YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True (1,1) 1. f15(A,B,C,D,E,F,G) -> f15(A,B,C,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f25(A,B,C,D,E,F,G) -> f25(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f33(A,B,C,D,E,F,G) -> f33(1 + A,B,C,D,E,F,G) [-50 + E >= 0 (?,1) && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 4. f42(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] 5. f52(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1 + G) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f60(A,B,C,D,E,F,G) -> f60(1 + A,B,C,D,E,F,G) [-50 + G >= 0 (?,1) && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 7. f60(A,B,C,D,E,F,G) -> f69(A,B,C,D,E,F,G) [-50 + G >= 0 (?,1) && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 8. f52(A,B,C,D,E,F,G) -> f60(0,B,C,D,E,F,G) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 9. f42(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] 10. f33(A,B,C,D,E,F,G) -> f42(A,B,C,D,E,0,G) [-50 + E >= 0 (?,1) && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 11. f25(A,B,C,D,E,F,G) -> f33(0,B,C,D,E,F,G) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 12. f15(A,B,C,D,E,F,G) -> f25(A,B,C,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1,12},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6,7},9->{5,8},10->{4,9} ,11->{3,10},12->{2,11}] + Applied Processor: ArgumentFilter [1,2] + Details: We remove following argument positions: [1,2]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,D,E,F,G) -> f15(0,0,E,F,G) True (1,1) 1. f15(A,D,E,F,G) -> f15(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f25(A,D,E,F,G) -> f25(A,D,1 + E,F,G) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f33(A,D,E,F,G) -> f33(1 + A,D,E,F,G) [-50 + E >= 0 (?,1) && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 4. f42(A,D,E,F,G) -> f42(A,D,E,1 + F,G) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] 5. f52(A,D,E,F,G) -> f52(A,D,E,F,1 + G) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f60(A,D,E,F,G) -> f60(1 + A,D,E,F,G) [-50 + G >= 0 (?,1) && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 7. f60(A,D,E,F,G) -> f69(A,D,E,F,G) [-50 + G >= 0 (?,1) && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 8. f52(A,D,E,F,G) -> f60(0,D,E,F,G) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 9. f42(A,D,E,F,G) -> f52(A,D,E,F,0) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] 10. f33(A,D,E,F,G) -> f42(A,D,E,0,G) [-50 + E >= 0 (?,1) && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 11. f25(A,D,E,F,G) -> f33(0,D,E,F,G) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 12. f15(A,D,E,F,G) -> f25(A,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1,12},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6,7},9->{5,8},10->{4,9} ,11->{3,10},12->{2,11}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12),(8,7),(9,8),(10,9),(11,10),(12,11)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,D,E,F,G) -> f15(0,0,E,F,G) True (1,1) 1. f15(A,D,E,F,G) -> f15(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f25(A,D,E,F,G) -> f25(A,D,1 + E,F,G) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f33(A,D,E,F,G) -> f33(1 + A,D,E,F,G) [-50 + E >= 0 (?,1) && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 4. f42(A,D,E,F,G) -> f42(A,D,E,1 + F,G) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] 5. f52(A,D,E,F,G) -> f52(A,D,E,F,1 + G) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f60(A,D,E,F,G) -> f60(1 + A,D,E,F,G) [-50 + G >= 0 (?,1) && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 7. f60(A,D,E,F,G) -> f69(A,D,E,F,G) [-50 + G >= 0 (?,1) && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 8. f52(A,D,E,F,G) -> f60(0,D,E,F,G) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 