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