YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + 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) [0 >= 1 + E] (?,1) 4. evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [E >= 1] (?,1) 5. evalwcet1bbin(A,B,C,D) -> evalwcet1bb4in(A,B,C,D) True (?,1) 6. evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [1 + B >= A] (?,1) 7. evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,1 + B) [A >= 2 + B] (?,1) 8. evalwcet1bb4in(A,B,C,D) -> evalwcet1bb5in(A,B,C,D) [1 >= B] (?,1) 9. evalwcet1bb4in(A,B,C,D) -> evalwcet1bb6in(A,B,C,-1 + B) [B >= 2] (?,1) 10. evalwcet1bb5in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) True (?,1) 11. evalwcet1bb6in(A,B,C,D) -> evalwcet1bbin(A,D,-1 + C,D) [C >= 2] (?,1) 12. evalwcet1bb6in(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [1 >= C] (?,1) 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: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalwcet1start(A,B,C,D) -> evalwcet1entryin(A,B,C,D) True evalwcet1entryin(A,B,C,D) -> evalwcet1bbin(A,0,A,D) [A >= 1] evalwcet1entryin(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [0 >= A] evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [0 >= 1 + E] evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [E >= 1] evalwcet1bbin(A,B,C,D) -> evalwcet1bb4in(A,B,C,D) True evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [1 + B >= A] evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,1 + B) [A >= 2 + B] evalwcet1bb4in(A,B,C,D) -> evalwcet1bb5in(A,B,C,D) [1 >= B] evalwcet1bb4in(A,B,C,D) -> evalwcet1bb6in(A,B,C,-1 + B) [B >= 2] evalwcet1bb5in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) True evalwcet1bb6in(A,B,C,D) -> evalwcet1bbin(A,D,-1 + C,D) [C >= 2] evalwcet1bb6in(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [1 >= C] evalwcet1returnin(A,B,C,D) -> evalwcet1stop(A,B,C,D) True Signature: {(evalwcet1bb1in,4) ;(evalwcet1bb4in,4) ;(evalwcet1bb5in,4) ;(evalwcet1bb6in,4) ;(evalwcet1bbin,4) ;(evalwcet1entryin,4) ;(evalwcet1returnin,4) ;(evalwcet1start,4) ;(evalwcet1stop,4)} Rule 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: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalwcet1start(A,B,C,D) -> evalwcet1entryin(A,B,C,D) True evalwcet1entryin(A,B,C,D) -> evalwcet1bbin(A,0,A,D) [A >= 1] evalwcet1entryin(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [0 >= A] evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [0 >= 1 + E] evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [E >= 1] evalwcet1bbin(A,B,C,D) -> evalwcet1bb4in(A,B,C,D) True evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [1 + B >= A] evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,1 + B) [A >= 2 + B] evalwcet1bb4in(A,B,C,D) -> evalwcet1bb5in(A,B,C,D) [1 >= B] evalwcet1bb4in(A,B,C,D) -> evalwcet1bb6in(A,B,C,-1 + B) [B >= 2] evalwcet1bb5in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) True evalwcet1bb6in(A,B,C,D) -> evalwcet1bbin(A,D,-1 + C,D) [C >= 2] evalwcet1bb6in(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [1 >= C] evalwcet1returnin(A,B,C,D) -> evalwcet1stop(A,B,C,D) True evalwcet1stop(A,B,C,D) -> exitus616(A,B,C,D) True evalwcet1stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalwcet1bb1in,4) ;(evalwcet1bb4in,4) ;(evalwcet1bb5in,4) ;(evalwcet1bb6in,4) ;(evalwcet1bbin,4) ;(evalwcet1entryin,4) ;(evalwcet1returnin,4) ;(evalwcet1start,4) ;(evalwcet1stop,4) ;(exitus616,4)} Rule 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->{14,15}] + 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] | `- p:[3,11,6,4,7,9,5,10,8] c: [3,4,5,6,7,8,9,10,11] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalwcet1start(A,B,C,D) -> evalwcet1entryin(A,B,C,D) True evalwcet1entryin(A,B,C,D) -> evalwcet1bbin(A,0,A,D) [A >= 1] evalwcet1entryin(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [0 >= A] evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [0 >= 1 + E] evalwcet1bbin(A,B,C,D) -> evalwcet1bb1in(A,B,C,D) [E >= 1] evalwcet1bbin(A,B,C,D) -> evalwcet1bb4in(A,B,C,D) True evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) [1 + B >= A] evalwcet1bb1in(A,B,C,D) -> evalwcet1bb6in(A,B,C,1 + B) [A >= 2 + B] evalwcet1bb4in(A,B,C,D) -> evalwcet1bb5in(A,B,C,D) [1 >= B] evalwcet1bb4in(A,B,C,D) -> evalwcet1bb6in(A,B,C,-1 + B) [B >= 2] evalwcet1bb5in(A,B,C,D) -> evalwcet1bb6in(A,B,C,0) True evalwcet1bb6in(A,B,C,D) -> evalwcet1bbin(A,D,-1 + C,D) [C >= 2] evalwcet1bb6in(A,B,C,D) -> evalwcet1returnin(A,B,C,D) [1 >= C] evalwcet1returnin(A,B,C,D) -> evalwcet1stop(A,B,C,D) True evalwcet1stop(A,B,C,D) -> exitus616(A,B,C,D) True evalwcet1stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalwcet1bb1in,4) ;(evalwcet1bb4in,4) ;(evalwcet1bb5in,4) ;(evalwcet1bb6in,4) ;(evalwcet1bbin,4) ;(evalwcet1entryin,4) ;(evalwcet1returnin,4) ;(evalwcet1start,4) ;(evalwcet1stop,4) ;(exitus616,4)} Rule 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->{14,15}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[3,11,6,4,7,9,5,10,8] c: [3,4,5,6,7,8,9,10,11]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,0.0] evalwcet1start ~> evalwcet1entryin [A <= A, B <= B, C <= C, D <= D] evalwcet1entryin ~> evalwcet1bbin [A <= A, B <= 0*K, C <= A, D <= D] evalwcet1entryin ~> evalwcet1returnin [A <= A, B <= B, C <= C, D <= D] evalwcet1bbin ~> evalwcet1bb1in [A <= A, B <= B, C <= C, D <= D] evalwcet1bbin ~> evalwcet1bb1in [A <= A, B <= B, C <= C, D <= D] evalwcet1bbin ~> evalwcet1bb4in [A <= A, B <= B, C <= C, D <= D] evalwcet1bb1in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= 0*K] evalwcet1bb1in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= A + B] evalwcet1bb4in ~> evalwcet1bb5in [A <= A, B <= B, C <= C, D <= D] evalwcet1bb4in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= B] evalwcet1bb5in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= 0*K] evalwcet1bb6in ~> evalwcet1bbin [A <= A, B <= D, C <= C, D <= D] evalwcet1bb6in ~> evalwcet1returnin [A <= A, B <= B, C <= C, D <= D] evalwcet1returnin ~> evalwcet1stop [A <= A, B <= B, C <= C, D <= D] evalwcet1stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] evalwcet1stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= 2*K + C] evalwcet1bbin ~> evalwcet1bb1in [A <= A, B <= B, C <= C, D <= D] evalwcet1bb6in ~> evalwcet1bbin [A <= A, B <= D, C <= C, D <= D] evalwcet1bb1in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= 0*K] evalwcet1bbin ~> evalwcet1bb1in [A <= A, B <= B, C <= C, D <= D] evalwcet1bb1in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= A + B] evalwcet1bb4in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= B] evalwcet1bbin ~> evalwcet1bb4in [A <= A, B <= B, C <= C, D <= D] evalwcet1bb5in ~> evalwcet1bb6in [A <= A, B <= B, C <= C, D <= 0*K] evalwcet1bb4in ~> evalwcet1bb5in [A <= A, B <= B, C <= C, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0] evalwcet1start ~> evalwcet1entryin [] evalwcet1entryin ~> evalwcet1bbin [A ~=> C,K ~=> B] evalwcet1entryin ~> evalwcet1returnin [] evalwcet1bbin ~> evalwcet1bb1in [] evalwcet1bbin ~> evalwcet1bb1in [] evalwcet1bbin ~> evalwcet1bb4in [] evalwcet1bb1in ~> evalwcet1bb6in [K ~=> D] evalwcet1bb1in ~> evalwcet1bb6in [A ~+> D,B ~+> D] evalwcet1bb4in ~> evalwcet1bb5in [] evalwcet1bb4in ~> evalwcet1bb6in [B ~=> D] evalwcet1bb5in ~> evalwcet1bb6in [K ~=> D] evalwcet1bb6in ~> evalwcet1bbin [D ~=> B] evalwcet1bb6in ~> evalwcet1returnin [] evalwcet1returnin ~> evalwcet1stop [] evalwcet1stop ~> exitus616 [] evalwcet1stop ~> exitus616 [] + Loop: [C ~+> 0.0,K ~*> 0.0] evalwcet1bbin ~> evalwcet1bb1in [] evalwcet1bb6in ~> evalwcet1bbin [D ~=> B] evalwcet1bb1in ~> evalwcet1bb6in [K ~=> D] evalwcet1bbin ~> evalwcet1bb1in [] evalwcet1bb1in ~> evalwcet1bb6in [A ~+> D,B ~+> D] evalwcet1bb4in ~> evalwcet1bb6in [B ~=> D] evalwcet1bbin ~> evalwcet1bb4in [] evalwcet1bb5in ~> evalwcet1bb6in [K ~=> D] evalwcet1bb4in ~> evalwcet1bb5in [] + Applied Processor: Lare + Details: evalwcet1start ~> exitus616 [A ~=> C ,K ~=> B ,K ~=> D ,A ~+> B ,A ~+> D ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,A ~*> B ,A ~*> D ,K ~*> B ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] + evalwcet1bb6in> [B ~=> D ,K ~=> B ,K ~=> D ,A ~+> B ,A ~+> D ,B ~+> B ,B ~+> D ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,A ~*> B ,A ~*> D ,C ~*> B ,C ~*> D ,K ~*> B ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))