YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A) [0 >= A && B = 1] (?,1) 1. eval(A,B) -> eval(A,A) [B >= 1 && 1 + B >= 0 && B >= 1 + A] (?,1) 2. eval(A,B) -> eval(A,0) [A >= 1 && B = 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 1 + B >= 0 && A >= B] (?,1) 4. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,0) ,(0,1) ,(0,2) ,(0,3) ,(1,0) ,(1,1) ,(2,0) ,(2,1) ,(2,2) ,(2,3) ,(3,0) ,(3,1)] * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A) [0 >= A && B = 1] (?,1) 1. eval(A,B) -> eval(A,A) [B >= 1 && 1 + B >= 0 && B >= 1 + A] (?,1) 2. eval(A,B) -> eval(A,0) [A >= 1 && B = 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 1 + B >= 0 && A >= B] (?,1) 4. start(A,B) -> eval(A,B) True (1,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1,2,3}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A) [0 >= A && B = 1] (?,1) 1. eval(A,B) -> eval(A,A) [B >= 1 && 1 + B >= 0 && B >= 1 + A] (?,1) 2. eval(A,B) -> eval(A,0) [A >= 1 && B = 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 1 + B >= 0 && A >= B] (?,1) 4. start(A,B) -> eval(A,B) True (1,1) 5. eval(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval,2);(exitus616,2);(start,2)} Flow Graph: [0->{0,1,2,3,5},1->{0,1,2,3,5},2->{0,1,2,3,5},3->{0,1,2,3,5},4->{0,1,2,3,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,0) ,(0,1) ,(0,2) ,(0,3) ,(1,0) ,(1,1) ,(2,0) ,(2,1) ,(2,2) ,(2,3) ,(3,0) ,(3,1)] * Step 4: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval(A,B) -> eval(A,A) [0 >= A && B = 1] (?,1) 1. eval(A,B) -> eval(A,A) [B >= 1 && 1 + B >= 0 && B >= 1 + A] (?,1) 2. eval(A,B) -> eval(A,0) [A >= 1 && B = 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 1 + B >= 0 && A >= B] (?,1) 4. start(A,B) -> eval(A,B) True (1,1) 5. eval(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval,2);(exitus616,2);(start,2)} Flow Graph: [0->{5},1->{2,3,5},2->{5},3->{2,3,5},4->{0,1,2,3,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[3] c: [3] * Step 5: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. eval(A,B) -> eval(A,A) [0 >= A && B = 1] (?,1) 1. eval(A,B) -> eval(A,A) [B >= 1 && 1 + B >= 0 && B >= 1 + A] (?,1) 2. eval(A,B) -> eval(A,0) [A >= 1 && B = 1] (?,1) 3. eval(A,B) -> eval(A,-1 + B) [B >= 1 && 1 + B >= 0 && A >= B] (?,1) 4. start(A,B) -> eval(A,B) True (1,1) 5. eval(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval,2);(exitus616,2);(start,2)} Flow Graph: [0->{5},1->{2,3,5},2->{5},3->{2,3,5},4->{0,1,2,3,5},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[3] c: [3]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] eval ~> eval [A <= A, B <= A] eval ~> eval [A <= A, B <= A] eval ~> eval [A <= A, B <= 0*K] eval ~> eval [A <= A, B <= B] start ~> eval [A <= A, B <= B] eval ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 2*K + B] eval ~> eval [A <= A, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] eval ~> eval [A ~=> B] eval ~> eval [A ~=> B] eval ~> eval [K ~=> B] eval ~> eval [] start ~> eval [] eval ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] eval ~> eval [] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~=> B,K ~=> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + eval> [B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(n^1))