/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 6640 ms] (2) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f4(A, B, C, D, E, F) -> Com_1(f14(A, B, C, D, E, F)) :|: 0 >= A f13(A, B, C, D, E, F) -> Com_1(f4(A, B, C, D, E, F)) :|: TRUE f13(A, B, C, D, E, F) -> Com_1(f400(A, B, C, D, E, F)) :|: B >= A + 1 f2(A, B, C, D, E, F) -> Com_1(f23(G, I, H, J, 1, F)) :|: G >= 1 && H >= 1 && 0 >= I f2(A, B, C, D, E, F) -> Com_1(f23(G, I, H, J, 1, 0)) :|: G >= 1 && H >= 1 && I >= 1 f23(A, B, C, D, E, F) -> Com_1(f4(A, B, C, D, E, F)) :|: E >= C f23(A, B, C, D, E, F) -> Com_1(f4(A, B, C, D, E, 1)) :|: C >= E + 1 f4(A, B, C, D, E, F) -> Com_1(f33(A - 1, B, H, J, C, F)) :|: H >= C && 0 >= B && A >= 1 f4(A, B, C, D, E, F) -> Com_1(f33(A - 1, B, H, J, C, 0)) :|: H >= C && B >= 1 && A >= 1 f33(A, B, C, D, E, F) -> Com_1(f6(A, B, C, D, E, F)) :|: E >= C f33(A, B, C, D, E, F) -> Com_1(f6(A, B, C, D, E, 1)) :|: C >= E + 1 f6(A, B, C, D, E, F) -> Com_1(f43(A, B, H, J, C, F)) :|: H >= C && 0 >= C && 0 >= B f6(A, B, C, D, E, F) -> Com_1(f43(A, B, H, J, C, 0)) :|: H >= C && 0 >= C && B >= 1 f43(A, B, C, D, E, F) -> Com_1(f6(A, B, C, D, C, F)) :|: C >= E && C <= E f43(A, B, C, D, E, F) -> Com_1(f6(A, B, C, D, E, 1)) :|: C >= E + 1 f6(A, B, C, D, E, F) -> Com_1(f53(A, B, H, J, C - 1, F)) :|: H + 1 >= C && C >= 1 && 0 >= B f6(A, B, C, D, E, F) -> Com_1(f53(A, B, H, J, C - 1, 0)) :|: H + 1 >= C && C >= 1 && B >= 1 f53(A, B, C, D, E, F) -> Com_1(f61(A, A, C, D, C, F)) :|: E >= C f53(A, B, C, D, E, F) -> Com_1(f61(A, A, C, D, C, 1)) :|: C >= E + 1 f61(A, B, C, D, E, F) -> Com_1(f63(A, B, H, J, E, F)) :|: 0 >= B && H >= E f61(A, B, C, D, E, F) -> Com_1(f63(A, B, H, J, E, 0)) :|: B >= 1 && H >= E f63(A, B, C, D, E, F) -> Com_1(f71(A, B, C, D + 1, C, F)) :|: E >= C f63(A, B, C, D, E, F) -> Com_1(f71(A, B, C, D + 1, C, 1)) :|: C >= E + 1 f71(A, B, C, D, E, F) -> Com_1(f73(A, B, H, J, E, F)) :|: 0 >= B && H >= E f71(A, B, C, D, E, F) -> Com_1(f73(A, B, H, J, E, 0)) :|: B >= 1 && H >= E f73(A, B, C, D, E, F) -> Com_1(f13(A, B, C, D, E, F)) :|: E >= C f73(A, B, C, D, E, F) -> Com_1(f13(A, B, C, D, E, 1)) :|: C >= E + 1 The start-symbols are:[f2_6] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f2 0: f4 -> f14 : [ 0>=A ], cost: 1 7: f4 -> f33 : A'=-1+A, C'=free_9, D'=free_8, E'=C, [ free_9>=C && 0>=B && A>=1 ], cost: 1 8: f4 -> f33 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=0, [ free_11>=C && B>=1 && A>=1 ], cost: 1 1: f13 -> f4 : [], cost: 1 2: f13 -> f400 : [ B>=1+A ], cost: 1 3: f2 -> f23 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free ], cost: 1 4: f2 -> f23 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 ], cost: 1 5: f23 -> f4 : [ E>=C ], cost: 1 6: f23 -> f4 : F'=1, [ C>=1+E ], cost: 1 9: f33 -> f6 : [ E>=C ], cost: 1 10: f33 -> f6 : F'=1, [ C>=1+E ], cost: 1 11: f6 -> f43 : C'=free_13, D'=free_12, E'=C, [ free_13>=C && 0>=C && 0>=B ], cost: 1 12: f6 -> f43 : C'=free_15, D'=free_14, E'=C, F'=0, [ free_15>=C && 0>=C && B>=1 ], cost: 1 15: f6 -> f53 : C'=free_17, D'=free_16, E'=-1+C, [ 1+free_17>=C && C>=1 && 0>=B ], cost: 1 16: f6 -> f53 : C'=free_19, D'=free_18, E'=-1+C, F'=0, [ 1+free_19>=C && C>=1 && B>=1 ], cost: 1 13: f43 -> f6 : E'=C, [ C==E ], cost: 1 14: f43 -> f6 : F'=1, [ C>=1+E ], cost: 1 17: f53 -> f61 : B'=A, E'=C, [ E>=C ], cost: 1 18: f53 -> f61 : B'=A, E'=C, F'=1, [ C>=1+E ], cost: 