YES(?,O(n^1)) * Step 1: UnreachableRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 1. group3(A,B,C) -> group3(-3 + A,B,C) [A >= 4] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},1->{1},2->{0}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [1] * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0},2->{0}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) 3. zip3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0,3},2->{0,3},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,2,3] | `- p:[0] c: [0] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] (?,1) 2. start(A,B,C) -> zip3(A,B,C) True (1,1) 3. zip3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(group3,3);(start,3);(zip3,3)} Flow Graph: [0->{0,3},2->{0,3},3->{}] ,We construct a looptree: P: [0,2,3] | `- p:[0] c: [0]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] zip3 ~> zip3 [A <= A, B <= B, C <= C] start ~> zip3 [A <= A, B <= B, C <= C] zip3 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A] zip3 ~> zip3 [A <= A, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] zip3 ~> zip3 [] start ~> zip3 [] zip3 ~> exitus616 [] + Loop: [A ~=> 0.0] zip3 ~> zip3 [] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~=> 0.0,A ~+> tick,tick ~+> tick] + zip3> [A ~=> 0.0,A ~+> tick,tick ~+> tick] YES(?,O(n^1))