YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval_speedpldi2_start(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) True (1,1) 1. eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) True (?,1) 2. eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) True (?,1) 3. eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) True (?,1) 4. eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_n,0) [v_n >= 0 && -1 + v_m >= 0] (?,1) 5. eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [-1 >= v_n] (?,1) 6. eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [0 >= v_m] (?,1) 7. eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 (?,1) && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_v1_0 >= 0] 8. eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 (?,1) && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_v1_0] 9. eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 (?,1) && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_v2_0] 10. eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,0) [v_v2_0 >= 0 (?,1) && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_v2_0 >= v_m] 11. eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,-1 + v_v1_0,1 + v_v2_0) [-1 + v_m + -1*v_v2_0 >= 0 (?,1) && v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 12. eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_stop(v_m,v_n,v_v1_0,v_v2_0) True (?,1) Signature: {(eval_speedpldi2_0,4) ;(eval_speedpldi2_1,4) ;(eval_speedpldi2_2,4) ;(eval_speedpldi2_bb0_in,4) ;(eval_speedpldi2_bb1_in,4) ;(eval_speedpldi2_bb2_in,4) ;(eval_speedpldi2_bb3_in,4) ;(eval_speedpldi2_bb4_in,4) ;(eval_speedpldi2_start,4) ;(eval_speedpldi2_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{7,8},5->{12},6->{12},7->{9,10},8->{12},9->{11},10->{7,8},11->{7,8} ,12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(10,8)] * Step 2: FromIts YES + Considered Problem: Rules: 0. eval_speedpldi2_start(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) True (1,1) 1. eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) True (?,1) 2. eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) True (?,1) 3. eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) True (?,1) 4. eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_n,0) [v_n >= 0 && -1 + v_m >= 0] (?,1) 5. eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [-1 >= v_n] (?,1) 6. eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [0 >= v_m] (?,1) 7. eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 (?,1) && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_v1_0 >= 0] 8. eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 (?,1) && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_v1_0] 9. eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 (?,1) && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_v2_0] 10. eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,0) [v_v2_0 >= 0 (?,1) && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_v2_0 >= v_m] 11. eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,-1 + v_v1_0,1 + v_v2_0) [-1 + v_m + -1*v_v2_0 >= 0 (?,1) && v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 12. eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_stop(v_m,v_n,v_v1_0,v_v2_0) True (?,1) Signature: {(eval_speedpldi2_0,4) ;(eval_speedpldi2_1,4) ;(eval_speedpldi2_2,4) ;(eval_speedpldi2_bb0_in,4) ;(eval_speedpldi2_bb1_in,4) ;(eval_speedpldi2_bb2_in,4) ;(eval_speedpldi2_bb3_in,4) ;(eval_speedpldi2_bb4_in,4) ;(eval_speedpldi2_start,4) ;(eval_speedpldi2_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{7,8},5->{12},6->{12},7->{9,10},8->{12},9->{11},10->{7},11->{7,8} ,12->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: eval_speedpldi2_start(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_n,0) [v_n >= 0 && -1 + v_m >= 0] eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [-1 >= v_n] eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [0 >= v_m] eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_v1_0 >= 0] eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_v1_0] eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_v2_0] eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,0) [v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_v2_0 >= v_m] eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,-1 + v_v1_0,1 + v_v2_0) [-1 + v_m + -1*v_v2_0 >= 0 && v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_stop(v_m,v_n,v_v1_0,v_v2_0) True Signature: {(eval_speedpldi2_0,4) ;(eval_speedpldi2_1,4) ;(eval_speedpldi2_2,4) ;(eval_speedpldi2_bb0_in,4) ;(eval_speedpldi2_bb1_in,4) ;(eval_speedpldi2_bb2_in,4) ;(eval_speedpldi2_bb3_in,4) ;(eval_speedpldi2_bb4_in,4) ;(eval_speedpldi2_start,4) ;(eval_speedpldi2_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{7,8},5->{12},6->{12},7->{9,10},8->{12},9->{11},10->{7},11->{7,8} ,12->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[7,10,11,9] c: [9,11] | `- p:[7,10] c: [7,10] * Step 4: CloseWith YES + Considered Problem: (Rules: eval_speedpldi2_start(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_bb0_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_0(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_1(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) True eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_n,0) [v_n >= 0 && -1 + v_m >= 0] eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [-1 >= v_n] eval_speedpldi2_2(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [0 >= v_m] eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_v1_0 >= 0] eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 && v_v1_0 + v_v2_0 >= 0 && v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && v_v1_0 >= 0 && v_n + v_v1_0 >= 0 && -1 + v_m + v_v1_0 >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_v1_0] eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) [v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_v2_0] eval_speedpldi2_bb2_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,v_v1_0,0) [v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_v2_0 >= v_m] eval_speedpldi2_bb3_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_bb1_in(v_m,v_n,-1 + v_v1_0,1 + v_v2_0) [-1 + v_m + -1*v_v2_0 >= 0 && v_v2_0 >= 0 && -1 + v_v1_0 + v_v2_0 >= 0 && -1 + v_n + v_v2_0 >= 0 && -1 + v_m + v_v2_0 >= 0 && v_n + -1*v_v1_0 >= 0 && -1 + v_v1_0 >= 0 && -2 + v_n + v_v1_0 >= 0 && -2 + v_m + v_v1_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_speedpldi2_bb4_in(v_m,v_n,v_v1_0,v_v2_0) -> eval_speedpldi2_stop(v_m,v_n,v_v1_0,v_v2_0) True Signature: {(eval_speedpldi2_0,4) ;(eval_speedpldi2_1,4) ;(eval_speedpldi2_2,4) ;(eval_speedpldi2_bb0_in,4) ;(eval_speedpldi2_bb1_in,4) ;(eval_speedpldi2_bb2_in,4) ;(eval_speedpldi2_bb3_in,4) ;(eval_speedpldi2_bb4_in,4) ;(eval_speedpldi2_start,4) ;(eval_speedpldi2_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{7,8},5->{12},6->{12},7->{9,10},8->{12},9->{11},10->{7},11->{7,8} ,12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[7,10,11,9] c: [9,11] | `- p:[7,10] c: [7,10]) + Applied Processor: CloseWith True + Details: () YES