* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a() -> c() a() -> d() div(x,y) -> div2(x,y,0()) div2(x,y,i) -> if1(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)) if1(false(),b,x,y,i,j) -> if2(b,x,y,i,j) if1(true(),b,x,y,i,j) -> divZeroError() if2(false(),x,y,i,j) -> i if2(true(),x,y,i,j) -> div2(minus(x,y),y,j) ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z)) ifPlus(true(),x,y,z) -> y inc(0()) -> 0() inc(s(i)) -> s(inc(i)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(x,y) plus(x,y) -> plusIter(x,y,0()) plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z) - Signature: {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3} / {0/0,c/0,d/0,divZeroError/0 ,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {a,div,div2,if1,if2,ifPlus,inc,le,minus,plus ,plusIter} and constructors {0,c,d,divZeroError,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a() -> c() a() -> d() div(x,y) -> div2(x,y,0()) div2(x,y,i) -> if1(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)) if1(false(),b,x,y,i,j) -> if2(b,x,y,i,j) if1(true(),b,x,y,i,j) -> divZeroError() if2(false(),x,y,i,j) -> i if2(true(),x,y,i,j) -> div2(minus(x,y),y,j) ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z)) ifPlus(true(),x,y,z) -> y inc(0()) -> 0() inc(s(i)) -> s(inc(i)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(x,y) plus(x,y) -> plusIter(x,y,0()) plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z) - Signature: {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3} / {0/0,c/0,d/0,divZeroError/0 ,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {a,div,div2,if1,if2,ifPlus,inc,le,minus,plus ,plusIter} and constructors {0,c,d,divZeroError,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: inc(x){x -> s(x)} = inc(s(x)) ->^+ s(inc(x)) = C[inc(x) = inc(x){}] WORST_CASE(Omega(n^1),?)