YES(?,O(1)) * Step 1: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> lbl41(E,B,C,D) [C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = B && C = D] (?,1) 1. lbl41(A,B,C,D) -> stop(A,B,A,D) [C + -1*D >= 0 && -1*C + D >= 0 && C = D] (?,1) 2. start0(A,B,C,D) -> start(B,B,D,D) True (1,1) Signature: {(lbl41,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{1},1->{},2->{0}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: start(A,B,C,D) -> lbl41(E,B,C,D) [C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = B && C = D] lbl41(A,B,C,D) -> stop(A,B,A,D) [C + -1*D >= 0 && -1*C + D >= 0 && C = D] start0(A,B,C,D) -> start(B,B,D,D) True Signature: {(lbl41,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{1},1->{},2->{0}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: start(A,B,C,D) -> lbl41(E,B,C,D) [C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = B && C = D] lbl41(A,B,C,D) -> stop(A,B,A,D) [C + -1*D >= 0 && -1*C + D >= 0 && C = D] start0(A,B,C,D) -> start(B,B,D,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(lbl41,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{1},1->{3},2->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3] * Step 4: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: start(A,B,C,D) -> lbl41(E,B,C,D) [C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = B && C = D] lbl41(A,B,C,D) -> stop(A,B,A,D) [C + -1*D >= 0 && -1*C + D >= 0 && C = D] start0(A,B,C,D) -> start(B,B,D,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(lbl41,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{1},1->{3},2->{0}] ,We construct a looptree: P: [0,1,2,3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D] start ~> lbl41 [A <= unknown, B <= B, C <= C, D <= D] lbl41 ~> stop [A <= A, B <= B, C <= A, D <= D] start0 ~> start [A <= B, B <= B, C <= D, D <= D] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D] start ~> lbl41 [huge ~=> A] lbl41 ~> stop [A ~=> C] start0 ~> start [B ~=> A,D ~=> C] stop ~> exitus616 [] + Applied Processor: Lare + Details: start0 ~> exitus616 [huge ~=> A,huge ~=> C] YES(?,O(1))