YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (?,1) Signature: {(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (1,1) Signature: {(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (1,1) Signature: {(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (?,1) 4. f5(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) Signature: {(exitus616,10);(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (?,1) 4. f5(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) Signature: {(exitus616,10);(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[1,2] c: [2] | `- p:[1] c: [1] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [31 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [31 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f28(A,B,C,D,B,B,K,L,L,L) [C >= 32] (?,1) 4. f5(A,B,C,D,E,F,G,H,I,J) -> exitus616(A,B,C,D,E,F,G,H,I,J) True (?,1) Signature: {(exitus616,10);(f0,10);(f28,10);(f5,10)} Flow Graph: [0->{1,2,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[1,2] c: [2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,I,J,0.0,0.0.0] f0 ~> f5 [A <= unknown, B <= 0*K, C <= 0*K, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] f5 ~> f5 [A <= A, B <= K + B, C <= K + C, D <= K, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] f5 ~> f5 [A <= A, B <= B, C <= K + C, D <= 0*K, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] f5 ~> f28 [A <= A, B <= B, C <= C, D <= D, E <= B, F <= B, G <= unknown, H <= unknown, I <= unknown, J <= unknown] f5 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] + Loop: [0.0 <= 32*K + C] f5 ~> f5 [A <= A, B <= K + B, C <= K + C, D <= K, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] f5 ~> f5 [A <= A, B <= B, C <= K + C, D <= 0*K, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] + Loop: [0.0.0 <= 32*K + C] f5 ~> f5 [A <= A, B <= K + B, C <= K + C, D <= K, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,I,J,0.0,0.0.0] f0 ~> f5 [K ~=> B,K ~=> C,huge ~=> A] f5 ~> f5 [K ~=> D,B ~+> B,C ~+> C,K ~+> B,K ~+> C] f5 ~> f5 [K ~=> D,C ~+> C,K ~+> C] f5 ~> f28 [B ~=> E,B ~=> F,huge ~=> G,huge ~=> H,huge ~=> I,huge ~=> J] f5 ~> exitus616 [] + Loop: [C ~+> 0.0,K ~*> 0.0] f5 ~> f5 [K ~=> D,B ~+> B,C ~+> C,K ~+> B,K ~+> C] f5 ~> f5 [K ~=> D,C ~+> C,K ~+> C] + Loop: [C ~+> 0.0.0,K ~*> 0.0.0] f5 ~> f5 [K ~=> D,B ~+> B,C ~+> C,K ~+> B,K ~+> C] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> B ,K ~=> C ,K ~=> D ,huge ~=> A ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,K ~^> C] f0 ~> f28 [K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,huge ~=> A ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> E ,K ~+> F ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> E ,K ~*> F ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,K ~^> C] + f5> [K ~=> D ,B ~+> B ,C ~+> C ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> B ,C ~*> C ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,C ~^> C ,K ~^> C] + f5> [K ~=> D ,B ~+> B ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick] YES(?,O(1))