YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B) -> eval(A,B) True (1,1) 1. eval(A,B) -> eval(A + -1*C,B + D) [A >= 1 + B && C >= 0 && D >= 1] (?,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{1},1->{1}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B) -> eval(A,B) True eval(A,B) -> eval(A + -1*C,B + D) [A >= 1 + B && C >= 0 && D >= 1] Signature: {(eval,2);(start,2)} Rule Graph: [0->{1},1->{1}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B) -> eval(A,B) True eval(A,B) -> eval(A + -1*C,B + D) [A >= 1 + B && C >= 0 && D >= 1] eval(A,B) -> exitus616(A,B) True Signature: {(eval,2);(exitus616,2);(start,2)} Rule Graph: [0->{1},1->{1,2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2] | `- p:[1] c: [1] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B) -> eval(A,B) True eval(A,B) -> eval(A + -1*C,B + D) [A >= 1 + B && C >= 0 && D >= 1] eval(A,B) -> exitus616(A,B) True Signature: {(eval,2);(exitus616,2);(start,2)} Rule Graph: [0->{1},1->{1,2}] ,We construct a looptree: P: [0,1,2] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] start ~> eval [A <= A, B <= B] eval ~> eval [A <= unknown, B <= unknown] eval ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + A + B] eval ~> eval [A <= unknown, B <= unknown] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] start ~> eval [] eval ~> eval [huge ~=> A,huge ~=> B] eval ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] eval ~> eval [huge ~=> A,huge ~=> B] + Applied Processor: Lare + Details: start ~> exitus616 [huge ~=> A ,huge ~=> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] + eval> [huge ~=> A ,huge ~=> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] YES(?,O(n^1))