YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalwhile2start.0(A,B,C) -> evalwhile2entryin.1(A,B,C) True evalwhile2entryin.1(A,B,C) -> evalwhile2bb4in.2(B,B,C) True evalwhile2entryin.1(A,B,C) -> evalwhile2bb4in.3(B,B,C) True evalwhile2bb4in.2(A,B,C) -> evalwhile2bb2in.4(A,B,B) [-1*A + B >= 0 && A >= 1] evalwhile2bb4in.3(A,B,C) -> evalwhile2returnin.8(A,B,C) [-1*A + B >= 0 && 0 >= A] evalwhile2bb2in.4(A,B,C) -> evalwhile2bb1in.6(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] evalwhile2bb2in.5(A,B,C) -> evalwhile2bb3in.7(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] evalwhile2bb1in.6(A,B,C) -> evalwhile2bb2in.4(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb1in.6(A,B,C) -> evalwhile2bb2in.5(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in.7(A,B,C) -> evalwhile2bb4in.2(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in.7(A,B,C) -> evalwhile2bb4in.3(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2returnin.8(A,B,C) -> evalwhile2stop.9(A,B,C) [-1*A + B >= 0 && -1*A >= 0] Signature: {(evalwhile2bb1in.6,3) ;(evalwhile2bb2in.4,3) ;(evalwhile2bb2in.5,3) ;(evalwhile2bb3in.7,3) ;(evalwhile2bb4in.2,3) ;(evalwhile2bb4in.3,3) ;(evalwhile2entryin.1,3) ;(evalwhile2returnin.8,3) ;(evalwhile2start.0,3) ;(evalwhile2stop.9,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{11},5->{7,8},6->{9,10},7->{5},8->{6},9->{3},10->{4},11->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalwhile2start.0(A,B,C) -> evalwhile2entryin.1(A,B,C) True evalwhile2entryin.1(A,B,C) -> evalwhile2bb4in.2(B,B,C) True evalwhile2entryin.1(A,B,C) -> evalwhile2bb4in.3(B,B,C) True evalwhile2bb4in.2(A,B,C) -> evalwhile2bb2in.4(A,B,B) [-1*A + B >= 0 && A >= 1] evalwhile2bb4in.3(A,B,C) -> evalwhile2returnin.8(A,B,C) [-1*A + B >= 0 && 0 >= A] evalwhile2bb2in.4(A,B,C) -> evalwhile2bb1in.6(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] evalwhile2bb2in.5(A,B,C) -> evalwhile2bb3in.7(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] evalwhile2bb1in.6(A,B,C) -> evalwhile2bb2in.4(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb1in.6(A,B,C) -> evalwhile2bb2in.5(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in.7(A,B,C) -> evalwhile2bb4in.2(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in.7(A,B,C) -> evalwhile2bb4in.3(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2returnin.8(A,B,C) -> evalwhile2stop.9(A,B,C) [-1*A + B >= 0 && -1*A >= 0] evalwhile2stop.9(A,B,C) -> exitus616(A,B,C) True evalwhile2stop.9(A,B,C) -> exitus616(A,B,C) True Signature: {(evalwhile2bb1in.6,3) ;(evalwhile2bb2in.4,3) ;(evalwhile2bb2in.5,3) ;(evalwhile2bb3in.7,3) ;(evalwhile2bb4in.2,3) ;(evalwhile2bb4in.3,3) ;(evalwhile2entryin.1,3) ;(evalwhile2returnin.8,3) ;(evalwhile2start.0,3) ;(evalwhile2stop.9,3) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{11},5->{7,8},6->{9,10},7->{5},8->{6},9->{3},10->{4},11->{12,13}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[3,9,6,8,5,7] c: [3,6,8,9] | `- p:[5,7] c: [5,7] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalwhile2start.0(A,B,C) -> evalwhile2entryin.1(A,B,C) True evalwhile2entryin.1(A,B,C) -> evalwhile2bb4in.2(B,B,C) True evalwhile2entryin.1(A,B,C) -> evalwhile2bb4in.3(B,B,C) True evalwhile2bb4in.2(A,B,C) -> evalwhile2bb2in.4(A,B,B) [-1*A + B >= 0 && A >= 1] evalwhile2bb4in.3(A,B,C) -> evalwhile2returnin.8(A,B,C) [-1*A + B >= 0 && 0 >= A] evalwhile2bb2in.4(A,B,C) -> evalwhile2bb1in.6(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] evalwhile2bb2in.5(A,B,C) -> evalwhile2bb3in.7(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] evalwhile2bb1in.6(A,B,C) -> evalwhile2bb2in.4(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb1in.6(A,B,C) -> evalwhile2bb2in.5(A,B,-1 + C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in.7(A,B,C) -> evalwhile2bb4in.2(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2bb3in.7(A,B,C) -> evalwhile2bb4in.3(-1 + A,B,C) [-1*C >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalwhile2returnin.8(A,B,C) -> evalwhile2stop.9(A,B,C) [-1*A + B >= 0 && -1*A >= 0] evalwhile2stop.9(A,B,C) -> exitus616(A,B,C) True evalwhile2stop.9(A,B,C) -> exitus616(A,B,C) True Signature: {(evalwhile2bb1in.6,3) ;(evalwhile2bb2in.4,3) ;(evalwhile2bb2in.5,3) ;(evalwhile2bb3in.7,3) ;(evalwhile2bb4in.2,3) ;(evalwhile2bb4in.3,3) ;(evalwhile2entryin.1,3) ;(evalwhile2returnin.8,3) ;(evalwhile2start.0,3) ;(evalwhile2stop.9,3) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{11},5->{7,8},6->{9,10},7->{5},8->{6},9->{3},10->{4},11->{12,13}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[3,9,6,8,5,7] c: [3,6,8,9] | `- p:[5,7] c: [5,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalwhile2start.0 ~> evalwhile2entryin.1 [A <= A, B <= B, C <= C] evalwhile2entryin.1 ~> evalwhile2bb4in.2 [A <= B, B <= B, C <= C] evalwhile2entryin.1 ~> evalwhile2bb4in.3 [A <= B, B <= B, C <= C] evalwhile2bb4in.2 ~> evalwhile2bb2in.4 [A <= A, B <= B, C <= B] evalwhile2bb4in.3 ~> evalwhile2returnin.8 [A <= A, B <= B, C <= C] evalwhile2bb2in.4 ~> evalwhile2bb1in.6 [A <= A, B <= B, C <= C] evalwhile2bb2in.5 ~> evalwhile2bb3in.7 [A <= A, B <= B, C <= C] evalwhile2bb1in.6 ~> evalwhile2bb2in.4 [A <= A, B <= B, C <= C] evalwhile2bb1in.6 ~> evalwhile2bb2in.5 [A <= A, B <= B, C <= C] evalwhile2bb3in.7 ~> evalwhile2bb4in.2 [A <= B, B <= B, C <= C] evalwhile2bb3in.7 ~> evalwhile2bb4in.3 [A <= B, B <= B, C <= C] evalwhile2returnin.8 ~> evalwhile2stop.9 [A <= A, B <= B, C <= C] evalwhile2stop.9 ~> exitus616 [A <= A, B <= B, C <= C] evalwhile2stop.9 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 2*K + A + B] evalwhile2bb4in.2 ~> evalwhile2bb2in.4 [A <= A, B <= B, C <= B] evalwhile2bb3in.7 ~> evalwhile2bb4in.2 [A <= B, B <= B, C <= C] evalwhile2bb2in.5 ~> evalwhile2bb3in.7 [A <= A, B <= B, C <= C] evalwhile2bb1in.6 ~> evalwhile2bb2in.5 [A <= A, B <= B, C <= C] evalwhile2bb2in.4 ~> evalwhile2bb1in.6 [A <= A, B <= B, C <= C] evalwhile2bb1in.6 ~> evalwhile2bb2in.4 [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= K + C] evalwhile2bb2in.4 ~> evalwhile2bb1in.6 [A <= A, B <= B, C <= C] evalwhile2bb1in.6 ~> evalwhile2bb2in.4 [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalwhile2start.0 ~> evalwhile2entryin.1 [] evalwhile2entryin.1 ~> evalwhile2bb4in.2 [B ~=> A] evalwhile2entryin.1 ~> evalwhile2bb4in.3 [B ~=> A] evalwhile2bb4in.2 ~> evalwhile2bb2in.4 [B ~=> C] evalwhile2bb4in.3 ~> evalwhile2returnin.8 [] evalwhile2bb2in.4 ~> evalwhile2bb1in.6 [] evalwhile2bb2in.5 ~> evalwhile2bb3in.7 [] evalwhile2bb1in.6 ~> evalwhile2bb2in.4 [] evalwhile2bb1in.6 ~> evalwhile2bb2in.5 [] evalwhile2bb3in.7 ~> evalwhile2bb4in.2 [B ~=> A] evalwhile2bb3in.7 ~> evalwhile2bb4in.3 [B ~=> A] evalwhile2returnin.8 ~> evalwhile2stop.9 [] evalwhile2stop.9 ~> exitus616 [] evalwhile2stop.9 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~*> 0.0] evalwhile2bb4in.2 ~> evalwhile2bb2in.4 [B ~=> C] evalwhile2bb3in.7 ~> evalwhile2bb4in.2 [B ~=> A] evalwhile2bb2in.5 ~> evalwhile2bb3in.7 [] evalwhile2bb1in.6 ~> evalwhile2bb2in.5 [] evalwhile2bb2in.4 ~> evalwhile2bb1in.6 [] evalwhile2bb1in.6 ~> evalwhile2bb2in.4 [] + Loop: [C ~+> 0.0.0,K ~+> 0.0.0] evalwhile2bb2in.4 ~> evalwhile2bb1in.6 [] evalwhile2bb1in.6 ~> evalwhile2bb2in.4 [] + Applied Processor: Lare + Details: evalwhile2start.0 ~> exitus616 [B ~=> A ,B ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0 ,B ~*> tick ,K ~*> 0.0 ,K ~*> tick] + evalwhile2bb3in.7> [B ~=> A ,B ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,K ~*> 0.0 ,K ~*> tick] + evalwhile2bb1in.6> [C ~+> 0.0.0,C ~+> tick,tick ~+> tick,K ~+> 0.0.0,K ~+> tick] YES(?,POLY)