YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (?,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [B >= 1 + C] (?,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 5. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [C >= B && A >= 0] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [0 >= 1 + D] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [D >= 1] (?,1) 8. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) True (?,1) 9. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) True (?,1) 10. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) True (?,1) 11. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (?,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3)} Flow Graph: [0->{1,2},1->{3,4,5},2->{11},3->{11},4->{11},5->{6,7,8},6->{9},7->{9},8->{10},9->{3,4,5},10->{3,4,5} ,11->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (1,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (1,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [B >= 1 + C] (1,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (1,1) 5. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [C >= B && A >= 0] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [0 >= 1 + D] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [D >= 1] (?,1) 8. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) True (?,1) 9. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) True (?,1) 10. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) True (?,1) 11. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (1,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3)} Flow Graph: [0->{1,2},1->{3,4,5},2->{11},3->{11},4->{11},5->{6,7,8},6->{9},7->{9},8->{10},9->{3,4,5},10->{3,4,5} ,11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,4)] * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (1,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (1,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [B >= 1 + C] (1,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (1,1) 5. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [C >= B && A >= 0] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [0 >= 1 + D] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [D >= 1] (?,1) 8. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) True (?,1) 9. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) True (?,1) 10. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) True (?,1) 11. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (1,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3)} Flow Graph: [0->{1,2},1->{3,5},2->{11},3->{11},4->{11},5->{6,7,8},6->{9},7->{9},8->{10},9->{3,4,5},10->{3,4,5},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (?,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [B >= 1 + C] (?,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 5. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [C >= B && A >= 0] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [0 >= 1 + D] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [D >= 1] (?,1) 8. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) True (?,1) 9. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) True (?,1) 10. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) True (?,1) 11. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (?,1) 12. evalaaron2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3) ;(exitus616,3)} Flow Graph: [0->{1,2},1->{3,4,5},2->{11,12},3->{11,12},4->{11,12},5->{6,7,8},6->{9},7->{9},8->{10},9->{3,4,5},10->{3,4 ,5},11->{},12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,4)] * Step 5: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (?,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [B >= 1 + C] (?,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 5. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [C >= B && A >= 0] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [0 >= 1 + D] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [D >= 1] (?,1) 8. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) True (?,1) 9. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) True (?,1) 10. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) True (?,1) 11. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (?,1) 12. evalaaron2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3) ;(exitus616,3)} Flow Graph: [0->{1,2},1->{3,5},2->{11,12},3->{11,12},4->{11,12},5->{6,7,8},6->{9},7->{9},8->{10},9->{3,4,5},10->{3,4 ,5},11->{},12->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[5,9,6,7,10,8] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (?,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [B >= 1 + C] (?,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 5. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [C >= B && A >= 0] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [0 >= 1 + D] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [D >= 1] (?,1) 8. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) True (?,1) 9. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) True (?,1) 10. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) True (?,1) 11. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (?,1) 12. evalaaron2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3) ;(exitus616,3)} Flow Graph: [0->{1,2},1->{3,5},2->{11,12},3->{11,12},4->{11,12},5->{6,7,8},6->{9},7->{9},8->{10},9->{3,4,5},10->{3,4 ,5},11->{},12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[5,9,6,7,10,8] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalaaron2start ~> evalaaron2entryin [A <= A, B <= B, C <= C] evalaaron2entryin ~> evalaaron2bb6in [A <= A, B <= C, C <= B] evalaaron2entryin ~> evalaaron2returnin [A <= A, B <= B, C <= C] evalaaron2bb6in ~> evalaaron2returnin [A <= A, B <= B, C <= C] evalaaron2bb6in ~> evalaaron2returnin [A <= A, B <= B, C <= C] evalaaron2bb6in ~> evalaaron2bb3in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb5in [A <= A, B <= B, C <= C] evalaaron2bb4in ~> evalaaron2bb6in [A <= A, B <= B, C <= K + A + C] evalaaron2bb5in ~> evalaaron2bb6in [A <= A, B <= K + A + B, C <= C] evalaaron2returnin ~> evalaaron2stop [A <= A, B <= B, C <= C] evalaaron2returnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 2*K + A + B + C] evalaaron2bb6in ~> evalaaron2bb3in [A <= A, B <= B, C <= C] evalaaron2bb4in ~> evalaaron2bb6in [A <= A, B <= B, C <= K + A + C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb5in ~> evalaaron2bb6in [A <= A, B <= K + A + B, C <= C] evalaaron2bb3in ~> evalaaron2bb5in [A <= A, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalaaron2start ~> evalaaron2entryin [] evalaaron2entryin ~> evalaaron2bb6in [B ~=> C,C ~=> B] evalaaron2entryin ~> evalaaron2returnin [] evalaaron2bb6in ~> evalaaron2returnin [] evalaaron2bb6in ~> evalaaron2returnin [] evalaaron2bb6in ~> evalaaron2bb3in [] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb3in ~> evalaaron2bb5in [] evalaaron2bb4in ~> evalaaron2bb6in [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb5in ~> evalaaron2bb6in [A ~+> B,B ~+> B,K ~+> B] evalaaron2returnin ~> evalaaron2stop [] evalaaron2returnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] evalaaron2bb6in ~> evalaaron2bb3in [] evalaaron2bb4in ~> evalaaron2bb6in [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb5in ~> evalaaron2bb6in [A ~+> B,B ~+> B,K ~+> B] evalaaron2bb3in ~> evalaaron2bb5in [] + Applied Processor: LareProcessor + Details: evalaaron2start ~> exitus616 [B ~=> C ,C ~=> B ,A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] evalaaron2start ~> evalaaron2stop [B ~=> C ,C ~=> B ,A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + evalaaron2bb6in> [A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))