YES(?,PRIMREC) * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1) 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1) 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1) 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [1 + E >= D] (?,1) 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D] (?,1) 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= C] (?,1) Signature: {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1) 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1) 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1) 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [1 + E >= D] (1,1) 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D] (?,1) 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [1 + E >= D] (1,1) 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= C] (1,1) Signature: {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 3: AddSinks MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1) 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1) 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1) 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [1 + E >= D] (1,1) 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D] (?,1) 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [1 + E >= D] (1,1) 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= C] (1,1) Signature: {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1) 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1) 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1) 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [1 + E >= D] (?,1) 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D] (?,1) 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= C] (?,1) 10. f34(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8} ,10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 5: LooptreeTransformer MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1) 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1) 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1) 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [1 + E >= D] (?,1) 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D] (?,1) 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= C] (?,1) 10. f34(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [2] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5] * Step 6: SizeAbstraction MAYBE + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1) 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1) 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1) 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1) 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [1 + E >= D] (?,1) 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D] (?,1) 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= C] (?,1) 10. f34(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [2] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction MAYBE + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0,0.1,0.1.0,0.1.0.0,0.2] f0 ~> f10 [A <= unknown, B <= 0*K, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] f10 ~> f10 [A <= A, B <= B + C, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] f18 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= E, G <= D + E, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= D + G, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= G, G <= D + G, H <= H] f34 ~> f34 [A <= A, B <= B, C <= C, D <= D, E <= D + E, F <= F, G <= G, H <= H] f34 ~> f43 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] f22 ~> f18 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G, H <= unknown] f18 ~> f34 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G, H <= H] f10 ~> f18 [A <= A, B <= B, C <= C, D <= C, E <= 0*K, F <= F, G <= G, H <= H] f34 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0 <= B + C] f10 ~> f10 [A <= A, B <= B + C, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.1 <= 2*K + D + E] f18 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= E, G <= D + E, H <= H] f22 ~> f18 