* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_2(true(),x,y,edge(u,v,i),h) -> true() or(false(),y) -> y or(true(),y) -> true() reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) reach(x,y,empty(),h) -> false() union(edge(x,y,i),h) -> edge(x,y,union(i,h)) union(empty(),h) -> h - Signature: {eq/2,if_reach_1/5,if_reach_2/5,or/2,reach/4,union/2} / {0/0,edge/3,empty/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {eq,if_reach_1,if_reach_2,or,reach ,union} 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: eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_2(true(),x,y,edge(u,v,i),h) -> true() or(false(),y) -> y or(true(),y) -> true() reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) reach(x,y,empty(),h) -> false() union(edge(x,y,i),h) -> edge(x,y,union(i,h)) union(empty(),h) -> h - Signature: {eq/2,if_reach_1/5,if_reach_2/5,or/2,reach/4,union/2} / {0/0,edge/3,empty/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {eq,if_reach_1,if_reach_2,or,reach ,union} 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),?)