1 19: f61 -> f63 : C'=free_21, D'=free_20, [ 0>=B && free_21>=E ], cost: 1 20: f61 -> f63 : C'=free_23, D'=free_22, F'=0, [ B>=1 && free_23>=E ], cost: 1 21: f63 -> f71 : D'=1+D, E'=C, [ E>=C ], cost: 1 22: f63 -> f71 : D'=1+D, E'=C, F'=1, [ C>=1+E ], cost: 1 23: f71 -> f73 : C'=free_25, D'=free_24, [ 0>=B && free_25>=E ], cost: 1 24: f71 -> f73 : C'=free_27, D'=free_26, F'=0, [ B>=1 && free_27>=E ], cost: 1 25: f73 -> f13 : [ E>=C ], cost: 1 26: f73 -> f13 : F'=1, [ C>=1+E ], cost: 1 Removed unreachable and leaf rules: Start location: f2 7: f4 -> f33 : A'=-1+A, C'=free_9, D'=free_8, E'=C, [ free_9>=C && 0>=B && A>=1 ], cost: 1 8: f4 -> f33 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=0, [ free_11>=C && B>=1 && A>=1 ], cost: 1 1: f13 -> f4 : [], cost: 1 3: f2 -> f23 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free ], cost: 1 4: f2 -> f23 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 ], cost: 1 5: f23 -> f4 : [ E>=C ], cost: 1 6: f23 -> f4 : F'=1, [ C>=1+E ], cost: 1 9: f33 -> f6 : [ E>=C ], cost: 1 10: f33 -> f6 : F'=1, [ C>=1+E ], cost: 1 11: f6 -> f43 : C'=free_13, D'=free_12, E'=C, [ free_13>=C && 0>=C && 0>=B ], cost: 1 12: f6 -> f43 : C'=free_15, D'=free_14, E'=C, F'=0, [ free_15>=C && 0>=C && B>=1 ], cost: 1 15: f6 -> f53 : C'=free_17, D'=free_16, E'=-1+C, [ 1+free_17>=C && C>=1 && 0>=B ], cost: 1 16: f6 -> f53 : C'=free_19, D'=free_18, E'=-1+C, F'=0, [ 1+free_19>=C && C>=1 && B>=1 ], cost: 1 13: f43 -> f6 : E'=C, [ C==E ], cost: 1 14: f43 -> f6 : F'=1, [ C>=1+E ], cost: 1 17: f53 -> f61 : B'=A, E'=C, [ E>=C ], cost: 1 18: f53 -> f61 : B'=A, E'=C, F'=1, [ C>=1+E ], cost: 1 19: f61 -> f63 : C'=free_21, D'=free_20, [ 0>=B && free_21>=E ], cost: 1 20: f61 -> f63 : C'=free_23, D'=free_22, F'=0, [ B>=1 && free_23>=E ], cost: 1 21: f63 -> f71 : D'=1+D, E'=C, [ E>=C ], cost: 1 22: f63 -> f71 : D'=1+D, E'=C, F'=1, [ C>=1+E ], cost: 1 23: f71 -> f73 : C'=free_25, D'=free_24, [ 0>=B && free_25>=E ], cost: 1 24: f71 -> f73 : C'=free_27, D'=free_26, F'=0, [ B>=1 && free_27>=E ], cost: 1 25: f73 -> f13 : [ E>=C ], cost: 1 26: f73 -> f13 : F'=1, [ C>=1+E ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on tree-shaped paths): Start location: f2 31: f4 -> f6 : A'=-1+A, C'=free_9, D'=free_8, E'=C, [ free_9>=C && 0>=B && A>=1 && C>=free_9 ], cost: 2 32: f4 -> f6 : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C ], cost: 2 33: f4 -> f6 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=0, [ free_11>=C && B>=1 && A>=1 && C>=free_11 ], cost: 2 34: f4 -> f6 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C ], cost: 2 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 35: f6 -> f6 : C'=free_13, D'=free_12, E'=free_13, [ 0>=C && 0>=B && free_13==C ], cost: 2 36: f6 -> f6 : C'=free_13, D'=free_12, E'=C, F'=1, [ 0>=C && 0>=B && free_13>=1+C ], cost: 2 37: f6 -> f6 : C'=free_15, D'=free_14, E'=free_15, F'=0, [ 0>=C && B>=1 && free_15==C ], cost: 2 38: f6 -> f6 : C'=free_15, D'=free_14, E'=C, F'=1, [ 0>=C && B>=1 && free_15>=1+C ], cost: 2 39: f6 -> f61 : B'=A, C'=free_17, D'=free_16, E'=free_17, [ 1+free_17>=C && C>=1 && 0>=B && -1+C>=free_17 ], cost: 2 40: f6 -> f61 : B'=A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ C>=1 && 0>=B && free_17>=C ], cost: 2 41: f6 -> f61 : B'=A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ 1+free_19>=C && C>=1 && B>=1 && -1+C>=free_19 ], cost: 2 42: f6 -> f61 : B'=A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ C>=1 && B>=1 && free_19>=C ], cost: 2 43: f61 -> f71 : C'=free_21, D'=1+free_20, E'=free_21, [ 0>=B && free_21>=E && E>=free_21 ], cost: 2 44: f61 -> f71 : C'=free_21, D'=1+free_20, E'=free_21, F'=1, [ 0>=B && free_21>=1+E ], cost: 2 45: f61 -> f71 : C'=free_23, D'=1+free_22, E'=free_23, F'=0, [ B>=1 && free_23>=E && E>=free_23 ], cost: 2 46: f61 -> f71 : C'=free_23, D'=1+free_22, E'=free_23, F'=1, [ B>=1 && free_23>=1+E ], cost: 2 47: f71 -> f13 : C'=free_25, D'=free_24, [ 0>=B && free_25>=E && E>=free_25 ], cost: 2 48: f71 -> f13 : C'=free_25, D'=free_24, F'=1, [ 0>=B && free_25>=1+E ], cost: 2 49: f71 -> f13 : C'=free_27, D'=free_26, F'=0, [ B>=1 && free_27>=E && E>=free_27 ], cost: 2 50: f71 -> f13 : C'=free_27, D'=free_26, F'=1, [ B>=1 && free_27>=1+E ], cost: 2 Accelerating simple loops of location 5. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 35: f6 -> f6 : D'=free_12, E'=C, [ 0>=C && 0>=B ], cost: 2 36: f6 -> f6 : C'=free_13, D'=free_12, E'=C, F'=1, [ 0>=C && 0>=B && free_13>=1+C ], cost: 2 37: f6 -> f6 : D'=free_14, E'=C, F'=0, [ 0>=C && B>=1 ], cost: 2 38: f6 -> f6 : C'=free_15, D'=free_14, E'=C, F'=1, [ 0>=C && B>=1 && free_15>=1+C ], cost: 2 Accelerated rule 35 with NONTERM, yielding the new rule 51. During metering: Instantiating temporary variables by {free_13==1+C} Accelerated rule 36 with metering function 1-C, yielding the new rule 52. Accelerated rule 37 with NONTERM, yielding the new rule 53. During metering: Instantiating temporary variables by {free_15==1+C} Accelerated rule 38 with metering function 1-C, yielding the new rule 54. Removing the simple loops: 35 36 37 38. Accelerated all simple loops using metering functions (where possible): Start location: f2 31: f4 -> f6 : A'=-1+A, C'=free_9, D'=free_8, E'=C, [ free_9>=C && 0>=B && A>=1 && C>=free_9 ], cost: 2 32: f4 -> f6 : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C ], cost: 2 33: f4 -> f6 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=0, [ free_11>=C && B>=1 && A>=1 && C>=free_11 ], cost: 2 34: f4 -> f6 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C ], cost: 2 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 39: f6 -> f61 : B'=A, C'=free_17, D'=free_16, E'=free_17, [ 1+free_17>=C && C>=1 && 0>=B && -1+C>=free_17 ], cost: 2 40: f6 -> f61 : B'=A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ C>=1 && 0>=B && free_17>=C ], cost: 2 41: f6 -> f61 : B'=A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ 1+free_19>=C && C>=1 && B>=1 && -1+C>=free_19 ], cost: 2 42: f6 -> f61 : B'=A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ C>=1 && B>=1 && free_19>=C ], cost: 2 51: f6 -> [14] : [ 0>=C && 0>=B ], cost: INF 52: f6 -> f6 : C'=1, D'=free_12, E'=0, F'=1, [ 0>=C && 0>=B ], cost: 2-2*C 53: f6 -> [14] : [ 0>=C && B>=1 ], cost: INF 54: f6 -> f6 : C'=1, D'=free_14, E'=0, F'=1, [ 0>=C && B>=1 ], cost: 2-2*C 43: f61 -> f71 : C'=free_21, D'=1+free_20, E'=free_21, [ 0>=B && free_21>=E && E>=free_21 ], cost: 2 44: f61 -> f71 : C'=free_21, D'=1+free_20, E'=free_21, F'=1, [ 0>=B && free_21>=1+E ], cost: 2 45: f61 -> f71 : C'=free_23, D'=1+free_22, E'=free_23, F'=0, [ B>=1 && free_23>=E && E>=free_23 ], cost: 2 46: f61 -> f71 : C'=free_23, D'=1+free_22, E'=free_23, F'=1, [ B>=1 && free_23>=1+E ], cost: 2 47: