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 [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 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[B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 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 >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 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 >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 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: ArgumentFilter [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] + Details: We remove following argument positions: [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. * Step 2: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f7(8,0) True (1,1) 1. f7(A,B) -> f7(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 2. f62(A,B) -> f62(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 3. f62(A,B) -> f118(A,B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 4. f7(A,B) -> f62(A,0) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f7(8,0) True (1,1) 1. f7(A,B) -> f7(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 2. f62(A,B) -> f62(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 3. f62(A,B) -> f118(A,B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (1,1) 4. f7(A,B) -> f62(A,0) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (1,1) 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 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f7(8,0) True (1,1) 1. f7(A,B) -> f7(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 2. f62(A,B) -> f62(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 3. f62(A,B) -> f118(A,B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (1,1) 4. f7(A,B) -> f62(A,0) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (1,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f7(8,0) True (1,1) 1. f7(A,B) -> f7(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 2. f62(A,B) -> f62(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 3. f62(A,B) -> f118(A,B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 4. f7(A,B) -> f62(A,0) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 5. f62(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3,5},3->{},4->{2,3,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 6: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f7(8,0) True (1,1) 1. f7(A,B) -> f7(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 2. f62(A,B) -> f62(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 3. f62(A,B) -> f118(A,B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 4. f7(A,B) -> f62(A,0) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 5. f62(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 7: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B) -> f7(8,0) True (1,1) 1. f7(A,B) -> f7(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 2. f62(A,B) -> f62(A,1 + B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && 7 >= B] (?,1) 3. f62(A,B) -> f118(A,B) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 4. f7(A,B) -> f62(A,0) [B >= 0 && -8 + A + B >= 0 && 8 + -1*A + B >= 0 && 8 + -1*A >= 0 && -8 + A >= 0 && B >= 8] (?,1) 5. f62(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- 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,0.0,0.1] f0 ~> f7 [A <= 8*K, B <= 0*K] f7 ~> f7 [A <= A, B <= 8*K] f62 ~> f62 [A <= A, B <= 8*K] f62 ~> f118 [A <= A, B <= B] f7 ~> f62 [A <= A, B <= 0*K] f62 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 8*K + B] f7 ~> f7 [A <= A, B <= 8*K] + Loop: [0.1 <= 8*K + B] f62 ~> f62 [A <= A, B <= 8*K] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] f0 ~> f7 [K ~=> A,K ~=> B] f7 ~> f7 [K ~=> B] f62 ~> f62 [K ~=> B] f62 ~> f118 [] f7 ~> f62 [K ~=> B] f62 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f7 ~> f7 [K ~=> B] + Loop: [B ~+> 0.1,K ~*> 0.1] f62 ~> f62 [K ~=> B] + Applied Processor: LareProcessor + Details: f0 ~> f118 [K ~=> A ,K ~=> B ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] f0 ~> exitus616 [K ~=> A ,K ~=> B ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f7> [K ~=> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f62> [K ~=> B,B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] YES(?,O(1))