NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(C,B,A) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && 0 >= C] (?,1) 4. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && C >= B] (?,1) 5. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] (?,1) 6. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] (?,1) 7. evalfbb1in(A,B,C) -> evalfbb3in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,-1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] 9. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-2 + B >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{9},4->{9},5->{7},6->{8},7->{2,3,4},8->{2,3,4},9->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths NO + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(C,B,A) [A >= 1 && B >= 1 + A] (1,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && 0 >= C] (1,1) 4. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && C >= B] (1,1) 5. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] (?,1) 6. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] (?,1) 7. evalfbb1in(A,B,C) -> evalfbb3in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,-1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] 9. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-2 + B >= 0] (1,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{9},4->{9},5->{7},6->{8},7->{2,3,4},8->{2,3,4},9->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(1,4),(7,3),(8,4)] * Step 3: Looptree NO + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(C,B,A) [A >= 1 && B >= 1 + A] (1,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [-2 + B >= 0 && C >= 1 && B >= 1 + C] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && 0 >= C] (1,1) 4. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [-2 + B >= 0 && C >= B] (1,1) 5. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && A >= 1] (?,1) 6. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + B >= 0 && 0 >= A] (?,1) 7. evalfbb1in(A,B,C) -> evalfbb3in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,-1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + -1*A + B >= 0 && -1*A >= 0] 9. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-2 + B >= 0] (1,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2},2->{5,6},3->{9},4->{9},5->{7},6->{8},7->{2,4},8->{2,3},9->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,7,5,8,6] c: [] NO