* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,b,y,z) -> loop(x,b,times(b,y),s(z)) if(true(),x,b,y,z) -> z le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) log(x,0()) -> baseError() log(x,s(0())) -> baseError() log(0(),s(s(b))) -> logZeroError() log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0()) loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(x,y)) - Signature: {if/5,le/2,log/2,loop/4,plus/2,times/2} / {0/0,baseError/0,false/0,logZeroError/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,le,log,loop,plus,times} and constructors {0,baseError ,false,logZeroError,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: if(false(),x,b,y,z) -> loop(x,b,times(b,y),s(z)) if(true(),x,b,y,z) -> z le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) log(x,0()) -> baseError() log(x,s(0())) -> baseError() log(0(),s(s(b))) -> logZeroError() log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0()) loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(x),y) -> plus(y,times(x,y)) - Signature: {if/5,le/2,log/2,loop/4,plus/2,times/2} / {0/0,baseError/0,false/0,logZeroError/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {if,le,log,loop,plus,times} and constructors {0,baseError ,false,logZeroError,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: le(x,y){x -> s(x),y -> s(y)} = le(s(x),s(y)) ->^+ le(x,y) = C[le(x,y) = le(x,y){}] WORST_CASE(Omega(n^1),?)