f71 -> f13 : C'=free_25, D'=free_24, [ 0>=B && free_25>=E && E>=free_25 ], cost: 2 48: f71 -> f13 : C'=free_25, D'=free_24, F'=1, [ 0>=B && free_25>=1+E ], cost: 2 49: f71 -> f13 : C'=free_27, D'=free_26, F'=0, [ B>=1 && free_27>=E && E>=free_27 ], cost: 2 50: f71 -> f13 : C'=free_27, D'=free_26, F'=1, [ B>=1 && free_27>=1+E ], cost: 2 Chained accelerated rules (with incoming rules): Start location: f2 31: f4 -> f6 : A'=-1+A, C'=free_9, D'=free_8, E'=C, [ free_9>=C && 0>=B && A>=1 && C>=free_9 ], cost: 2 32: f4 -> f6 : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C ], cost: 2 33: f4 -> f6 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=0, [ free_11>=C && B>=1 && A>=1 && C>=free_11 ], cost: 2 34: f4 -> f6 : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C ], cost: 2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 57: f4 -> f6 : A'=-1+A, C'=1, D'=free_12, E'=0, F'=1, [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 58: f4 -> f6 : A'=-1+A, C'=1, D'=free_12, E'=0, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 61: f4 -> f6 : A'=-1+A, C'=1, D'=free_14, E'=0, F'=1, [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 62: f4 -> f6 : A'=-1+A, C'=1, D'=free_14, E'=0, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 39: f6 -> f61 : B'=A, C'=free_17, D'=free_16, E'=free_17, [ 1+free_17>=C && C>=1 && 0>=B && -1+C>=free_17 ], cost: 2 40: f6 -> f61 : B'=A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ C>=1 && 0>=B && free_17>=C ], cost: 2 41: f6 -> f61 : B'=A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ 1+free_19>=C && C>=1 && B>=1 && -1+C>=free_19 ], cost: 2 42: f6 -> f61 : B'=A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ C>=1 && B>=1 && free_19>=C ], cost: 2 43: f61 -> f71 : C'=free_21, D'=1+free_20, E'=free_21, [ 0>=B && free_21>=E && E>=free_21 ], cost: 2 44: f61 -> f71 : C'=free_21, D'=1+free_20, E'=free_21, F'=1, [ 0>=B && free_21>=1+E ], cost: 2 45: f61 -> f71 : C'=free_23, D'=1+free_22, E'=free_23, F'=0, [ B>=1 && free_23>=E && E>=free_23 ], cost: 2 46: f61 -> f71 : C'=free_23, D'=1+free_22, E'=free_23, F'=1, [ B>=1 && free_23>=1+E ], cost: 2 47: f71 -> f13 : C'=free_25, D'=free_24, [ 0>=B && free_25>=E && E>=free_25 ], cost: 2 48: f71 -> f13 : C'=free_25, D'=free_24, F'=1, [ 0>=B && free_25>=1+E ], cost: 2 49: f71 -> f13 : C'=free_27, D'=free_26, F'=0, [ B>=1 && free_27>=E && E>=free_27 ], cost: 2 50: f71 -> f13 : C'=free_27, D'=free_26, F'=1, [ B>=1 && free_27>=1+E ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 63: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, [ free_9>=C && 0>=B && A>=1 && C>=free_9 && 1+free_17>=free_9 && free_9>=1 && -1+free_9>=free_17 ], cost: 4 64: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ free_9>=C && 0>=B && A>=1 && C>=free_9 && free_9>=1 && free_17>=free_9 ], cost: 4 65: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 1+free_17>=free_9 && free_9>=1 && -1+free_9>=free_17 ], cost: 4 66: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && free_9>=1+C && free_9>=1 && free_17>=free_9 ], cost: 4 67: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ free_11>=C && B>=1 && A>=1 && C>=free_11 && 1+free_19>=free_11 && free_11>=1 && -1+free_11>=free_19 ], cost: 4 68: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ free_11>=C && B>=1 && A>=1 && C>=free_11 && free_11>=1 && free_19>=free_11 ], cost: 4 69: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ B>=1 && A>=1 && free_11>=1+C && 1+free_19>=free_11 && free_11>=1 && -1+free_11>=free_19 ], cost: 4 70: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ B>=1 && A>=1 && free_11>=1+C && free_11>=1 && free_19>=free_11 ], cost: 4 71: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && 0>=C && 1+free_17>=1 && 0>=free_17 ], cost: 6-2*C 72: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && 0>=C && free_17>=1 ], cost: 6-2*C 73: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 ], cost: 6-2*free_9 74: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 ], cost: 6-2*free_9 75: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ B>=1 && A>=1 && 0>=C && 1+free_19>=1 && 0>=free_19 ], cost: 6-2*C 76: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ B>=1 && A>=1 && 0>=C && free_19>=1 ], cost: 6-2*C 77: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=0, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && 1+free_19>=1 && 0>=free_19 ], cost: 6-2*free_11 78: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 ], cost: 6-2*free_11 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 83: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, [ 0>=B && free_21>=E && E>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 4 84: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && free_21>=E && E>=free_21 && free_25>=1+free_21 ], cost: 4 85: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && free_21>=1+E && free_25>=free_21 && free_21>=free_25 ], cost: 4 86: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && free_21>=1+E && free_25>=1+free_21 ], cost: 4 87: f61 -> f13 : C'=free_27, D'=free_26, E'=free_23, F'=0, [ B>=1 && free_23>=E && E>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 4 88: f61 -> f13 : C'=free_27, D'=free_26, E'=free_23, F'=1, [ B>=1 && free_23>=E && E>=free_23 && free_27>=1+free_23 ], cost: 4 89: f61 -> f13 : C'=free_27, D'=free_26, E'=free_23, F'=0, [ B>=1 && free_23>=1+E && free_27>=free_23 && free_23>=free_27 ], cost: 4 90: f61 -> f13 : C'=free_27, D'=free_26, E'=free_23, F'=1, [ B>=1 && free_23>=1+E && free_27>=1+free_23 ], cost: 4 Applied pruning (of leafs and parallel rules): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 72: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && 0>=C && free_17>=1 ], cost: 6-2*C 73: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 ], cost: 6-2*free_9 74: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_16, E'=free_17, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 ], cost: 6-2*free_9 76: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ B>=1 && A>=1 && 0>=C && free_19>=1 ], cost: 6-2*C 78: f4 -> f61 : A'=-1+A, B'=-1+A, C'=free_19, D'=free_18, E'=free_19, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 ], cost: 6-2*free_11 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 83: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, [ 0>=B && free_21>=E && E>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 4 84: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && free_21>=E && E>=free_21 && free_25>=1+free_21 ], cost: 4 86: f61 -> f13 : C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && free_21>=1+E && free_25>=1+free_21 ], cost: 4 87: f61 -> f13 : C'=free_27, D'=free_26, E'=free_23, F'=0, [ B>=1 && free_23>=E && E>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 4 88: f61 -> f13 : C'=free_27, D'=free_26, E'=free_23, F'=1, [ B>=1 && free_23>=E && E>=free_23 && free_27>=1+free_23 ], cost: 4 Eliminated locations (on tree-shaped paths): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 91: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && 0>=C && free_17>=1 && 0>=-1+A && free_21>=free_17 && free_17>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 10-2*C 92: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && 0>=C && free_17>=1 && 0>=-1+A && free_21>=free_17 && free_17>=free_21 && free_25>=1+free_21 ], cost: 10-2*C 93: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && 0>=C && free_17>=1 && 0>=-1+A && free_21>=1+free_17 && free_25>=1+free_21 ], cost: 10-2*C 94: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && 0>=C && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*C 95: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ 0>=B && 0>=C && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=1+free_23 ], cost: 10-2*C 96: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 && 0>=-1+A && free_21>=free_17 && free_17>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 10-2*free_9 97: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 && 0>=-1+A && free_21>=free_17 && free_17>=free_21 && free_25>=1+free_21 ], cost: 10-2*free_9 98: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 && 0>=-1+A && free_21>=1+free_17 && free_25>=1+free_21 ], cost: 10-2*free_9 99: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*free_9 100: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ 0>=B && free_9>=1+C && 0>=free_9 && 1+free_17>=1 && 0>=free_17 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=1+free_23 ], cost: 10-2*free_9 101: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 && 0>=-1+A && free_21>=free_17 && free_17>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 10-2*free_9 102: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 && 0>=-1+A && free_21>=free_17 && free_17>=free_21 && free_25>=1+free_21 ], cost: 10-2*free_9 103: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 && 0>=-1+A && free_21>=1+free_17 && free_25>=1+free_21 ], cost: 10-2*free_9 104: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && free_9>=1+C && 0>=free_9 && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*free_9 105: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ 0>=B && free_9>=1+C && 0>=free_9 && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=1+free_23 ], cost: 10-2*free_9 106: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && 0>=C && free_19>=1 && 0>=-1+A && free_21>=free_19 && free_19>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 10-2*C 107: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && 0>=C && free_19>=1 && 0>=-1+A && free_21>=free_19 && free_19>=free_21 && free_25>=1+free_21 ], cost: 10-2*C 108: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && 0>=C && free_19>=1 && 0>=-1+A && free_21>=1+free_19 && free_25>=1+free_21 ], cost: 10-2*C 109: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ B>=1 && 0>=C && free_19>=1 && -1+A>=1 && free_23>=free_19 && free_19>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*C 110: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ B>=1 && 0>=C && free_19>=1 && -1+A>=1 && free_23>=free_19 && free_19>=free_23 && free_27>=1+free_23 ], cost: 10-2*C 111: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && 0>=-1+A && free_21>=free_19 && free_19>=free_21 && free_25>=free_21 && free_21>=free_25 ], cost: 10-2*free_11 112: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && 0>=-1+A && free_21>=free_19 && free_19>=free_21 && free_25>=1+free_21 ], cost: 10-2*free_11 113: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && 0>=-1+A && free_21>=1+free_19 && free_25>=1+free_21 ], cost: 10-2*free_11 114: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ B>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && -1+A>=1 && free_23>=free_19 && free_19>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*free_11 115: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ B>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && -1+A>=1 && free_23>=free_19 && free_19>=free_23 && free_27>=1+free_23 ], cost: 10-2*free_11 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 Applied pruning (of leafs and parallel rules): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 94: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && 0>=C && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*C 103: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 && 0>=-1+A && free_21>=1+free_17 && free_25>=1+free_21 ], cost: 10-2*free_9 104: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && free_9>=1+C && 0>=free_9 && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 10-2*free_9 105: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ 0>=B && free_9>=1+C && 0>=free_9 && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=1+free_23 ], cost: 10-2*free_9 113: f4 -> f13 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && 0>=-1+A && free_21>=1+free_19 && free_25>=1+free_21 ], cost: 10-2*free_11 1: f13 -> f4 : [], cost: 1 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 116: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && 0>=C && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 11-2*C 117: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 && free_17>=1 && 0>=-1+A && free_21>=1+free_17 && free_25>=1+free_21 ], cost: 11-2*free_9 118: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=0, [ 0>=B && free_9>=1+C && 0>=free_9 && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=free_23 && free_23>=free_27 ], cost: 11-2*free_9 119: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_23, F'=1, [ 0>=B && free_9>=1+C && 0>=free_9 && free_17>=1 && -1+A>=1 && free_23>=free_17 && free_17>=free_23 && free_27>=1+free_23 ], cost: 11-2*free_9 120: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 && free_19>=1 && 0>=-1+A && free_21>=1+free_19 && free_25>=1+free_21 ], cost: 11-2*free_11 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 Accelerating simple loops of location 0. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 116: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_26, E'=free_17, F'=0, [ 0>=B && 0>=C && -1+A>=1 ], cost: 11-2*C 117: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && 1-A==0 && free_9>=1+C && 0>=free_9 && free_25>=1+free_21 && 1<=-1+free_21 ], cost: 11-2*free_9 118: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_26, E'=free_17, F'=0, [ 0>=B && free_9>=1+C && 0>=free_9 && -1+A>=1 ], cost: 11-2*free_9 119: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_17, F'=1, [ 