YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (?,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] (?,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (1,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] (1,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,3)] * Step 3: Looptree YES + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (1,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] (1,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2},7->{2,3},8->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,6,4,7,5] c: [7] | `- p:[2,6,4] c: [6] YES