YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f6(0,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f6(U,1 + B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && 63 >= B] (?,1) 2. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 3. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,-1 + C,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V[7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) ,A1 + B1 + X + Y,-1*A1 + -1*B1 + X + Y,G1,H1,I1 + J1,J1 + K1,J1) 4. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f101(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 5. f14(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f57(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 6. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f14(A,B,7,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 0 && B >= 64] (?,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + Applied Processor: ArgumentFilter [0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] + Details: We remove following argument positions: [0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. * Step 2: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f6(0,C) True (1,1) 1. f6(B,C) -> f6(1 + B,C) [B >= 0 && 63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 5. f14(B,C) -> f57(B,7) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 6. f6(B,C) -> f14(B,7) [B >= 0 && B >= 64] (?,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f6(0,C) True (1,1) 1. f6(B,C) -> f6(1 + B,C) [B >= 0 && 63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 5. f14(B,C) -> f57(B,7) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 6. f6(B,C) -> f14(B,7) [B >= 0 && B >= 64] (1,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6),(5,4),(6,5)] * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f6(0,C) True (1,1) 1. f6(B,C) -> f6(1 + B,C) [B >= 0 && 63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 5. f14(B,C) -> f57(B,7) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (1,1) 6. f6(B,C) -> f14(B,7) [B >= 0 && B >= 64] (1,1) Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3},6->{2}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f6(0,C) True (1,1) 1. f6(B,C) -> f6(1 + B,C) [B >= 0 && 63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 5. f14(B,C) -> f57(B,7) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 6. f6(B,C) -> f14(B,7) [B >= 0 && B >= 64] (?,1) 7. f57(B,C) -> exitus616(B,C) True (?,1) Signature: {(exitus616,2);(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4,7},4->{},5->{3,4,7},6->{2,5},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6),(5,4),(6,5)] * Step 6: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f6(0,C) True (1,1) 1. f6(B,C) -> f6(1 + B,C) [B >= 0 && 63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 5. f14(B,C) -> f57(B,7) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 6. f6(B,C) -> f14(B,7) [B >= 0 && B >= 64] (?,1) 7. f57(B,C) -> exitus616(B,C) True (?,1) Signature: {(exitus616,2);(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4,7},4->{},5->{3,7},6->{2},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | +- p:[2] c: [2] | `- p:[3] c: [3] * Step 7: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(B,C) -> f6(0,C) True (1,1) 1. f6(B,C) -> f6(1 + B,C) [B >= 0 && 63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 5. f14(B,C) -> f57(B,7) [7 + -1*C >= 0 && -57 + B + -1*C >= 0 && -64 + B >= 0 && 0 >= 1 + C] (?,1) 6. f6(B,C) -> f14(B,7) [B >= 0 && B >= 64] (?,1) 7. f57(B,C) -> exitus616(B,C) True (?,1) Signature: {(exitus616,2);(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4,7},4->{},5->{3,7},6->{2},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | +- p:[2] c: [2] | `- p:[3] c: [3]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 8: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [B,C,0.0,0.1,0.2] f0 ~> f6 [B <= 0*K, C <= C] f6 ~> f6 [B <= 64*K, C <= C] f14 ~> f14 [B <= B, C <= 6*K] f57 ~> f57 [B <= B, C <= 6*K] f57 ~> f101 [B <= B, C <= C] f14 ~> f57 [B <= B, C <= 7*K] f6 ~> f14 [B <= B, C <= 7*K] f57 ~> exitus616 [B <= B, C <= C] + Loop: [0.0 <= 64*K + B] f6 ~> f6 [B <= 64*K, C <= C] + Loop: [0.1 <= K + C] f14 ~> f14 [B <= B, C <= 6*K] + Loop: [0.2 <= K + C] f57 ~> f57 [B <= B, C <= 6*K] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,B,C,0.0,0.1,0.2] f0 ~> f6 [K ~=> B] f6 ~> f6 [K ~=> B] f14 ~> f14 [K ~=> C] f57 ~> f57 [K ~=> C] f57 ~> f101 [] f14 ~> f57 [K ~=> C] f6 ~> f14 [K ~=> C] f57 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f6 ~> f6 [K ~=> B] + Loop: [C ~+> 0.1,K ~+> 0.1] f14 ~> f14 [K ~=> C] + Loop: [C ~+> 0.2,K ~+> 0.2] f57 ~> f57 [K ~=> C] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> B ,K ~=> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] f0 ~> f101 [K ~=> B ,K ~=> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] + f6> [K ~=> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f14> [K ~=> C,C ~+> 0.1,C ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] + f57> [K ~=> C,C ~+> 0.2,C ~+> tick,tick ~+> tick,K ~+> 0.2,K ~+> tick] YES(?,O(1))