YES * Step 1: UnsatPaths YES + 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: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12),(8,7),(9,8),(10,9),(11,10),(12,11)] * Step 2: FromIts YES + 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},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 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True 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] f25(A,B,C,D,E,F,G) -> f25(A,B,C,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,B,C,D,E,F,G) -> f33(1 + A,B,C,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,B,C,D,E,F,G) -> f42(A,B,C,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,B,C,D,E,F,G) -> f52(A,B,C,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,B,C,D,E,F,G) -> f60(1 + A,B,C,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,B,C,D,E,F,G) -> f69(A,B,C,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,B,C,D,E,F,G) -> f60(0,B,C,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,B,C,D,E,F,G) -> f52(A,B,C,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,B,C,D,E,F,G) -> f42(A,B,C,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,B,C,D,E,F,G) -> f33(0,B,C,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,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] 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: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | +- p:[1] c: [1] | +- p:[2] c: [2] | +- p:[3] c: [3] | +- p:[4] c: [4] | +- p:[5] c: [5] | `- p:[6] c: [6] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E,F,G) -> f15(0,H,I,0,E,F,G) True 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] f25(A,B,C,D,E,F,G) -> f25(A,B,C,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,B,C,D,E,F,G) -> f33(1 + A,B,C,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,B,C,D,E,F,G) -> f42(A,B,C,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,B,C,D,E,F,G) -> f52(A,B,C,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,B,C,D,E,F,G) -> f60(1 + A,B,C,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,B,C,D,E,F,G) -> f69(A,B,C,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,B,C,D,E,F,G) -> f60(0,B,C,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,B,C,D,E,F,G) -> f52(A,B,C,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,B,C,D,E,F,G) -> f42(A,B,C,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,B,C,D,E,F,G) -> f33(0,B,C,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,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] 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}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | +- p:[1] c: [1] | +- p:[2] c: [2] | +- p:[3] c: [3] | +- p:[4] c: [4] | +- p:[5] c: [5] | `- p:[6] c: [6]) + Applied Processor: CloseWith True + Details: () YES