* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: cond1(false(),x,y) -> cond2(gt(x,y),x,y) cond1(true(),x,y) -> 0() cond2(false(),x,y) -> s(diff(s(x),y)) cond2(true(),x,y) -> s(diff(x,s(y))) diff(x,y) -> cond1(equal(x,y),x,y) 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) - Signature: {cond1/3,cond2/3,diff/2,equal/2,gt/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond1,cond2,diff,equal,gt} 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: cond1(false(),x,y) -> cond2(gt(x,y),x,y) cond1(true(),x,y) -> 0() cond2(false(),x,y) -> s(diff(s(x),y)) cond2(true(),x,y) -> s(diff(x,s(y))) diff(x,y) -> cond1(equal(x,y),x,y) 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) - Signature: {cond1/3,cond2/3,diff/2,equal/2,gt/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond1,cond2,diff,equal,gt} and constructors {0,false,s ,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: equal(x,y){x -> s(x),y -> s(y)} = equal(s(x),s(y)) ->^+ equal(x,y) = C[equal(x,y) = equal(x,y){}] WORST_CASE(Omega(n^1),?)