YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f18(A,B,C,D,E,F) -> f18(A,1 + B,C,D,E,F) [A >= 1 + B] (?,1) 1. f24(A,B,C,D,E,F) -> f24(A,1 + B,C,D,E,F) [A >= 1 + B] (?,1) 2. f31(A,B,C,D,E,F) -> f31(A,1 + B,C,D,E,F) [A >= 1 + B] (?,1) 3. f31(A,B,C,D,E,F) -> f39(A,B,C,D,E,F) [B >= A] (?,1) 4. f24(A,B,C,D,E,F) -> f31(A,0,C,D,E,F) [B >= A] (?,1) 5. f18(A,B,C,D,E,F) -> f24(A,0,C,D,E,F) [B >= A] (?,1) 6. f0(A,B,C,D,E,F) -> f18(10,0,10,G,10,H) True (1,1) Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{0,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,5)] * Step 2: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f18(A,B,C,D,E,F) -> f18(A,1 + B,C,D,E,F) [A >= 1 + B] (?,1) 1. f24(A,B,C,D,E,F) -> f24(A,1 + B,C,D,E,F) [A >= 1 + B] (?,1) 2. f31(A,B,C,D,E,F) -> f31(A,1 + B,C,D,E,F) [A >= 1 + B] (?,1) 3. f31(A,B,C,D,E,F) -> f39(A,B,C,D,E,F) [B >= A] (?,1) 4. f24(A,B,C,D,E,F) -> f31(A,0,C,D,E,F) [B >= A] (?,1) 5. f18(A,B,C,D,E,F) -> f24(A,0,C,D,E,F) [B >= A] (?,1) 6. f0(A,B,C,D,E,F) -> f18(10,0,10,G,10,H) True (1,1) Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{0}] + Applied Processor: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,O(1)) + Considered Problem: Rules: f18(A,B,C,D,E,F) -> f18(A,1 + B,C,D,E,F) [A >= 1 + B] f24(A,B,C,D,E,F) -> f24(A,1 + B,C,D,E,F) [A >= 1 + B] f31(A,B,C,D,E,F) -> f31(A,1 + B,C,D,E,F) [A >= 1 + B] f31(A,B,C,D,E,F) -> f39(A,B,C,D,E,F) [B >= A] f24(A,B,C,D,E,F) -> f31(A,0,C,D,E,F) [B >= A] f18(A,B,C,D,E,F) -> f24(A,0,C,D,E,F) [B >= A] f0(A,B,C,D,E,F) -> f18(10,0,10,G,10,H) True Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Rule Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{0}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f18.0(A,B,C,D,E,F) -> f18.0(A,1 + B,C,D,E,F) [A >= 1 + B] f18.0(A,B,C,D,E,F) -> f18.5(A,1 + B,C,D,E,F) [A >= 1 + B] f24.1(A,B,C,D,E,F) -> f24.1(A,1 + B,C,D,E,F) [A >= 1 + B] f24.1(A,B,C,D,E,F) -> f24.4(A,1 + B,C,D,E,F) [A >= 1 + B] f31.2(A,B,C,D,E,F) -> f31.2(A,1 + B,C,D,E,F) [A >= 1 + B] f31.2(A,B,C,D,E,F) -> f31.3(A,1 + B,C,D,E,F) [A >= 1 + B] f31.3(A,B,C,D,E,F) -> f39.7(A,B,C,D,E,F) [B >= A] f24.4(A,B,C,D,E,F) -> f31.2(A,0,C,D,E,F) [B >= A] f24.4(A,B,C,D,E,F) -> f31.3(A,0,C,D,E,F) [B >= A] f18.5(A,B,C,D,E,F) -> f24.1(A,0,C,D,E,F) [B >= A] f18.5(A,B,C,D,E,F) -> f24.4(A,0,C,D,E,F) [B >= A] f0.6(A,B,C,D,E,F) -> f18.0(10,0,10,G,10,H) True Signature: {(f0.6,6);(f18.0,6);(f18.5,6);(f24.1,6);(f24.4,6);(f31.2,6);(f31.3,6);(f39.7,6)} Rule Graph: [0->{0,1},1->{9,10},2->{2,3},3->{7,8},4->{4,5},5->{6},6->{},7->{4,5},8->{6},9->{2,3},10->{7,8},11->{0,1}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f18.0(A,B,C,D,E,F) -> f18.0(A,1 + B,C,D,E,F) [A >= 1 + B] f18.0(A,B,C,D,E,F) -> f18.5(A,1 + B,C,D,E,F) [A >= 1 + B] f24.1(A,B,C,D,E,F) -> f24.1(A,1 + B,C,D,E,F) [A >= 1 + B] f24.1(A,B,C,D,E,F) -> f24.4(A,1 + B,C,D,E,F) [A >= 1 + B] f31.2(A,B,C,D,E,F) -> f31.2(A,1 + B,C,D,E,F) [A >= 1 + B] f31.2(A,B,C,D,E,F) -> f31.3(A,1 + B,C,D,E,F) [A >= 1 + B] f31.3(A,B,C,D,E,F) -> f39.7(A,B,C,D,E,F) [B >= A] f24.4(A,B,C,D,E,F) -> f31.2(A,0,C,D,E,F) [B >= A] f24.4(A,B,C,D,E,F) -> f31.3(A,0,C,D,E,F) [B >= A] f18.5(A,B,C,D,E,F) -> f24.1(A,0,C,D,E,F) [B >= A] f18.5(A,B,C,D,E,F) -> f24.4(A,0,C,D,E,F) [B >= A] f0.6(A,B,C,D,E,F) -> f18.0(10,0,10,G,10,H) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(f0.6,6);(f18.0,6);(f18.5,6);(f24.1,6);(f24.4,6);(f31.2,6);(f31.3,6);(f39.7,6)} Rule Graph: [0->{0,1},1->{9,10},2->{2,3},3->{7,8},4->{4,5},5->{6},6->{12,13,14,15},7->{4,5},8->{6},9->{2,3},10->{7,8} ,11->{0,1}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | +- p:[0] c: [0] | +- p:[2] c: [2] | `- p:[4] c: [4] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f18.0(A,B,C,D,E,F) -> f18.0(A,1 + B,C,D,E,F) [A >= 1 + B] f18.0(A,B,C,D,E,F) -> f18.5(A,1 + B,C,D,E,F) [A >= 1 + B] f24.1(A,B,C,D,E,F) -> f24.1(A,1 + B,C,D,E,F) [A >= 1 + B] f24.1(A,B,C,D,E,F) -> f24.4(A,1 + B,C,D,E,F) [A >= 1 + B] f31.2(A,B,C,D,E,F) -> f31.2(A,1 + B,C,D,E,F) [A >= 1 + B] f31.2(A,B,C,D,E,F) -> f31.3(A,1 + B,C,D,E,F) [A >= 1 + B] f31.3(A,B,C,D,E,F) -> f39.7(A,B,C,D,E,F) [B >= A] f24.4(A,B,C,D,E,F) -> f31.2(A,0,C,D,E,F) [B >= A] f24.4(A,B,C,D,E,F) -> f31.3(A,0,C,D,E,F) [B >= A] f18.5(A,B,C,D,E,F) -> f24.1(A,0,C,D,E,F) [B >= A] f18.5(A,B,C,D,E,F) -> f24.4(A,0,C,D,E,F) [B >= A] f0.6(A,B,C,D,E,F) -> f18.0(10,0,10,G,10,H) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True f39.7(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(f0.6,6);(f18.0,6);(f18.5,6);(f24.1,6);(f24.4,6);(f31.2,6);(f31.3,6);(f39.7,6)} Rule Graph: [0->{0,1},1->{9,10},2->{2,3},3->{7,8},4->{4,5},5->{6},6->{12,13,14,15},7->{4,5},8->{6},9->{2,3},10->{7,8} ,11->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | +- p:[0] c: [0] | +- p:[2] c: [2] | `- p:[4] c: [4]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.1,0.2] f18.0 ~> f18.0 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f18.0 ~> f18.5 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f24.1 ~> f24.1 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f24.1 ~> f24.4 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f31.2 ~> f31.2 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f31.2 ~> f31.3 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f31.3 ~> f39.7 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] f24.4 ~> f31.2 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F] f24.4 ~> f31.3 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F] f18.5 ~> f24.1 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F] f18.5 ~> f24.4 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F] f0.6 ~> f18.0 [A <= 10*K, B <= 0*K, C <= 10*K, D <= unknown, E <= 10*K, F <= unknown] f39.7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] f39.7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] f39.7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] f39.7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= K + A + B] f18.0 ~> f18.0 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.1 <= K + A + B] f24.1 ~> f24.1 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.2 <= K + A + B] f31.2 ~> f31.2 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.1,0.2] f18.0 ~> f18.0 [A ~+> B,B ~+> B] f18.0 ~> f18.5 [A ~+> B,B ~+> B] f24.1 ~> f24.1 [A ~+> B,B ~+> B] f24.1 ~> f24.4 [A ~+> B,B ~+> B] f31.2 ~> f31.2 [A ~+> B,B ~+> B] f31.2 ~> f31.3 [A ~+> B,B ~+> B] f31.3 ~> f39.7 [] f24.4 ~> f31.2 [K ~=> B] f24.4 ~> f31.3 [K ~=> B] f18.5 ~> f24.1 [K ~=> B] f18.5 ~> f24.4 [K ~=> B] f0.6 ~> f18.0 [K ~=> A,K ~=> B,K ~=> C,K ~=> E,huge ~=> D,huge ~=> F] f39.7 ~> exitus616 [] f39.7 ~> exitus616 [] f39.7 ~> exitus616 [] f39.7 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] f18.0 ~> f18.0 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.1,B ~+> 0.1,K ~+> 0.1] f24.1 ~> f24.1 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.2,B ~+> 0.2,K ~+> 0.2] f31.2 ~> f31.2 [A ~+> B,B ~+> B] + Applied Processor: Lare + Details: f0.6 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> E ,huge ~=> D ,huge ~=> F ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] + f18.0> [A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] + f24.1> [A ~+> B ,A ~+> 0.1 ,A ~+> tick ,B ~+> B ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] + f31.2> [A ~+> B ,A ~+> 0.2 ,A ~+> tick ,B ~+> B ,B ~+> 0.2 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.2 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,O(1))