* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: assrewrite(exp) -> rewrite(exp) first(Op(x,y)) -> x first(Val(n)) -> Val(n) isOp(Op(x,y)) -> True() isOp(Val(n)) -> False() rewrite(Op(Op(x,y),y')) -> rewrite[Let](Op(Op(x,y),y'),Op(x,y),rewrite(x)) rewrite(Op(Val(n),y)) -> Op(rewrite(y),Val(n)) rewrite(Val(n)) -> Val(n) second(Op(x,y)) -> y - Weak TRS: rewrite[Let](exp,Op(x,y),a1) -> rewrite[Let][Let](exp,Op(x,y),a1,rewrite(y)) rewrite[Let][Let](Op(x,y),opab,a1,b1) -> rewrite[Let][Let][Let](Op(x,y),a1,b1,rewrite(y)) rewrite[Let][Let][Let](exp,a1,b1,c1) -> rewrite(Op(a1,Op(b1,rewrite(c1)))) - Signature: {assrewrite/1,first/1,isOp/1,rewrite/1,rewrite[Let]/3,rewrite[Let][Let]/4,rewrite[Let][Let][Let]/4 ,second/1} / {False/0,Op/2,True/0,Val/1} - Obligation: innermost runtime complexity wrt. defined symbols {assrewrite,first,isOp,rewrite,rewrite[Let] ,rewrite[Let][Let],rewrite[Let][Let][Let],second} and constructors {False,Op,True,Val} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: assrewrite(exp) -> rewrite(exp) first(Op(x,y)) -> x first(Val(n)) -> Val(n) isOp(Op(x,y)) -> True() isOp(Val(n)) -> False() rewrite(Op(Op(x,y),y')) -> rewrite[Let](Op(Op(x,y),y'),Op(x,y),rewrite(x)) rewrite(Op(Val(n),y)) -> Op(rewrite(y),Val(n)) rewrite(Val(n)) -> Val(n) second(Op(x,y)) -> y - Weak TRS: rewrite[Let](exp,Op(x,y),a1) -> rewrite[Let][Let](exp,Op(x,y),a1,rewrite(y)) rewrite[Let][Let](Op(x,y),opab,a1,b1) -> rewrite[Let][Let][Let](Op(x,y),a1,b1,rewrite(y)) rewrite[Let][Let][Let](exp,a1,b1,c1) -> rewrite(Op(a1,Op(b1,rewrite(c1)))) - Signature: {assrewrite/1,first/1,isOp/1,rewrite/1,rewrite[Let]/3,rewrite[Let][Let]/4,rewrite[Let][Let][Let]/4 ,second/1} / {False/0,Op/2,True/0,Val/1} - Obligation: innermost runtime complexity wrt. defined symbols {assrewrite,first,isOp,rewrite,rewrite[Let] ,rewrite[Let][Let],rewrite[Let][Let][Let],second} and constructors {False,Op,True,Val} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: rewrite(x){x -> Op(Op(x,y),z)} = rewrite(Op(Op(x,y),z)) ->^+ rewrite[Let](Op(Op(x,y),z),Op(x,y),rewrite(x)) = C[rewrite(x) = rewrite(x){}] WORST_CASE(Omega(n^1),?)