9. f42(A,D,E,F,G) -> f52(A,D,E,F,0) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] 10. f33(A,D,E,F,G) -> f42(A,D,E,0,G) [-50 + E >= 0 (?,1) && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 11. f25(A,D,E,F,G) -> f33(0,D,E,F,G) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 12. f15(A,D,E,F,G) -> f25(A,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Flow Graph: [0->{1},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6},9->{5},10->{4},11->{3} ,12->{2}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,D,E,F,G) -> f15(0,0,E,F,G) True f15(A,D,E,F,G) -> f15(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] f25(A,D,E,F,G) -> f25(A,D,1 + E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] f33(A,D,E,F,G) -> f33(1 + A,D,E,F,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f42(A,D,E,F,G) -> f42(A,D,E,1 + F,G) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] f52(A,D,E,F,G) -> f52(A,D,E,F,1 + G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] f60(A,D,E,F,G) -> f60(1 + A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f60(A,D,E,F,G) -> f69(A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f52(A,D,E,F,G) -> f60(0,D,E,F,G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] f42(A,D,E,F,G) -> f52(A,D,E,F,0) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] f33(A,D,E,F,G) -> f42(A,D,E,0,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f25(A,D,E,F,G) -> f33(0,D,E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] f15(A,D,E,F,G) -> f25(A,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] Signature: {(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Rule Graph: [0->{1},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{},8->{6},9->{5},10->{4},11->{3} ,12->{2}] + Applied Processor: AddSinks + Details: () * Step 5: Unfold WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,D,E,F,G) -> f15(0,0,E,F,G) True f15(A,D,E,F,G) -> f15(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] f25(A,D,E,F,G) -> f25(A,D,1 + E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] f33(A,D,E,F,G) -> f33(1 + A,D,E,F,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f42(A,D,E,F,G) -> f42(A,D,E,1 + F,G) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] f52(A,D,E,F,G) -> f52(A,D,E,F,1 + G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] f60(A,D,E,F,G) -> f60(1 + A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f60(A,D,E,F,G) -> f69(A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f52(A,D,E,F,G) -> f60(0,D,E,F,G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] f42(A,D,E,F,G) -> f52(A,D,E,F,0) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] f33(A,D,E,F,G) -> f42(A,D,E,0,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f25(A,D,E,F,G) -> f33(0,D,E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] f15(A,D,E,F,G) -> f25(A,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] f69(A,D,E,F,G) -> exitus616(A,D,E,F,G) True Signature: {(exitus616,5);(f0,7);(f15,7);(f25,7);(f33,7);(f42,7);(f52,7);(f60,7);(f69,7)} Rule Graph: [0->{1},1->{1,12},2->{2,11},3->{3,10},4->{4,9},5->{5,8},6->{6,7},7->{13},8->{6},9->{5},10->{4},11->{3} ,12->{2}] + Applied Processor: Unfold + Details: () * Step 6: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0.0(A,D,E,F,G) -> f15.1(0,0,E,F,G) True f15.1(A,D,E,F,G) -> f15.1(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] f15.1(A,D,E,F,G) -> f15.12(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] f25.2(A,D,E,F,G) -> f25.2(A,D,1 + E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] f25.2(A,D,E,F,G) -> f25.11(A,D,1 + E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] f33.3(A,D,E,F,G) -> f33.3(1 + A,D,E,F,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f33.3(A,D,E,F,G) -> f33.10(1 + A,D,E,F,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f42.4(A,D,E,F,G) -> f42.4(A,D,E,1 + F,G) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] f42.4(A,D,E,F,G) -> f42.9(A,D,E,1 + F,G) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] f52.5(A,D,E,F,G) -> f52.5(A,D,E,F,1 + G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] f52.5(A,D,E,F,G) -> f52.8(A,D,E,F,1 + G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] f60.6(A,D,E,F,G) -> f60.6(1 + A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f60.6(A,D,E,F,G) -> f60.7(1 + A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f60.7(A,D,E,F,G) -> f69.13(A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f52.8(A,D,E,F,G) -> f60.6(0,D,E,F,G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] f42.9(A,D,E,F,G) -> f52.5(A,D,E,F,0) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] f33.10(A,D,E,F,G) -> f42.4(A,D,E,0,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f25.11(A,D,E,F,G) -> f33.3(0,D,E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] f15.12(A,D,E,F,G) -> f25.2(A,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] f69.13(A,D,E,F,G) -> exitus616.14(A,D,E,F,G) True Signature: {(exitus616.14,5) ;(f0.0,5) ;(f15.1,5) ;(f15.12,5) ;(f25.11,5) ;(f25.2,5) ;(f33.10,5) ;(f33.3,5) ;(f42.4,5) ;(f42.9,5) ;(f52.5,5) ;(f52.8,5) ;(f60.6,5) ;(f60.7,5) ;(f69.13,5)} Rule Graph: [0->{1,2},1->{1,2},2->{18},3->{3,4},4->{17},5->{5,6},6->{16},7->{7,8},8->{15},9->{9,10},10->{14},11->{11 ,12},12->{13},13->{19},14->{11,12},15->{9,10},16->{7,8},17->{5,6},18->{3,4},19->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | +- p:[1] c: [1] | +- p:[3] c: [3] | +- p:[5] c: [5] | +- p:[7] c: [7] | +- p:[9] c: [9] | `- p:[11] c: [11] * Step 7: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0.0(A,D,E,F,G) -> f15.1(0,0,E,F,G) True f15.1(A,D,E,F,G) -> f15.1(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] f15.1(A,D,E,F,G) -> f15.12(A,1 + D,E,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] f25.2(A,D,E,F,G) -> f25.2(A,D,1 + E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] f25.2(A,D,E,F,G) -> f25.11(A,D,1 + E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] f33.3(A,D,E,F,G) -> f33.3(1 + A,D,E,F,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f33.3(A,D,E,F,G) -> f33.10(1 + A,D,E,F,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f42.4(A,D,E,F,G) -> f42.4(A,D,E,1 + F,G) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] f42.4(A,D,E,F,G) -> f42.9(A,D,E,1 + F,G) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= F] f52.5(A,D,E,F,G) -> f52.5(A,D,E,F,1 + G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] f52.5(A,D,E,F,G) -> f52.8(A,D,E,F,1 + G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] f60.6(A,D,E,F,G) -> f60.6(1 + A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f60.6(A,D,E,F,G) -> f60.7(1 + A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] f60.7(A,D,E,F,G) -> f69.13(A,D,E,F,G) [-50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f52.8(A,D,E,F,G) -> f60.6(0,D,E,F,G) [G >= 0 && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] f42.9(A,D,E,F,G) -> f52.5(A,D,E,F,0) [F >= 0 && -50 + E + F >= 0 && -50 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && F >= 50] f33.10(A,D,E,F,G) -> f42.4(A,D,E,0,G) [-50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] f25.11(A,D,E,F,G) -> f33.3(0,D,E,F,G) [E >= 0 && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] f15.12(A,D,E,F,G) -> f25.2(A,D,0,F,G) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] f69.13(A,D,E,F,G) -> exitus616.14(A,D,E,F,G) True Signature: {(exitus616.14,5) ;(f0.0,5) ;(f15.1,5) ;(f15.12,5) ;(f25.11,5) ;(f25.2,5) ;(f33.10,5) ;(f33.3,5) ;(f42.4,5) ;(f42.9,5) ;(f52.5,5) ;(f52.8,5) ;(f60.6,5) ;(f60.7,5) ;(f69.13,5)} Rule Graph: [0->{1,2},1->{1,2},2->{18},3->{3,4},4->{17},5->{5,6},6->{16},7->{7,8},8->{15},9->{9,10},10->{14},11->{11 ,12},12->{13},13->{19},14->{11,12},15->{9,10},16->{7,8},17->{5,6},18->{3,4},19->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | +- p:[1] c: [1] | +- p:[3] c: [3] | +- p:[5] c: [5] | +- p:[7] c: [7] | +- p:[9] c: [9] | `- p:[11] c: [11]) + Applied Processor: AbstractSize Minimize + Details: () * Step 8: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,D,E,F,G,0.0,0.1,0.2,0.3,0.4,0.5] f0.0 ~> f15.1 [A <= 0*K, D <= 0*K, E <= E, F <= F, G <= G] f15.1 ~> f15.1 [A <= A, D <= 50*K, E <= E, F <= F, G <= G] f15.1 ~> f15.12 [A <= A, D <= 50*K, E <= E, F <= F, G <= G] f25.2 ~> f25.2 [A <= A, D <= D, E <= 50*K, F <= F, G <= G] f25.2 ~> f25.11 [A <= A, D <= D, E <= 50*K, F <= F, G <= G] f33.3 ~> f33.3 [A <= 50*K, D <= D, E <= E, F <= F, G <= G] f33.3 ~> f33.10 [A <= 50*K, D <= D, E <= E, F <= F, G <= G] f42.4 ~> f42.4 [A <= A, D <= D, E <= E, F <= 50*K, G <= G] f42.4 ~> f42.9 [A <= A, D <= D, E <= E, F <= 50*K, G <= G] f52.5 ~> f52.5 [A <= A, D <= D, E <= E, F <= F, G <= 50*K] f52.5 ~> f52.8 [A <= A, D <= D, E <= E, F <= F, G <= 50*K] f60.6 ~> f60.6 [A <= 50*K, D <= D, E <= E, F <= F, G <= G] f60.6 ~> f60.7 [A <= 50*K, D <= D, E <= E, F <= F, G <= G] f60.7 ~> f69.13 [A <= A, D <= D, E <= E, F <= F, G <= G] f52.8 ~> f60.6 [A <= 0*K, D <= D, E <= E, F <= F, G <= G] f42.9 ~> f52.5 [A <= A, D <= D, E <= E, F <= F, G <= 0*K] f33.10 ~> f42.4 [A <= A, D <= D, E <= E, F <= 0*K, G <= G] f25.11 ~> f33.3 [A <= 0*K, D <= D, E <= E, F <= F, G <= G] f15.12 ~> f25.2 [A <= A, D <= D, E <= 0*K, F <= F, G <= G] f69.13 ~> exitus616.14 [A <= A, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 49*K + D] f15.1 ~> f15.1 [A <= A, D <= 50*K, E <= E, F <= F, G <= G] + Loop: [0.1 <= 49*K + E] f25.2 ~> f25.2 [A <= A, D <= D, E <= 50*K, F <= F, G <= G] + Loop: [0.2 <= 49*K + A] f33.3 ~> f33.3 [A <= 50*K, D <= D, E <= E, F <= F, G <= G] + Loop: [0.3 <= 49*K + F] f42.4 ~> f42.4 [A <= A, D <= D, E <= E, F <= 50*K, G <= G] + Loop: [0.4 <= 49*K + G] f52.5 ~> f52.5 [A <= A, D <= D, E <= E, F <= F, G <= 50*K] + Loop: [0.5 <= 49*K + A] f60.6 ~> f60.6 [A <= 50*K, D <= D, E <= E, F <= F, G <= G] + Applied Processor: AbstractFlow + Details: () * Step 9: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,D,E,F,G,0.0,0.1,0.2,0.3,0.4,0.5] f0.0 ~> f15.1 [K ~=> A,K ~=> D] f15.1 ~> f15.1 [K ~=> D] f15.1 ~> f15.12 [K ~=> D] f25.2 ~> f25.2 [K ~=> E] f25.2 ~> f25.11 [K ~=> E] f33.3 ~> f33.3 [K ~=> A] f33.3 ~> f33.10 [K ~=> A] f42.4 ~> f42.4 [K ~=> F] f42.4 ~> f42.9 [K ~=> F] f52.5 ~> f52.5 [K ~=> G] f52.5 ~> f52.8 [K ~=> G] f60.6 ~> f60.6 [K ~=> A] f60.6 ~> f60.7 [K ~=> A] f60.7 ~> f69.13 [] f52.8 ~> f60.6 [K ~=> A] f42.9 ~> f52.5 [K ~=> G] f33.10 ~> f42.4 [K ~=> F] f25.11 ~> f33.3 [K ~=> A] f15.12 ~> f25.2 [K ~=> E] f69.13 ~> exitus616.14 [] + Loop: [D ~+> 0.0,K ~*> 0.0] f15.1 ~> f15.1 [K ~=> D] + Loop: [E ~+> 0.1,K ~*> 0.1] f25.2 ~> f25.2 [K ~=> E] + Loop: [A ~+> 0.2,K ~*> 0.2] f33.3 ~> f33.3 [K ~=> A] + Loop: [F ~+> 0.3,K ~*> 0.3] f42.4 ~> f42.4 [K ~=> F] + Loop: [G ~+> 0.4,K ~*> 0.4] f52.5 ~> f52.5 [K ~=> G] + Loop: [A ~+> 0.5,K ~*> 0.5] f60.6 ~> f60.6 [K ~=> A] + Applied Processor: Lare + Details: f0.0 ~> exitus616.14 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> 0.3 ,K ~+> 0.4 ,K ~+> 0.5 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> 0.3 ,K ~*> 0.4 ,K ~*> 0.5 ,K ~*> tick] + f15.1> [K ~=> D,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f25.2> [K ~=> E,E ~+> 0.1,E ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] + f33.3> [K ~=> A,A ~+> 0.2,A ~+> tick,tick ~+> tick,K ~*> 0.2,K ~*> tick] + f42.4> [K ~=> F,F ~+> 0.3,F ~+> tick,tick ~+> tick,K ~*> 0.3,K ~*> tick] + f52.5> [K ~=> G,G ~+> 0.4,G ~+> tick,tick ~+> tick,K ~*> 0.4,K ~*> tick] + f60.6> [K ~=> A,A ~+> 0.5,A ~+> tick,tick ~+> tick,K ~*> 0.5,K ~*> tick] YES(?,O(1))