* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: and(false(),y) -> false() and(true(),y) -> y eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if1(false(),x,y,c,i,j) -> if2(le(c,size(j)),x,y,c,i,j) if1(true(),x,y,c,i,j) -> true() if2(false(),x,y,c,i,j) -> false() if2(true(),x,y,c,edge(u,v,i),j) -> or(if2(true(),x,y,c,i,j),and(eq(x,u),reach(v,y,s(c),j,j))) if2(true(),x,y,c,empty(),j) -> false() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) or(false(),y) -> y or(true(),y) -> true() reach(x,y,c,i,j) -> if1(eq(x,y),x,y,c,i,j) reachable(x,y,i) -> reach(x,y,0(),i,i) size(edge(x,y,i)) -> s(size(i)) size(empty()) -> 0() - Signature: {and/2,eq/2,if1/6,if2/6,le/2,or/2,reach/5,reachable/3,size/1} / {0/0,edge/3,empty/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,eq,if1,if2,le,or,reach,reachable ,size} and constructors {0,edge,empty,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: and(false(),y) -> false() and(true(),y) -> y eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if1(false(),x,y,c,i,j) -> if2(le(c,size(j)),x,y,c,i,j) if1(true(),x,y,c,i,j) -> true() if2(false(),x,y,c,i,j) -> false() if2(true(),x,y,c,edge(u,v,i),j) -> or(if2(true(),x,y,c,i,j),and(eq(x,u),reach(v,y,s(c),j,j))) if2(true(),x,y,c,empty(),j) -> false() le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) or(false(),y) -> y or(true(),y) -> true() reach(x,y,c,i,j) -> if1(eq(x,y),x,y,c,i,j) reachable(x,y,i) -> reach(x,y,0(),i,i) size(edge(x,y,i)) -> s(size(i)) size(empty()) -> 0() - Signature: {and/2,eq/2,if1/6,if2/6,le/2,or/2,reach/5,reachable/3,size/1} / {0/0,edge/3,empty/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,eq,if1,if2,le,or,reach,reachable ,size} and constructors {0,edge,empty,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: eq(x,y){x -> s(x),y -> s(y)} = eq(s(x),s(y)) ->^+ eq(x,y) = C[eq(x,y) = eq(x,y){}] WORST_CASE(Omega(n^1),?)