YES * Step 1: TrivialSCCs YES + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + 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 (1,1) 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] (1,1) 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] (1,1) 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 3: Looptree YES + 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 (1,1) 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] (1,1) 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] (1,1) 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: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,7,5,6,4] c: [7] | `- p:[4,6] c: [6] YES