YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalndecrstart(A) -> evalndecrentryin(A) True (1,1) 1. evalndecrentryin(A) -> evalndecrbb1in(-1 + A) True (?,1) 2. evalndecrbb1in(A) -> evalndecrbbin(A) [A >= 2] (?,1) 3. evalndecrbb1in(A) -> evalndecrreturnin(A) [1 >= A] (?,1) 4. evalndecrbbin(A) -> evalndecrbb1in(-1 + A) [-2 + A >= 0] (?,1) 5. evalndecrreturnin(A) -> evalndecrstop(A) [1 + -1*A >= 0] (?,1) Signature: {(evalndecrbb1in,1) ;(evalndecrbbin,1) ;(evalndecrentryin,1) ;(evalndecrreturnin,1) ;(evalndecrstart,1) ;(evalndecrstop,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalndecrstart(A) -> evalndecrentryin(A) True (1,1) 1. evalndecrentryin(A) -> evalndecrbb1in(-1 + A) True (1,1) 2. evalndecrbb1in(A) -> evalndecrbbin(A) [A >= 2] (?,1) 3. evalndecrbb1in(A) -> evalndecrreturnin(A) [1 >= A] (1,1) 4. evalndecrbbin(A) -> evalndecrbb1in(-1 + A) [-2 + A >= 0] (?,1) 5. evalndecrreturnin(A) -> evalndecrstop(A) [1 + -1*A >= 0] (1,1) Signature: {(evalndecrbb1in,1) ;(evalndecrbbin,1) ;(evalndecrentryin,1) ;(evalndecrreturnin,1) ;(evalndecrstart,1) ;(evalndecrstop,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalndecrstart(A) -> evalndecrentryin(A) True (1,1) 1. evalndecrentryin(A) -> evalndecrbb1in(-1 + A) True (?,1) 2. evalndecrbb1in(A) -> evalndecrbbin(A) [A >= 2] (?,1) 3. evalndecrbb1in(A) -> evalndecrreturnin(A) [1 >= A] (?,1) 4. evalndecrbbin(A) -> evalndecrbb1in(-1 + A) [-2 + A >= 0] (?,1) 5. evalndecrreturnin(A) -> evalndecrstop(A) [1 + -1*A >= 0] (?,1) 6. evalndecrreturnin(A) -> exitus616(A) True (?,1) Signature: {(evalndecrbb1in,1) ;(evalndecrbbin,1) ;(evalndecrentryin,1) ;(evalndecrreturnin,1) ;(evalndecrstart,1) ;(evalndecrstop,1) ;(exitus616,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{2,3},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,4] c: [4] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. evalndecrstart(A) -> evalndecrentryin(A) True (1,1) 1. evalndecrentryin(A) -> evalndecrbb1in(-1 + A) True (?,1) 2. evalndecrbb1in(A) -> evalndecrbbin(A) [A >= 2] (?,1) 3. evalndecrbb1in(A) -> evalndecrreturnin(A) [1 >= A] (?,1) 4. evalndecrbbin(A) -> evalndecrbb1in(-1 + A) [-2 + A >= 0] (?,1) 5. evalndecrreturnin(A) -> evalndecrstop(A) [1 + -1*A >= 0] (?,1) 6. evalndecrreturnin(A) -> exitus616(A) True (?,1) Signature: {(evalndecrbb1in,1) ;(evalndecrbbin,1) ;(evalndecrentryin,1) ;(evalndecrreturnin,1) ;(evalndecrstart,1) ;(evalndecrstop,1) ;(exitus616,1)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{2,3},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,0.0] evalndecrstart ~> evalndecrentryin [A <= A] evalndecrentryin ~> evalndecrbb1in [A <= K + A] evalndecrbb1in ~> evalndecrbbin [A <= A] evalndecrbb1in ~> evalndecrreturnin [A <= A] evalndecrbbin ~> evalndecrbb1in [A <= A] evalndecrreturnin ~> evalndecrstop [A <= A] evalndecrreturnin ~> exitus616 [A <= A] + Loop: [0.0 <= K + A] evalndecrbb1in ~> evalndecrbbin [A <= A] evalndecrbbin ~> evalndecrbb1in [A <= A] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] evalndecrstart ~> evalndecrentryin [] evalndecrentryin ~> evalndecrbb1in [A ~+> A,K ~+> A] evalndecrbb1in ~> evalndecrbbin [] evalndecrbb1in ~> evalndecrreturnin [] evalndecrbbin ~> evalndecrbb1in [] evalndecrreturnin ~> evalndecrstop [] evalndecrreturnin ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] evalndecrbb1in ~> evalndecrbbin [] evalndecrbbin ~> evalndecrbb1in [] + Applied Processor: LareProcessor + Details: evalndecrstart ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] evalndecrstart ~> evalndecrstop [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + evalndecrbb1in> [A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] YES(?,O(n^1))