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) [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[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[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) [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) [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 >= 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: 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) [63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [0 >= 1 + C] (?,1) 5. f14(B,C) -> f57(B,7) [0 >= 1 + C] (?,1) 6. f6(B,C) -> f14(B,7) [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: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6),(5,4),(6,5)] * Step 3: FromIts 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) [63 >= B] (?,1) 2. f14(B,C) -> f14(B,-1 + C) [C >= 0] (?,1) 3. f57(B,C) -> f57(B,-1 + C) [C >= 0] (?,1) 4. f57(B,C) -> f101(B,C) [0 >= 1 + C] (?,1) 5. f14(B,C) -> f57(B,7) [0 >= 1 + C] (?,1) 6. f6(B,C) -> f14(B,7) [B >= 64] (?,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: FromIts + Details: () * Step 4: Unfold WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B,C) -> f6(0,C) True f6(B,C) -> f6(1 + B,C) [63 >= B] f14(B,C) -> f14(B,-1 + C) [C >= 0] f57(B,C) -> f57(B,-1 + C) [C >= 0] f57(B,C) -> f101(B,C) [0 >= 1 + C] f14(B,C) -> f57(B,7) [0 >= 1 + C] f6(B,C) -> f14(B,7) [B >= 64] Signature: {(f0,20);(f101,20);(f14,20);(f57,20);(f6,20)} Rule Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3},6->{2}] + Applied Processor: Unfold + Details: () * Step 5: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(B,C) -> f6.1(0,C) True f6.1(B,C) -> f6.1(1 + B,C) [63 >= B] f6.1(B,C) -> f6.6(1 + B,C) [63 >= B] f14.2(B,C) -> f14.2(B,-1 + C) [C >= 0] f14.2(B,C) -> f14.5(B,-1 + C) [C >= 0] f57.3(B,C) -> f57.3(B,-1 + C) [C >= 0] f57.3(B,C) -> f57.4(B,-1 + C) [C >= 0] f57.4(B,C) -> f101.7(B,C) [0 >= 1 + C] f14.5(B,C) -> f57.3(B,7) [0 >= 1 + C] f6.6(B,C) -> f14.2(B,7) [B >= 64] Signature: {(f0.0,2);(f101.7,2);(f14.2,2);(f14.5,2);(f57.3,2);(f57.4,2);(f6.1,2);(f6.6,2)} Rule Graph: [0->{1,2},1->{1,2},2->{9},3->{3,4},4->{8},5->{5,6},6->{7},7->{},8->{5,6},9->{3,4}] + Applied Processor: AddSinks + Details: () * Step 6: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(B,C) -> f6.1(0,C) True f6.1(B,C) -> f6.1(1 + B,C) [63 >= B] f6.1(B,C) -> f6.6(1 + B,C) [63 >= B] f14.2(B,C) -> f14.2(B,-1 + C) [C >= 0] f14.2(B,C) -> f14.5(B,-1 + C) [C >= 0] f57.3(B,C) -> f57.3(B,-1 + C) [C >= 0] f57.3(B,C) -> f57.4(B,-1 + C) [C >= 0] f57.4(B,C) -> f101.7(B,C) [0 >= 1 + C] f14.5(B,C) -> f57.3(B,7) [0 >= 1 + C] f6.6(B,C) -> f14.2(B,7) [B >= 64] f101.7(B,C) -> exitus616(B,C) True Signature: {(exitus616,2);(f0.0,2);(f101.7,2);(f14.2,2);(f14.5,2);(f57.3,2);(f57.4,2);(f6.1,2);(f6.6,2)} Rule Graph: [0->{1,2},1->{1,2},2->{9},3->{3,4},4->{8},5->{5,6},6->{7},7->{10},8->{5,6},9->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[3] c: [3] | `- p:[5] c: [5] * Step 7: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0.0(B,C) -> f6.1(0,C) True f6.1(B,C) -> f6.1(1 + B,C) [63 >= B] f6.1(B,C) -> f6.6(1 + B,C) [63 >= B] f14.2(B,C) -> f14.2(B,-1 + C) [C >= 0] f14.2(B,C) -> f14.5(B,-1 + C) [C >= 0] f57.3(B,C) -> f57.3(B,-1 + C) [C >= 0] f57.3(B,C) -> f57.4(B,-1 + C) [C >= 0] f57.4(B,C) -> f101.7(B,C) [0 >= 1 + C] f14.5(B,C) -> f57.3(B,7) [0 >= 1 + C] f6.6(B,C) -> f14.2(B,7) [B >= 64] f101.7(B,C) -> exitus616(B,C) True Signature: {(exitus616,2);(f0.0,2);(f101.7,2);(f14.2,2);(f14.5,2);(f57.3,2);(f57.4,2);(f6.1,2);(f6.6,2)} Rule Graph: [0->{1,2},1->{1,2},2->{9},3->{3,4},4->{8},5->{5,6},6->{7},7->{10},8->{5,6},9->{3,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[3] c: [3] | `- p:[5] c: [5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 8: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [B,C,0.0,0.1,0.2] f0.0 ~> f6.1 [B <= 0*K, C <= C] f6.1 ~> f6.1 [B <= K + B, C <= C] f6.1 ~> f6.6 [B <= K + B, C <= C] f14.2 ~> f14.2 [B <= B, C <= K + C] f14.2 ~> f14.5 [B <= B, C <= K + C] f57.3 ~> f57.3 [B <= B, C <= K + C] f57.3 ~> f57.4 [B <= B, C <= K + C] f57.4 ~> f101.7 [B <= B, C <= C] f14.5 ~> f57.3 [B <= B, C <= 7*K] f6.6 ~> f14.2 [B <= B, C <= 7*K] f101.7 ~> exitus616 [B <= B, C <= C] + Loop: [0.0 <= 63*K + B] f6.1 ~> f6.1 [B <= K + B, C <= C] + Loop: [0.1 <= C] f14.2 ~> f14.2 [B <= B, C <= K + C] + Loop: [0.2 <= C] f57.3 ~> f57.3 [B <= B, C <= K + C] + Applied Processor: AbstractFlow + Details: () * Step 9: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,B,C,0.0,0.1,0.2] f0.0 ~> f6.1 [K ~=> B] f6.1 ~> f6.1 [B ~+> B,K ~+> B] f6.1 ~> f6.6 [B ~+> B,K ~+> B] f14.2 ~> f14.2 [C ~+> C,K ~+> C] f14.2 ~> f14.5 [C ~+> C,K ~+> C] f57.3 ~> f57.3 [C ~+> C,K ~+> C] f57.3 ~> f57.4 [C ~+> C,K ~+> C] f57.4 ~> f101.7 [] f14.5 ~> f57.3 [K ~=> C] f6.6 ~> f14.2 [K ~=> C] f101.7 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f6.1 ~> f6.1 [B ~+> B,K ~+> B] + Loop: [C ~=> 0.1] f14.2 ~> f14.2 [C ~+> C,K ~+> C] + Loop: [C ~=> 0.2] f57.3 ~> f57.3 [C ~+> C,K ~+> C] + Applied Processor: Lare + Details: f0.0 ~> exitus616 [K ~=> 0.1 ,K ~=> 0.2 ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + f6.1> [B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f14.2> [C ~=> 0.1,C ~+> C,C ~+> tick,tick ~+> tick,K ~+> C,C ~*> C,K ~*> C] + f57.3> [C ~=> 0.2,C ~+> C,C ~+> tick,tick ~+> tick,K ~+> C,C ~*> C,K ~*> C] YES(?,O(1))