MAYBE * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(E,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [-1*B >= 0 && A >= 1] (?,1) 2. f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [A >= 0 && B >= 1] (?,1) 3. f14(A,B,C,D) -> f14(A,B,-1 + C,0) [-1 + A + -1*C >= 0 (?,1) && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1] 4. f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 (?,1) && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && 0 >= 1 + E] 5. f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 (?,1) && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && E >= 1] 6. f14(A,B,C,D) -> f10(A,B,C,D) [-1 + A + -1*C >= 0 (?,1) && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= C] 7. f10(A,B,C,D) -> f6(A,B,C,D) [A >= 0 && 0 >= B] (?,1) 8. f6(A,B,C,D) -> f25(A,B,C,D) [-1*B >= 0 && 0 >= A] (?,1) Signature: {(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Flow Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},7->{1,8},8->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f6(E,0,C,D) True f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [-1*B >= 0 && A >= 1] f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [A >= 0 && B >= 1] f14(A,B,C,D) -> f14(A,B,-1 + C,0) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && 0 >= 1 + E] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && E >= 1] f14(A,B,C,D) -> f10(A,B,C,D) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= C] f10(A,B,C,D) -> f6(A,B,C,D) [A >= 0 && 0 >= B] f6(A,B,C,D) -> f25(A,B,C,D) [-1*B >= 0 && 0 >= A] Signature: {(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Rule Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},7->{1,8},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f6(E,0,C,D) True f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [-1*B >= 0 && A >= 1] f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [A >= 0 && B >= 1] f14(A,B,C,D) -> f14(A,B,-1 + C,0) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && 0 >= 1 + E] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && E >= 1] f14(A,B,C,D) -> f10(A,B,C,D) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= C] f10(A,B,C,D) -> f6(A,B,C,D) [A >= 0 && 0 >= B] f6(A,B,C,D) -> f25(A,B,C,D) [-1*B >= 0 && 0 >= A] f25(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Rule Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},7->{1,8},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[1,7,6,2,3,4,5] c: [1,2,4,5,6,7] | `- p:[3] c: [3] * Step 4: AbstractSize MAYBE + Considered Problem: (Rules: f0(A,B,C,D) -> f6(E,0,C,D) True f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [-1*B >= 0 && A >= 1] f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [A >= 0 && B >= 1] f14(A,B,C,D) -> f14(A,B,-1 + C,0) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && 0 >= 1 + E] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 && E >= 1] f14(A,B,C,D) -> f10(A,B,C,D) [-1 + A + -1*C >= 0 && 1 + C >= 0 && 1 + B + C >= 0 && 1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= C] f10(A,B,C,D) -> f6(A,B,C,D) [A >= 0 && 0 >= B] f6(A,B,C,D) -> f25(A,B,C,D) [-1*B >= 0 && 0 >= A] f25(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Rule Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},7->{1,8},8->{9}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[1,7,6,2,3,4,5] c: [1,2,4,5,6,7] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] f0 ~> f6 [A <= unknown, B <= 0*K, C <= C, D <= D] f6 ~> f10 [A <= A, B <= K + B, C <= C, D <= D] f10 ~> f14 [A <= A, B <= B, C <= K + A, D <= D] f14 ~> f14 [A <= A, B <= B, C <= C, D <= 0*K] f14 ~> f14 [A <= A, B <= B + C, C <= C, D <= unknown] f14 ~> f14 [A <= A, B <= B + C, C <= C, D <= unknown] f14 ~> f10 [A <= A, B <= B, C <= C, D <= D] f10 ~> f6 [A <= A, B <= B, C <= C, D <= D] f6 ~> f25 [A <= A, B <= B, C <= C, D <= D] f25 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + B] f6 ~> f10 [A <= A, B <= K + B, C <= C, D <= D] f10 ~> f6 [A <= A, B <= B, C <= C, D <= D] f14 ~> f10 [A <= A, B <= B, C <= C, D <= D] f10 ~> f14 [A <= A, B <= B, C <= K + A, D <= D] f14 ~> f14 [A <= A, B <= B, C <= C, D <= 0*K] f14 ~> f14 [A <= A, B <= B + C, C <= C, D <= unknown] f14 ~> f14 [A <= A, B <= B + C, C <= C, D <= unknown] + Loop: [0.0.0 <= K + C] f14 ~> f14 [A <= A, B <= B, C <= C, D <= 0*K] + Applied Processor: AbstractFlow + Details: () * Step 6: Failure MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] f0 ~> f6 [K ~=> B,huge ~=> A] f6 ~> f10 [B ~+> B,K ~+> B] f10 ~> f14 [A ~+> C,K ~+> C] f14 ~> f14 [K ~=> D] f14 ~> f14 [huge ~=> D,B ~+> B,C ~+> B] f14 ~> f14 [huge ~=> D,B ~+> B,C ~+> B] f14 ~> f10 [] f10 ~> f6 [] f6 ~> f25 [] f25 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] f6 ~> f10 [B ~+> B,K ~+> B] f10 ~> f6 [] f14 ~> f10 [] f10 ~> f14 [A ~+> C,K ~+> C] f14 ~> f14 [K ~=> D] f14 ~> f14 [huge ~=> D,B ~+> B,C ~+> B] f14 ~> f14 [huge ~=> D,B ~+> B,C ~+> B] + Loop: [C ~+> 0.0.0,K ~+> 0.0.0] f14 ~> f14 [K ~=> D] + Applied Processor: Lare + Details: Unknown bound. MAYBE