YES(?,O(n^1)) * Step 1: FromIts 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. start(A,B,C) -> zip3(A,B,C) True (1,1) Signature: {(start,3);(zip3,3)} Flow Graph: [0->{0},1->{0}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] start(A,B,C) -> zip3(A,B,C) True Signature: {(start,3);(zip3,3)} Rule Graph: [0->{0},1->{0}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] start(A,B,C) -> zip3(A,B,C) True zip3(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(start,3);(zip3,3)} Rule Graph: [0->{0,2},1->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2] | `- p:[0] c: [0] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: zip3(A,B,C) -> zip3(-1 + A,-1 + B,-1 + C) [A >= 1 && B >= 1 && C >= 1] start(A,B,C) -> zip3(A,B,C) True zip3(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(start,3);(zip3,3)} Rule Graph: [0->{0,2},1->{0}] ,We construct a looptree: P: [0,1,2] | `- p:[0] c: [0]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow 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 <= K + C] zip3 ~> zip3 [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] zip3 ~> zip3 [] start ~> zip3 [] zip3 ~> exitus616 [] + Loop: [C ~+> 0.0,K ~+> 0.0] zip3 ~> zip3 [] + Applied Processor: Lare + Details: start ~> exitus616 [C ~+> 0.0,C ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] + zip3> [C ~+> 0.0,C ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] YES(?,O(n^1))