YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (?,1) && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [A + -1*F >= 0 (?,1) && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [A + -1*F >= 0 (?,1) && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7},3->{},4->{3,4,5},5->{6,7},6->{6,7},7->{3,4,5},8->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,5),(7,3)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] 3. lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (?,1) && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] 4. lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] 5. lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [A + -1*F >= 0 (?,1) && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] 6. lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [A + -1*F >= 0 (?,1) && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] 7. lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] 8. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4},2->{6,7},3->{},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{3,4},2->{6,7},3->{},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl101(A,2,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] lbl121(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121(A,B,C,D,E,F) -> lbl121(A,1,C,-1 + D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121(A,B,C,D,E,F) -> lbl101(A,2,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl101(A,B,C,D,E,F) -> lbl101(A,2*B,C,D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101(A,B,C,D,E,F) -> lbl121(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(lbl101,6);(lbl121,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{11},1->{3,4},2->{6,7},3->{9,10},4->{3,4},5->{6,7},6->{6,7},7->{4,5},8->{0,1,2}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start.0(A,B,C,D,E,F) -> stop.11(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl121.3(A,1,C,-1 + F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl121.4(A,1,C,-1 + F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl101.6(A,2,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl101.7(A,2,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] lbl121.3(A,B,C,D,E,F) -> stop.9(A,B,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121.3(A,B,C,D,E,F) -> stop.10(A,B,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121.4(A,B,C,D,E,F) -> lbl121.3(A,1,C,-1 + D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121.4(A,B,C,D,E,F) -> lbl121.4(A,1,C,-1 + D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121.5(A,B,C,D,E,F) -> lbl101.6(A,2,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121.5(A,B,C,D,E,F) -> lbl101.7(A,2,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl101.6(A,B,C,D,E,F) -> lbl101.6(A,2*B,C,D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101.6(A,B,C,D,E,F) -> lbl101.7(A,2*B,C,D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101.7(A,B,C,D,E,F) -> lbl121.4(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101.7(A,B,C,D,E,F) -> lbl121.5(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] start0.8(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.8(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True start0.8(A,B,C,D,E,F) -> start.2(A,C,C,E,E,A) True stop.9(A,B,C,D,E,F) -> exitus616.12(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616.12(A,B,C,D,E,F) True stop.11(A,B,C,D,E,F) -> exitus616.12(A,B,C,D,E,F) True Signature: {(exitus616.12,6) ;(lbl101.6,6) ;(lbl101.7,6) ;(lbl121.3,6) ;(lbl121.4,6) ;(lbl121.5,6) ;(start.0,6) ;(start.1,6) ;(start.2,6) ;(start0.8,6) ;(stop.10,6) ;(stop.11,6) ;(stop.9,6)} Rule Graph: [0->{20},1->{5,6},2->{7,8},3->{11,12},4->{13,14},5->{18},6->{19},7->{5,6},8->{7,8},9->{11,12},10->{13,14} ,11->{11,12},12->{13,14},13->{7,8},14->{9,10},15->{0},16->{1,2},17->{3,4},18->{},19->{},20->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] | +- p:[11,9,14,10,12] c: [9,10,12,14] | | | `- p:[11] c: [11] | `- p:[8] c: [8] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start.0(A,B,C,D,E,F) -> stop.11(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl121.3(A,1,C,-1 + F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl121.4(A,1,C,-1 + F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 1 >= A && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl101.6(A,2,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl101.7(A,2,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = E && F = A] lbl121.3(A,B,C,D,E,F) -> stop.9(A,B,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121.3(A,B,C,D,E,F) -> stop.10(A,B,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 0 && B >= 1 && 1 + D = 0 && F = A] lbl121.4(A,B,C,D,E,F) -> lbl121.3(A,1,C,-1 + D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121.4(A,B,C,D,E,F) -> lbl121.4(A,1,C,-1 + D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 0 && 1 >= D && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121.5(A,B,C,D,E,F) -> lbl101.6(A,2,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl121.5(A,B,C,D,E,F) -> lbl101.7(A,2,C,D,E,F) [A + -1*F >= 0 && F >= 0 && 1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && 1 + D >= 0 && B + D >= 0 && 1 + A + D >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && D >= 2 && A >= 1 + D && B >= 1 + D && B >= 1 && F = A] lbl101.6(A,B,C,D,E,F) -> lbl101.6(A,2*B,C,D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101.6(A,B,C,D,E,F) -> lbl101.7(A,2*B,C,D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && D >= 1 + B && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101.7(A,B,C,D,E,F) -> lbl121.4(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] lbl101.7(A,B,C,D,E,F) -> lbl121.5(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -2 + F >= 0 && -4 + D + F >= 0 && -1*D + F >= 0 && -4 + B + F >= 0 && -4 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -4 + B + D >= 0 && -4 + A + D >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -2 + A >= 0 && B >= D && B >= 2 && 2*D >= 2 + B && A >= D && F = A] start0.8(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.8(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True start0.8(A,B,C,D,E,F) -> start.2(A,C,C,E,E,A) True stop.9(A,B,C,D,E,F) -> exitus616.12(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616.12(A,B,C,D,E,F) True stop.11(A,B,C,D,E,F) -> exitus616.12(A,B,C,D,E,F) True Signature: {(exitus616.12,6) ;(lbl101.6,6) ;(lbl101.7,6) ;(lbl121.3,6) ;(lbl121.4,6) ;(lbl121.5,6) ;(start.0,6) ;(start.1,6) ;(start.2,6) ;(start0.8,6) ;(stop.10,6) ;(stop.11,6) ;(stop.9,6)} Rule Graph: [0->{20},1->{5,6},2->{7,8},3->{11,12},4->{13,14},5->{18},6->{19},7->{5,6},8->{7,8},9->{11,12},10->{13,14} ,11->{11,12},12->{13,14},13->{7,8},14->{9,10},15->{0},16->{1,2},17->{3,4},18->{},19->{},20->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] | +- p:[11,9,14,10,12] c: [9,10,12,14] | | | `- p:[11] c: [11] | `- p:[8] c: [8]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.0.0,0.1] start.0 ~> stop.11 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] start.1 ~> lbl121.3 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] start.1 ~> lbl121.4 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] start.2 ~> lbl101.6 [A <= A, B <= 2*K, C <= C, D <= F, E <= E, F <= F] start.2 ~> lbl101.7 [A <= A, B <= 2*K, C <= C, D <= F, E <= E, F <= F] lbl121.3 ~> stop.9 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl121.3 ~> stop.10 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl121.4 ~> lbl121.3 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] lbl121.4 ~> lbl121.4 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] lbl121.5 ~> lbl101.6 [A <= A, B <= 2*K, C <= C, D <= D, E <= E, F <= F] lbl121.5 ~> lbl101.7 [A <= A, B <= 2*K, C <= C, D <= D, E <= E, F <= F] lbl101.6 ~> lbl101.6 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] lbl101.6 ~> lbl101.7 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] lbl101.7 ~> lbl121.4 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F] lbl101.7 ~> lbl121.5 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F] start0.8 ~> start.0 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] start0.8 ~> start.1 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] start0.8 ~> start.2 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] stop.9 ~> exitus616.12 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.10 ~> exitus616.12 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.11 ~> exitus616.12 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= 2*K + D] lbl101.6 ~> lbl101.6 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] lbl121.5 ~> lbl101.6 [A <= A, B <= 2*K, C <= C, D <= D, E <= E, F <= F] lbl101.7 ~> lbl121.5 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F] lbl121.5 ~> lbl101.7 [A <= A, B <= 2*K, C <= C, D <= D, E <= E, F <= F] lbl101.6 ~> lbl101.7 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0.0 <= 2*K + B + 2*D] lbl101.6 ~> lbl101.6 [A <= A, B <= A + F, C <= C, D <= D, E <= E, F <= F] + Loop: [0.1 <= K + D] lbl121.4 ~> lbl121.4 [A <= A, B <= K, C <= C, D <= K, E <= E, F <= F] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.0.0,0.1] start.0 ~> stop.11 [F ~=> D] start.1 ~> lbl121.3 [K ~=> B,K ~=> D] start.1 ~> lbl121.4 [K ~=> B,K ~=> D] start.2 ~> lbl101.6 [F ~=> D,K ~=> B] start.2 ~> lbl101.7 [F ~=> D,K ~=> B] lbl121.3 ~> stop.9 [] lbl121.3 ~> stop.10 [] lbl121.4 ~> lbl121.3 [K ~=> B,K ~=> D] lbl121.4 ~> lbl121.4 [K ~=> B,K ~=> D] lbl121.5 ~> lbl101.6 [K ~=> B] lbl121.5 ~> lbl101.7 [K ~=> B] lbl101.6 ~> lbl101.6 [A ~+> B,F ~+> B] lbl101.6 ~> lbl101.7 [A ~+> B,F ~+> B] lbl101.7 ~> lbl121.4 [A ~=> D] lbl101.7 ~> lbl121.5 [A ~=> D] start0.8 ~> start.0 [A ~=> F,C ~=> B,E ~=> D] start0.8 ~> start.1 [A ~=> F,C ~=> B,E ~=> D] start0.8 ~> start.2 [A ~=> F,C ~=> B,E ~=> D] stop.9 ~> exitus616.12 [] stop.10 ~> exitus616.12 [] stop.11 ~> exitus616.12 [] + Loop: [D ~+> 0.0,K ~*> 0.0] lbl101.6 ~> lbl101.6 [A ~+> B,F ~+> B] lbl121.5 ~> lbl101.6 [K ~=> B] lbl101.7 ~> lbl121.5 [A ~=> D] lbl121.5 ~> lbl101.7 [K ~=> B] lbl101.6 ~> lbl101.7 [A ~+> B,F ~+> B] + Loop: [B ~+> 0.0.0,D ~*> 0.0.0,K ~*> 0.0.0] lbl101.6 ~> lbl101.6 [A ~+> B,F ~+> B] + Loop: [D ~+> 0.1,K ~+> 0.1] lbl121.4 ~> lbl121.4 [K ~=> B,K ~=> D] + Applied Processor: Lare + Details: start0.8 ~> exitus616.12 [A ~=> D ,A ~=> F ,C ~=> B ,K ~=> B ,K ~=> D ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> 0.1 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> tick] + lbl101.7> [A ~=> D ,K ~=> B ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> B ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,D ~*> tick ,F ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] lbl101.7> [A ~=> D ,K ~=> B ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> B ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> tick ,D ~*> 0.0.0 ,D ~*> tick ,F ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + lbl101.6> [A ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,F ~+> B ,tick ~+> tick ,D ~*> 0.0.0 ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + lbl121.4> [K ~=> B,K ~=> D,D ~+> 0.1,D ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,POLY)