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) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + Applied Processor: ArgumentFilter [0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] + Details: We remove following argument positions: [0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f7(0) True (1,1) 1. f7(B) -> f7(1 + B) [7 >= B] (?,1) 2. f62(B) -> f62(1 + B) [7 >= B] (?,1) 3. f62(B) -> f118(B) [B >= 8] (?,1) 4. f7(B) -> f62(0) [B >= 8] (?,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f7(0) True (1,1) 1. f7(B) -> f7(1 + B) [7 >= B] (?,1) 2. f62(B) -> f62(1 + B) [7 >= B] (?,1) 3. f62(B) -> f118(B) [B >= 8] (?,1) 4. f7(B) -> f62(0) [B >= 8] (?,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: FromIts + Details: () * Step 4: Unfold WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B) -> f7(0) True f7(B) -> f7(1 + B) [7 >= B] f62(B) -> f62(1 + B) [7 >= B] f62(B) -> f118(B) [B >= 8] f7(B) -> f62(0) [B >= 8] Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Rule Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: Unfold + Details: () * Step 5: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(B) -> f7.1(0) True f7.1(B) -> f7.1(1 + B) [7 >= B] f7.1(B) -> f7.4(1 + B) [7 >= B] f62.2(B) -> f62.2(1 + B) [7 >= B] f62.2(B) -> f62.3(1 + B) [7 >= B] f62.3(B) -> f118.5(B) [B >= 8] f7.4(B) -> f62.2(0) [B >= 8] Signature: {(f0.0,1);(f118.5,1);(f62.2,1);(f62.3,1);(f7.1,1);(f7.4,1)} Rule Graph: [0->{1,2},1->{1,2},2->{6},3->{3,4},4->{5},5->{},6->{3,4}] + Applied Processor: AddSinks + Details: () * Step 6: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(B) -> f7.1(0) True f7.1(B) -> f7.1(1 + B) [7 >= B] f7.1(B) -> f7.4(1 + B) [7 >= B] f62.2(B) -> f62.2(1 + B) [7 >= B] f62.2(B) -> f62.3(1 + B) [7 >= B] f62.3(B) -> f118.5(B) [B >= 8] f7.4(B) -> f62.2(0) [B >= 8] f118.5(B) -> exitus616(B) True Signature: {(exitus616,1);(f0.0,1);(f118.5,1);(f62.2,1);(f62.3,1);(f7.1,1);(f7.4,1)} Rule Graph: [0->{1,2},1->{1,2},2->{6},3->{3,4},4->{5},5->{7},6->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | `- p:[3] c: [3] * Step 7: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0.0(B) -> f7.1(0) True f7.1(B) -> f7.1(1 + B) [7 >= B] f7.1(B) -> f7.4(1 + B) [7 >= B] f62.2(B) -> f62.2(1 + B) [7 >= B] f62.2(B) -> f62.3(1 + B) [7 >= B] f62.3(B) -> f118.5(B) [B >= 8] f7.4(B) -> f62.2(0) [B >= 8] f118.5(B) -> exitus616(B) True Signature: {(exitus616,1);(f0.0,1);(f118.5,1);(f62.2,1);(f62.3,1);(f7.1,1);(f7.4,1)} Rule Graph: [0->{1,2},1->{1,2},2->{6},3->{3,4},4->{5},5->{7},6->{3,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 8: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [B,0.0,0.1] f0.0 ~> f7.1 [B <= 0*K] f7.1 ~> f7.1 [B <= K + B] f7.1 ~> f7.4 [B <= K + B] f62.2 ~> f62.2 [B <= K + B] f62.2 ~> f62.3 [B <= K + B] f62.3 ~> f118.5 [B <= B] f7.4 ~> f62.2 [B <= 0*K] f118.5 ~> exitus616 [B <= B] + Loop: [0.0 <= 7*K + B] f7.1 ~> f7.1 [B <= K + B] + Loop: [0.1 <= 7*K + B] f62.2 ~> f62.2 [B <= K + B] + Applied Processor: AbstractFlow + Details: () * Step 9: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,B,0.0,0.1] f0.0 ~> f7.1 [K ~=> B] f7.1 ~> f7.1 [B ~+> B,K ~+> B] f7.1 ~> f7.4 [B ~+> B,K ~+> B] f62.2 ~> f62.2 [B ~+> B,K ~+> B] f62.2 ~> f62.3 [B ~+> B,K ~+> B] f62.3 ~> f118.5 [] f7.4 ~> f62.2 [K ~=> B] f118.5 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f7.1 ~> f7.1 [B ~+> B,K ~+> B] + Loop: [B ~+> 0.1,K ~*> 0.1] f62.2 ~> f62.2 [B ~+> B,K ~+> B] + Applied Processor: Lare + Details: f0.0 ~> exitus616 [tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f7.1> [B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f62.2> [B ~+> B ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,K ~*> B ,K ~*> 0.1 ,K ~*> tick] YES(?,O(1))