YES(?,POLY) * Step 1: UnsatRules WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f1(A,B,2,D) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B && 0 >= 2] (?,1) 2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B] (?,1) 3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C] (?,1) 4. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C && 0 >= 2] (?,1) 5. f1(A,B,C,D) -> f1(A,B,C,B) [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1) 6. f1(A,B,C,D) -> f1(A,B,C,B) [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1) Signature: {(f0,4);(f1,4)} Flow Graph: [0->{1,2,3,4,5,6},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3,4,5,6},4->{1,2,3,4,5,6},5->{1,2,3,4,5,6} ,6->{1,2,3,4,5,6}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [1,4,5,6] * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f1(A,B,2,D) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B] (?,1) 3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C] (?,1) Signature: {(f0,4);(f1,4)} Flow Graph: [0->{2,3},2->{2,3},3->{2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,3),(3,2)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f1(A,B,2,D) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B] (?,1) 3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C] (?,1) Signature: {(f0,4);(f1,4)} Flow Graph: [0->{2,3},2->{2},3->{3}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f1(A,B,2,D) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B] (?,1) 3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C] (?,1) 4. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f1,4)} Flow Graph: [0->{2,3,4},2->{2,3,4},3->{2,3,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,3),(3,2)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f1(A,B,2,D) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B] (?,1) 3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C] (?,1) 4. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f1,4)} Flow Graph: [0->{2,3,4},2->{2,4},3->{3,4},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,2,3,4] | +- p:[3] c: [3] | `- p:[2] c: [2] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. f0(A,B,C,D) -> f1(A,B,2,D) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B) [A + C >= 1 + 2*B] (?,1) 3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C] (?,1) 4. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f0,4);(f1,4)} Flow Graph: [0->{2,3,4},2->{2,4},3->{3,4},4->{}] ,We construct a looptree: P: [0,2,3,4] | +- p:[3] c: [3] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.1] f0 ~> f1 [A <= A, B <= B, C <= 2*K, D <= D] f1 ~> f1 [A <= A, B <= K + B, C <= C, D <= K + B] f1 ~> f1 [A <= A, B <= K + B, C <= C, D <= K + B] f1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + 2*B + C] f1 ~> f1 [A <= A, B <= K + B, C <= C, D <= K + B] + Loop: [0.1 <= A + 2*B + C] f1 ~> f1 [A <= A, B <= K + B, C <= C, D <= K + B] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.1] f0 ~> f1 [K ~=> C] f1 ~> f1 [B ~+> B,B ~+> D,K ~+> B,K ~+> D] f1 ~> f1 [B ~+> B,B ~+> D,K ~+> B,K ~+> D] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,C ~+> 0.0,K ~+> 0.0,B ~*> 0.0] f1 ~> f1 [B ~+> B,B ~+> D,K ~+> B,K ~+> D] + Loop: [A ~+> 0.1,C ~+> 0.1,B ~*> 0.1] f1 ~> f1 [B ~+> B,B ~+> D,K ~+> B,K ~+> D] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> C ,A ~+> 0.0 ,A ~+> 0.1 ,A ~+> tick ,B ~+> B ,B ~+> D ,tick ~+> tick ,K ~+> B ,K ~+> D ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,B ~*> B ,B ~*> 0.0 ,B ~*> 0.1 ,B ~*> tick ,K ~*> B ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] + f1> [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> D ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,B ~*> 0.0 ,B ~*> tick ,C ~*> B ,K ~*> B ,K ~*> D] + f1> [A ~+> 0.1 ,A ~+> tick ,B ~+> B ,B ~+> D ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,A ~*> B ,B ~*> B ,B ~*> 0.1 ,B ~*> tick ,C ~*> B ,K ~*> B ,K ~*> D] YES(?,POLY)