0>=B && free_9>=1+C && 0>=free_9 && -1+A>=1 && 1<=-1+free_27 ], cost: 11-2*free_9 120: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && 1-A==0 && free_11>=1+C && 0>=free_11 && free_25>=1+free_21 && 1<=-1+free_21 ], cost: 11-2*free_11 Found no metering function for rule 116. Accelerated rule 117 with metering function -1+A, yielding the new rule 121. Found no metering function for rule 118. Accelerated rule 119 with NONTERM (after strengthening guard), yielding the new rule 122. Accelerated rule 120 with metering function -1+A, yielding the new rule 123. Removing the simple loops: 117 120. Accelerated all simple loops using metering functions (where possible): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 116: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_26, E'=free_17, F'=0, [ 0>=B && 0>=C && -1+A>=1 ], cost: 11-2*C 118: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_17, D'=free_26, E'=free_17, F'=0, [ 0>=B && free_9>=1+C && 0>=free_9 && -1+A>=1 ], cost: 11-2*free_9 119: f4 -> f4 : A'=-1+A, B'=-1+A, C'=free_27, D'=free_26, E'=free_17, F'=1, [ 0>=B && free_9>=1+C && 0>=free_9 && -1+A>=1 && 1<=-1+free_27 ], cost: 11-2*free_9 121: f4 -> f4 : A'=1, B'=1, C'=free_25, D'=free_24, E'=free_21, F'=1, [ 0>=B && 1-A==0 && free_9>=1+C && 0>=free_9 && free_25>=1+free_21 && 1<=-1+free_21 && -1+A>=1 ], cost: -11-2*(-1+A)*free_9+11*A 122: f4 -> [16] : [ 0>=B && free_9>=1+C && 0>=free_9 && -1+A>=1 && 1<=-1+free_27 && free_9>=1+free_27 && 11-2*free_9>=1 ], cost: INF 123: f4 -> f4 : A'=1, B'=1, C'=free_25, D'=free_24, E'=free_21, F'=1, [ B>=1 && 1-A==0 && free_11>=1+C && 0>=free_11 && free_25>=1+free_21 && 1<=-1+free_21 && -1+A>=1 ], cost: -11-2*free_11*(-1+A)+11*A 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 Removed unreachable locations (and leaf rules with constant cost): Start location: f2 55: f4 -> [14] : A'=-1+A, D'=free_8, E'=C, [ 0>=B && A>=1 && 0>=C ], cost: INF 56: f4 -> [14] : A'=-1+A, C'=free_9, D'=free_8, E'=C, F'=1, [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: INF 59: f4 -> [14] : A'=-1+A, D'=free_10, E'=C, F'=0, [ B>=1 && A>=1 && 0>=C ], cost: INF 60: f4 -> [14] : A'=-1+A, C'=free_11, D'=free_10, E'=C, F'=1, [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: INF 79: f4 -> [15] : [ 0>=B && A>=1 && 0>=C ], cost: 4-2*C 80: f4 -> [15] : [ 0>=B && A>=1 && free_9>=1+C && 0>=free_9 ], cost: 4-2*free_9 81: f4 -> [15] : [ B>=1 && A>=1 && 0>=C ], cost: 4-2*C 82: f4 -> [15] : [ B>=1 && A>=1 && free_11>=1+C && 0>=free_11 ], cost: 4-2*free_11 27: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, [ free_2>=1 && free_3>=1 && 0>=free && 1>=free_3 ], cost: 2 28: f2 -> f4 : A'=free_2, B'=free, C'=free_3, D'=free_1, E'=1, F'=1, [ free_2>=1 && 0>=free && free_3>=2 ], cost: 2 29: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=0, [ free_6>=1 && free_7>=1 && free_4>=1 && 1>=free_7 ], cost: 2 30: f2 -> f4 : A'=free_6, B'=free_4, C'=free_7, D'=free_5, E'=1, F'=1, [ free_6>=1 && free_4>=1 && free_7>=2 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: f2 Applied pruning (of leafs and parallel rules): Start location: f2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f2 Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Unknown Cpx degree: ? Solved cost: 0 Rule cost: 0 Rule guard: [] WORST_CASE(Omega(0),?) ---------------------------------------- (2) BOUNDS(1, INF)