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