YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(start,2)} Flow Graph: [0->{2,3},1->{4,5},2->{2,3},3->{0,1},4->{4,5},5->{0,1},6->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(1,5),(3,0),(3,1),(5,0),(5,1)] * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(start,2)} Flow Graph: [0->{2},1->{4},2->{2,3},3->{},4->{4,5},5->{},6->{0,1}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) 7. eval3(A,B) -> exitus616(A,B) True (?,1) 8. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(exitus616,2);(start,2)} Flow Graph: [0->{2,3,8},1->{4,5,7},2->{2,3,8},3->{0,1},4->{4,5,7},5->{0,1},6->{0,1},7->{},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(1,5),(3,0),(3,1),(5,0),(5,1)] * Step 4: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) 7. eval3(A,B) -> exitus616(A,B) True (?,1) 8. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(exitus616,2);(start,2)} Flow Graph: [0->{2,8},1->{4,7},2->{2,3,8},3->{},4->{4,5,7},5->{},6->{0,1},7->{},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[4] c: [4] | `- p:[2] c: [2] * Step 5: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1 && B >= 1 && A >= 1 + B] (?,1) 1. eval1(A,B) -> eval3(A,B) [A >= 1 && B >= 1 && B >= A] (?,1) 2. eval2(A,B) -> eval2(-1 + A,B) [A >= 1] (?,1) 3. eval2(A,B) -> eval1(A,B) [0 >= A] (?,1) 4. eval3(A,B) -> eval3(A,-1 + B) [B >= 1] (?,1) 5. eval3(A,B) -> eval1(A,B) [0 >= B] (?,1) 6. start(A,B) -> eval1(A,B) True (1,1) 7. eval3(A,B) -> exitus616(A,B) True (?,1) 8. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(eval3,2);(exitus616,2);(start,2)} Flow Graph: [0->{2,8},1->{4,7},2->{2,3,8},3->{},4->{4,5,7},5->{},6->{0,1},7->{},8->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[4] c: [4] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.1] eval1 ~> eval2 [A <= A, B <= B] eval1 ~> eval3 [A <= A, B <= B] eval2 ~> eval2 [A <= A, B <= B] eval2 ~> eval1 [A <= A, B <= B] eval3 ~> eval3 [A <= A, B <= B] eval3 ~> eval1 [A <= A, B <= B] start ~> eval1 [A <= A, B <= B] eval3 ~> exitus616 [A <= A, B <= B] eval2 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= B] eval3 ~> eval3 [A <= A, B <= B] + Loop: [0.1 <= A] eval2 ~> eval2 [A <= A, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] eval1 ~> eval2 [] eval1 ~> eval3 [] eval2 ~> eval2 [] eval2 ~> eval1 [] eval3 ~> eval3 [] eval3 ~> eval1 [] start ~> eval1 [] eval3 ~> exitus616 [] eval2 ~> exitus616 [] + Loop: [B ~=> 0.0] eval3 ~> eval3 [] + Loop: [A ~=> 0.1] eval2 ~> eval2 [] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~=> 0.1,B ~=> 0.0,A ~+> tick,B ~+> tick,tick ~+> tick,A ~*> tick] + eval3> [B ~=> 0.0,B ~+> tick,tick ~+> tick] + eval2> [A ~=> 0.1,A ~+> tick,tick ~+> tick] YES(?,POLY)