YES(?,PRIMREC) * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(1,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [-1 + A >= 0 && B >= A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [-1 + A >= 0 && A >= 1 + B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [B + -1*C >= 0 (?,1) && A + -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] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-2 + C >= 0 (?,1) && -3 + B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1 + A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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 MAYBE + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(1,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [-1 + A >= 0 && B >= A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [-1 + A >= 0 && A >= 1 + B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [B + -1*C >= 0 (?,1) && A + -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] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-2 + C >= 0 (?,1) && -3 + B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1 + A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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: AddSinks MAYBE + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(1,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [-1 + A >= 0 && B >= A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [-1 + A >= 0 && A >= 1 + B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-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 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-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 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [B + -1*C >= 0 && A + -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] evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-2 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1 + A + -1*B >= 0 && -1 + A >= 0] Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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: AddSinks + Details: () * Step 4: Decompose MAYBE + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(1,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [-1 + A >= 0 && B >= A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [-1 + A >= 0 && A >= 1 + B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-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 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-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 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [B + -1*C >= 0 && A + -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] evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-2 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,7,5,6,4] c: [2,5,7] | `- p:[4,6] c: [4,6] * Step 5: AbstractSize MAYBE + Considered Problem: (Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(1,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [-1 + A >= 0 && B >= A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [-1 + A >= 0 && A >= 1 + B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-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 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-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 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [B + -1*C >= 0 && A + -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] evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-2 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{9}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,7,5,6,4] c: [2,5,7] | `- p:[4,6] c: [4,6]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C] evalfentryin ~> evalfbb4in [A <= K, B <= B, C <= C] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= K] evalfbb4in ~> evalfreturnin [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B + C] evalfbb3in ~> evalfbb4in [A <= C, B <= B, C <= C] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C] evalfstop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= K] evalfbb3in ~> evalfbb4in [A <= C, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= A + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B + C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb4in [K ~=> A] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb4in ~> evalfreturnin [] evalfbb2in ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~+> C,C ~+> C] evalfbb3in ~> evalfbb4in [C ~=> A] evalfreturnin ~> evalfstop [] evalfstop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb3in ~> evalfbb4in [C ~=> A] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~+> C,C ~+> C] evalfbb2in ~> evalfbb1in [] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0] evalfbb2in ~> evalfbb1in [] evalfbb1in ~> evalfbb2in [B ~+> C,C ~+> C] + Applied Processor: Lare + Details: evalfstart ~> exitus616 [K ~=> A ,K ~=> C ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> A ,B ~^> C ,B ~^> 0.0.0 ,B ~^> tick ,K ~^> A ,K ~^> C ,K ~^> 0.0.0 ,K ~^> tick] + evalfbb4in> [K ~=> A ,K ~=> C ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> A ,A ~^> C ,A ~^> 0.0.0 ,A ~^> tick ,B ~^> A ,B ~^> C ,B ~^> 0.0.0 ,B ~^> tick] + evalfbb2in> [A ~+> 0.0.0 ,A ~+> tick ,B ~+> C ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,A ~*> C ,B ~*> C ,C ~*> C] YES(?,PRIMREC)