YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f8(A,B,C,D) -> f8(-1 + A,B,C,D) [A >= 0] (?,1) 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (?,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (?,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 6. f8(A,B,C,D) -> f19(A,999,C,D) [0 >= 1 + A] (?,1) Signature: {(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [0->{0,6},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{1,4}] + 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. f8(A,B,C,D) -> f8(-1 + A,B,C,D) [A >= 0] (?,1) 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (1,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (1,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 6. f8(A,B,C,D) -> f19(A,999,C,D) [0 >= 1 + A] (1,1) Signature: {(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [0->{0,6},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{1,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,3),(5,4),(6,4)] * Step 3: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f8(A,B,C,D) -> f8(-1 + A,B,C,D) [A >= 0] (?,1) 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (1,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (1,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 6. f8(A,B,C,D) -> f19(A,999,C,D) [0 >= 1 + A] (1,1) Signature: {(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [0->{0,6},1->{1,4},2->{2,3},3->{},4->{2},5->{1},6->{1}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [0,6] * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (1,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (1,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) Signature: {(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [1->{1,4},2->{2,3},3->{},4->{2},5->{1}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (?,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (?,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 6. f28(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [1->{1,4},2->{2,3,6},3->{},4->{2,3,6},5->{1,4},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,3),(5,4)] * Step 6: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (?,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (?,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 6. f28(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [1->{1,4},2->{2,3,6},3->{},4->{2,6},5->{1},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [1,2,3,4,5,6] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 7: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [B >= 0] (?,1) 2. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [C >= 0] (?,1) 3. f28(A,B,C,D) -> f36(A,B,C,D) [0 >= 1 + C] (?,1) 4. f19(A,B,C,D) -> f28(A,B,999,D) [0 >= 1 + B] (?,1) 5. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 6. f28(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f19,4);(f28,4);(f36,4);(f8,4)} Flow Graph: [1->{1,4},2->{2,3,6},3->{},4->{2,6},5->{1},6->{}] ,We construct a looptree: P: [1,2,3,4,5,6] | +- p:[1] c: [1] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 8: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.1] f19 ~> f19 [A <= A, B <= K + B, C <= C, D <= D] f28 ~> f28 [A <= A, B <= B, C <= K + C, D <= D] f28 ~> f36 [A <= A, B <= B, C <= C, D <= D] f19 ~> f28 [A <= A, B <= B, C <= 999*K, D <= D] f0 ~> f19 [A <= A, B <= 999*K, C <= C, D <= K] f28 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + B] f19 ~> f19 [A <= A, B <= K + B, C <= C, D <= D] + Loop: [0.1 <= K + C] f28 ~> f28 [A <= A, B <= B, C <= K + C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.1] f19 ~> f19 [B ~+> B,K ~+> B] f28 ~> f28 [C ~+> C,K ~+> C] f28 ~> f36 [] f19 ~> f28 [K ~=> C] f0 ~> f19 [K ~=> B,K ~=> D] f28 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~+> 0.0] f19 ~> f19 [B ~+> B,K ~+> B] + Loop: [C ~+> 0.1,K ~+> 0.1] f28 ~> f28 [C ~+> C,K ~+> C] + Applied Processor: LareProcessor + Details: f0 ~> f36 [K ~=> B ,K ~=> C ,K ~=> D ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] f0 ~> exitus616 [K ~=> B ,K ~=> C ,K ~=> D ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f19> [B ~+> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~+> B,K ~+> 0.0,K ~+> tick,B ~*> B,K ~*> B] + f28> [C ~+> C,C ~+> 0.1,C ~+> tick,tick ~+> tick,K ~+> C,K ~+> 0.1,K ~+> tick,C ~*> C,K ~*> C] YES(?,O(1))