)