YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [A >= 0 && 99 >= A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 0 && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f5,7)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: ArgumentFilter [1,2,3,4,5,6] + Details: We remove following argument positions: [1,2,3,4,5,6]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f5(0) True (1,1) 1. f5(A) -> f5(1 + A) [A >= 0 && 99 >= A] (?,1) 2. f5(A) -> f13(A) [A >= 0 && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f5,7)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f5(0) True (1,1) 1. f5(A) -> f5(1 + A) [A >= 0 && 99 >= A] (?,1) 2. f5(A) -> f13(A) [A >= 0 && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f5,7)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A) -> f5(0) True f5(A) -> f5(1 + A) [A >= 0 && 99 >= A] f5(A) -> f13(A) [A >= 0 && A >= 100] Signature: {(f0,7);(f13,7);(f5,7)} Rule Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A) -> f5(0) True f5(A) -> f5(1 + A) [A >= 0 && 99 >= A] f5(A) -> f13(A) [A >= 0 && A >= 100] f13(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,7);(f13,7);(f5,7)} Rule Graph: [0->{1},1->{1,2},2->{3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(A) -> f5(0) True f5(A) -> f5(1 + A) [A >= 0 && 99 >= A] f5(A) -> f13(A) [A >= 0 && A >= 100] f13(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,7);(f13,7);(f5,7)} Rule Graph: [0->{1},1->{1,2},2->{3}] ,We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,0.0] f0 ~> f5 [A <= 0*K] f5 ~> f5 [A <= 100*K] f5 ~> f13 [A <= A] f13 ~> exitus616 [A <= A] + Loop: [0.0 <= 99*K + A] f5 ~> f5 [A <= 100*K] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f0 ~> f5 [K ~=> A] f5 ~> f5 [K ~=> A] f5 ~> f13 [] f13 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f5 ~> f5 [K ~=> A] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f5> [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(1))