YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. evalwcet1start(A,B,C,D) -> evalwcet1entryin(A,B,C,D) True (1,1) 1. evalwcet1entryin(A,B,C,D) -> evalwcet1bbin(A,0,A,D) [A >= 1] (?,1) 2. evalwcet1entryin(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [0 >= A] (?,1) 3. evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] 4. evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1] 5. evalwcet1bbin(A,B,C,D) -> evalwcet1bb4in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 6. evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 1 + B >= A] 7. evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,1 + B) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 2 + B] 8. evalwcet1bb4in(A,B,C,D) -> evalwcet1bb5in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 1 >= B] 9. evalwcet1bb4in(A,B,C,D) -> evalwcet1bb6in(A,B,C,-1 + B) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 2] 10. evalwcet1bb5in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 11. evalwcet1bb6in(A,B,C,D) -> evalwcet1bbin(A,D,-1 + C,D) [1 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 2] 12. evalwcet1bb6in(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [1 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 1 >= C] 13. evalwcet1returnin(A,B,C,D) -> evalwcet1stop(A,B,C,D) True (?,1) Signature: {(evalwcet1bb1in,4) ;(evalwcet1bb4in,4) ;(evalwcet1bb5in,4) ;(evalwcet1bb6in,4) ;(evalwcet1bbin,4) ;(evalwcet1entryin,4) ;(evalwcet1returnin,4) ;(evalwcet1start,4) ;(evalwcet1stop,4)} Flow Graph: [0->{1,2},1->{3,4,5},2->{13},3->{6,7},4->{6,7},5->{8,9},6->{11,12},7->{11,12},8->{10},9->{11,12},10->{11 ,12},11->{3,4,5},12->{13},13->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. evalwcet1start(A,B,C,D) -> evalwcet1entryin(A,B,C,D) True (1,1) 1. evalwcet1entryin(A,B,C,D) -> evalwcet1bbin(A,0,A,D) [A >= 1] (1,1) 2. evalwcet1entryin(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [0 >= A] (1,1) 3. evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] 4. evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1] 5. evalwcet1bbin(A,B,C,D) -> evalwcet1bb4in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 6. evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 1 + B >= A] 7. evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,1 + B) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 2 + B] 8. evalwcet1bb4in(A,B,C,D) -> evalwcet1bb5in(A,B,C,D) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 1 >= B] 9. evalwcet1bb4in(A,B,C,D) -> evalwcet1bb6in(A,B,C,-1 + B) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 2] 10. evalwcet1bb5in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 11. evalwcet1bb6in(A,B,C,D) -> evalwcet1bbin(A,D,-1 + C,D) [1 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 2] 12. evalwcet1bb6in(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [1 + B + -1*D >= 0 (1,1) && -1 + A + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -2 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 1 >= C] 13. evalwcet1returnin(A,B,C,D) -> evalwcet1stop(A,B,C,D) True (1,1) Signature: {(evalwcet1bb1in,4) ;(evalwcet1bb4in,4) ;(evalwcet1bb5in,4) ;(evalwcet1bb6in,4) ;(evalwcet1bbin,4) ;(evalwcet1entryin,4) ;(evalwcet1returnin,4) ;(evalwcet1start,4) ;(evalwcet1stop,4)} Flow Graph: [0->{1,2},1->{3,4,5},2->{13},3->{6,7},4->{6,7},5->{8,9},6->{11,12},7->{11,12},8->{10},9->{11,12},10->{11 ,12},11->{3,4,5},12->{13},13->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[3,11,6,4,7,9,5,10,8] c: [11] YES