* Step 1: Sum WORST_CASE(NON_POLY,?) + Considered Problem: - Strict TRS: cond1(false(),n,l) -> cond2(gt(n,max(l)),n,l) cond1(true(),n,l) -> cons(n,st(s(n),l)) cond2(false(),n,l) -> st(s(n),l) cond2(true(),n,l) -> nil() equal(0(),0()) -> true() equal(0(),s(y)) -> false() equal(s(x),0()) -> false() equal(s(x),s(y)) -> equal(x,y) gt(0(),v) -> false() gt(s(u),0()) -> true() gt(s(u),s(v)) -> gt(u,v) if(false(),u,v) -> v if(true(),u,v) -> u max(cons(u,l)) -> if(gt(u,max(l)),u,max(l)) max(nil()) -> 0() member(n,cons(m,l)) -> or(equal(n,m),member(n,l)) member(n,nil()) -> false() or(x,false()) -> x or(x,true()) -> true() sort(l) -> st(0(),l) st(n,l) -> cond1(member(n,l),n,l) - Signature: {cond1/3,cond2/3,equal/2,gt/2,if/3,max/1,member/2,or/2,sort/1,st/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond1,cond2,equal,gt,if,max,member,or,sort ,st} and constructors {0,cons,false,nil,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(NON_POLY,?) + Considered Problem: - Strict TRS: cond1(false(),n,l) -> cond2(gt(n,max(l)),n,l) cond1(true(),n,l) -> cons(n,st(s(n),l)) cond2(false(),n,l) -> st(s(n),l) cond2(true(),n,l) -> nil() equal(0(),0()) -> true() equal(0(),s(y)) -> false() equal(s(x),0()) -> false() equal(s(x),s(y)) -> equal(x,y) gt(0(),v) -> false() gt(s(u),0()) -> true() gt(s(u),s(v)) -> gt(u,v) if(false(),u,v) -> v if(true(),u,v) -> u max(cons(u,l)) -> if(gt(u,max(l)),u,max(l)) max(nil()) -> 0() member(n,cons(m,l)) -> or(equal(n,m),member(n,l)) member(n,nil()) -> false() or(x,false()) -> x or(x,true()) -> true() sort(l) -> st(0(),l) st(n,l) -> cond1(member(n,l),n,l) - Signature: {cond1/3,cond2/3,equal/2,gt/2,if/3,max/1,member/2,or/2,sort/1,st/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond1,cond2,equal,gt,if,max,member,or,sort ,st} and constructors {0,cons,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: max(y){y -> cons(x,y)} = max(cons(x,y)) ->^+ if(gt(x,max(y)),x,max(y)) = C[max(y) = max(y){}] max(y){y -> cons(x,y)} = max(cons(x,y)) ->^+ if(gt(x,max(y)),x,max(y)) = C[max(y) = max(y){}] WORST_CASE(NON_POLY,?)