YES(?,O(1)) * Step 1: TrivialSCCs 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: 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] (1,1) 4. f24(A,B,C,D,E,F) -> f31(A,0,C,D,E,F) [B >= A] (1,1) 5. f18(A,B,C,D,E,F) -> f24(A,0,C,D,E,F) [B >= A] (1,1) 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 3: AddSinks 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] (1,1) 4. f24(A,B,C,D,E,F) -> f31(A,0,C,D,E,F) [B >= A] (1,1) 5. f18(A,B,C,D,E,F) -> f24(A,0,C,D,E,F) [B >= A] (1,1) 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: AddSinks + Details: () * Step 4: 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) 7. f31(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3,7},3->{},4->{2,3,7},5->{1,4},6->{0,5},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,5)] * Step 5: LooptreeTransformer 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) 7. f31(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3,7},3->{},4->{2,3,7},5->{1,4},6->{0},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[0] c: [0] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 6: SizeAbstraction 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) 7. f31(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3,7},3->{},4->{2,3,7},5->{1,4},6->{0},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[0] c: [0] | +- p:[1] c: [1] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.1,0.2] f18 ~> f18 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f24 ~> f24 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f31 ~> f31 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] f31 ~> f39 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] f24 ~> f31 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F] f18 ~> f24 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F] f0 ~> f18 [A <= 10*K, B <= 0*K, C <= 10*K, D <= unknown, E <= 10*K, F <= unknown] f31 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= A + B] f18 ~> f18 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.1 <= A + B] f24 ~> f24 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.2 <= A + B] f31 ~> f31 [A <= A, B <= A + B, C <= C, D <= D, E <= E, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.1,0.2] f18 ~> f18 [A ~+> B,B ~+> B] f24 ~> f24 [A ~+> B,B ~+> B] f31 ~> f31 [A ~+> B,B ~+> B] f31 ~> f39 [] f24 ~> f31 [K ~=> B] f18 ~> f24 [K ~=> B] f0 ~> f18 [K ~=> A,K ~=> B,K ~=> C,K ~=> E,huge ~=> D,huge ~=> F] f31 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] f18 ~> f18 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.1,B ~+> 0.1] f24 ~> f24 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.2,B ~+> 0.2] f31 ~> f31 [A ~+> B,B ~+> B] + Applied Processor: LareProcessor + Details: f0 ~> 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] f0 ~> f39 [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> [A ~+> B,A ~+> 0.0,A ~+> tick,B ~+> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,A ~*> B,B ~*> B] + f24> [A ~+> B,A ~+> 0.1,A ~+> tick,B ~+> B,B ~+> 0.1,B ~+> tick,tick ~+> tick,A ~*> B,B ~*> B] + f31> [A ~+> B,A ~+> 0.2,A ~+> tick,B ~+> B,B ~+> 0.2,B ~+> tick,tick ~+> tick,A ~*> B,B ~*> B] YES(?,O(1))