YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalSimpleSingle2start(A,B,C,D) -> evalSimpleSingle2entryin(A,B,C,D) True (1,1) 1. evalSimpleSingle2entryin(A,B,C,D) -> evalSimpleSingle2bb4in(0,0,C,D) True (?,1) 2. evalSimpleSingle2bb4in(A,B,C,D) -> evalSimpleSingle2bbin(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] (?,1) 3. evalSimpleSingle2bb4in(A,B,C,D) -> evalSimpleSingle2bbin(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= 1] (?,1) 4. evalSimpleSingle2bb4in(A,B,C,D) -> evalSimpleSingle2returnin(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) 5. evalSimpleSingle2bbin(A,B,C,D) -> evalSimpleSingle2bb1in(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 6. evalSimpleSingle2bbin(A,B,C,D) -> evalSimpleSingle2bb2in(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && B >= C] (?,1) 7. evalSimpleSingle2bb1in(A,B,C,D) -> evalSimpleSingle2bb4in(1 + A,1 + B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] 8. evalSimpleSingle2bb2in(A,B,C,D) -> evalSimpleSingle2bb3in(A,B,C,D) [B + -1*C >= 0 (?,1) && A + -1*C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && D >= 1 + A] 9. evalSimpleSingle2bb2in(A,B,C,D) -> evalSimpleSingle2returnin(A,B,C,D) [B + -1*C >= 0 (?,1) && A + -1*C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= D] 10. evalSimpleSingle2bb3in(A,B,C,D) -> evalSimpleSingle2bb4in(1 + A,1 + B,C,D) [-1 + D >= 0 (?,1) && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] 11. evalSimpleSingle2returnin(A,B,C,D) -> evalSimpleSingle2stop(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) Signature: {(evalSimpleSingle2bb1in,4) ;(evalSimpleSingle2bb2in,4) ;(evalSimpleSingle2bb3in,4) ;(evalSimpleSingle2bb4in,4) ;(evalSimpleSingle2bbin,4) ;(evalSimpleSingle2entryin,4) ;(evalSimpleSingle2returnin,4) ;(evalSimpleSingle2start,4) ;(evalSimpleSingle2stop,4)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{5,6},4->{11},5->{7},6->{8,9},7->{2,3,4},8->{10},9->{11},10->{2,3,4} ,11->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalSimpleSingle2start(A,B,C,D) -> evalSimpleSingle2entryin(A,B,C,D) True (1,1) 1. evalSimpleSingle2entryin(A,B,C,D) -> evalSimpleSingle2bb4in(0,0,C,D) True (1,1) 2. evalSimpleSingle2bb4in(A,B,C,D) -> evalSimpleSingle2bbin(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] (?,1) 3. evalSimpleSingle2bb4in(A,B,C,D) -> evalSimpleSingle2bbin(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= 1] (?,1) 4. evalSimpleSingle2bb4in(A,B,C,D) -> evalSimpleSingle2returnin(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (1,1) 5. evalSimpleSingle2bbin(A,B,C,D) -> evalSimpleSingle2bb1in(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 6. evalSimpleSingle2bbin(A,B,C,D) -> evalSimpleSingle2bb2in(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && B >= C] (?,1) 7. evalSimpleSingle2bb1in(A,B,C,D) -> evalSimpleSingle2bb4in(1 + A,1 + B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] 8. evalSimpleSingle2bb2in(A,B,C,D) -> evalSimpleSingle2bb3in(A,B,C,D) [B + -1*C >= 0 (?,1) && A + -1*C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && D >= 1 + A] 9. evalSimpleSingle2bb2in(A,B,C,D) -> evalSimpleSingle2returnin(A,B,C,D) [B + -1*C >= 0 (1,1) && A + -1*C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= D] 10. evalSimpleSingle2bb3in(A,B,C,D) -> evalSimpleSingle2bb4in(1 + A,1 + B,C,D) [-1 + D >= 0 (?,1) && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] 11. evalSimpleSingle2returnin(A,B,C,D) -> evalSimpleSingle2stop(A,B,C,D) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (1,1) Signature: {(evalSimpleSingle2bb1in,4) ;(evalSimpleSingle2bb2in,4) ;(evalSimpleSingle2bb3in,4) ;(evalSimpleSingle2bb4in,4) ;(evalSimpleSingle2bbin,4) ;(evalSimpleSingle2entryin,4) ;(evalSimpleSingle2returnin,4) ;(evalSimpleSingle2start,4) ;(evalSimpleSingle2stop,4)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{5,6},4->{11},5->{7},6->{8,9},7->{2,3,4},8->{10},9->{11},10->{2,3,4} ,11->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,7,5,3,10,8,6] c: [10] | `- p:[2,7,5,3] c: [7] YES