* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: id(0()) -> 0() id(s(x)) -> s(id(x)) if2(false(),b2,x,y) -> if3(b2,x,y) if2(true(),b2,x,y) -> 0() if3(false(),x,y) -> x if3(true(),x,y) -> mod(minus(x,y),s(y)) if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y) if_mod(true(),b1,b2,x,y) -> 0() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) zero(0()) -> true() zero(s(x)) -> false() - Signature: {id/1,if2/4,if3/3,if_mod/5,le/2,minus/2,mod/2,zero/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {id,if2,if3,if_mod,le,minus,mod,zero} and constructors {0 ,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: id(0()) -> 0() id(s(x)) -> s(id(x)) if2(false(),b2,x,y) -> if3(b2,x,y) if2(true(),b2,x,y) -> 0() if3(false(),x,y) -> x if3(true(),x,y) -> mod(minus(x,y),s(y)) if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y) if_mod(true(),b1,b2,x,y) -> 0() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) zero(0()) -> true() zero(s(x)) -> false() - Signature: {id/1,if2/4,if3/3,if_mod/5,le/2,minus/2,mod/2,zero/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {id,if2,if3,if_mod,le,minus,mod,zero} and constructors {0 ,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: id(x){x -> s(x)} = id(s(x)) ->^+ s(id(x)) = C[id(x) = id(x){}] WORST_CASE(Omega(n^1),?)