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G, H <= unknown] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= D + G, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= G, G <= D + G, H <= H] + Loop: [0.1.0 <= D + G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= D + G, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= G, G <= D + G, H <= H] + Loop: [0.1.0.0 <= D + G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= D + G, H <= H] + Loop: [0.2 <= K + D + E] f34 ~> f34 [A <= A, B <= B, C <= C, D <= D, E <= D + E, F <= F, G <= G, H <= H] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,0.0,0.1,0.1.0,0.1.0.0,0.2] f0 ~> f10 [K ~=> B,huge ~=> A] f10 ~> f10 [B ~+> B,C ~+> B] f18 ~> f22 [E ~=> F,D ~+> G,E ~+> G] f22 ~> f22 [D ~+> G,G ~+> G] f22 ~> f22 [G ~=> F,D ~+> G,G ~+> G] f34 ~> f34 [D ~+> E,E ~+> E] f34 ~> f43 [] f22 ~> f18 [huge ~=> H,E ~+> E,K ~+> E] f18 ~> f34 [K ~=> E] f10 ~> f18 [C ~=> D,K ~=> E] f34 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0] f10 ~> f10 [B ~+> B,C ~+> B] + Loop: [D ~+> 0.1,E ~+> 0.1,K ~*> 0.1] f18 ~> f22 [E ~=> F,D ~+> G,E ~+> G] f22 ~> f18 [huge ~=> H,E ~+> E,K ~+> E] f22 ~> f22 [D ~+> G,G ~+> G] f22 ~> f22 [G ~=> F,D ~+> G,G ~+> G] + Loop: [D ~+> 0.1.0,G ~+> 0.1.0] f22 ~> f22 [D ~+> G,G ~+> G] f22 ~> f22 [G ~=> F,D ~+> G,G ~+> G] + Loop: [D ~+> 0.1.0.0,G ~+> 0.1.0.0] f22 ~> f22 [D ~+> G,G ~+> G] + Loop: [D ~+> 0.2,E ~+> 0.2,K ~+> 0.2] f34 ~> f34 [D ~+> E,E ~+> E] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [C ~=> D ,K ~=> B ,K ~=> E ,K ~=> F ,huge ~=> A ,huge ~=> H ,C ~+> B ,C ~+> E ,C ~+> F ,C ~+> G ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> 0.2 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> E ,K ~+> F ,K ~+> G ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> 0.2 ,K ~+> tick ,C ~*> B ,C ~*> E ,C ~*> F ,C ~*> G ,C ~*> 0.1.0 ,C ~*> 0.1.0.0 ,C ~*> tick ,K ~*> B ,K ~*> E ,K ~*> F ,K ~*> G ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> 0.2 ,K ~*> tick ,C ~^> F ,C ~^> G ,C ~^> 0.1.0 ,C ~^> 0.1.0.0 ,C ~^> tick ,K ~^> F ,K ~^> G ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] f0 ~> f43 [C ~=> D ,K ~=> B ,K ~=> E ,K ~=> F ,huge ~=> A ,huge ~=> H ,C ~+> B ,C ~+> E ,C ~+> F ,C ~+> G ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> 0.2 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> E ,K ~+> F ,K ~+> G ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> 0.2 ,K ~+> tick ,C ~*> B ,C ~*> E ,C ~*> F ,C ~*> G ,C ~*> 0.1.0 ,C ~*> 0.1.0.0 ,C ~*> tick ,K ~*> B ,K ~*> E ,K ~*> F ,K ~*> G ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> 0.2 ,K ~*> tick ,C ~^> F ,C ~^> G ,C ~^> 0.1.0 ,C ~^> 0.1.0.0 ,C ~^> tick ,K ~^> F ,K ~^> G ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] + f10> [B ~+> B,B ~+> 0.0,B ~+> tick,C ~+> B,C ~+> 0.0,C ~+> tick,tick ~+> tick,B ~*> B,C ~*> B] + f18> [E ~=> F ,huge ~=> H ,D ~+> F ,D ~+> G ,D ~+> 0.1 ,D ~+> 0.1.0 ,D ~+> 0.1.0.0 ,D ~+> tick ,E ~+> E ,E ~+> F ,E ~+> G ,E ~+> 0.1 ,E ~+> 0.1.0 ,E ~+> 0.1.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,K ~+> F ,K ~+> G ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> E ,D ~*> F ,D ~*> G ,D ~*> 0.1.0 ,D ~*> 0.1.0.0 ,D ~*> tick ,E ~*> E ,E ~*> F ,E ~*> G ,E ~*> 0.1.0 ,E ~*> 0.1.0.0 ,E ~*> tick ,K ~*> E ,K ~*> F ,K ~*> G ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,D ~^> F ,D ~^> G ,D ~^> 0.1.0 ,D ~^> 0.1.0.0 ,D ~^> tick ,E ~^> F ,E ~^> G ,E ~^> 0.1.0 ,E ~^> 0.1.0.0 ,E ~^> tick ,K ~^> F ,K ~^> G ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] + f22> [G ~=> F ,D ~+> F ,D ~+> G ,D ~+> 0.1.0 ,D ~+> 0.1.0.0 ,D ~+> tick ,G ~+> F ,G ~+> G ,G ~+> 0.1.0 ,G ~+> 0.1.0.0 ,G ~+> tick ,tick ~+> tick ,D ~*> F ,D ~*> G ,D ~*> 0.1.0.0 ,D ~*> tick ,G ~*> F ,G ~*> G ,G ~*> 0.1.0.0 ,G ~*> tick ,D ~^> G ,G ~^> G] + f22> [D ~+> G ,D ~+> 0.1.0.0 ,D ~+> tick ,G ~+> G ,G ~+> 0.1.0.0 ,G ~+> tick ,tick ~+> tick ,D ~*> G ,G ~*> G] + f34> [D ~+> E ,D ~+> 0.2 ,D ~+> tick ,E ~+> E ,E ~+> 0.2 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.2 ,K ~+> tick ,D ~*> E ,E ~*> E ,K ~*> E] YES(?,PRIMREC)