4.69/2.16	WORST_CASE(NON_POLY, ?)
4.69/2.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.69/2.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.69/2.17	
4.69/2.17	
4.69/2.17	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
4.69/2.17	
4.69/2.17	(0) CpxIntTrs
4.69/2.17	(1) Loat Proof [FINISHED, 506 ms]
4.69/2.17	(2) BOUNDS(INF, INF)
4.69/2.17	
4.69/2.17	
4.69/2.17	----------------------------------------
4.69/2.17	
4.69/2.17	(0)
4.69/2.17	Obligation:
4.69/2.17	Complexity Int TRS consisting of the following rules:
4.69/2.17	f18(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f24(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= A
4.69/2.17	f32(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE
4.69/2.17	f34(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE
4.69/2.17	f24(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(A, L, C, D, E, F, G, H, I, J, K)) :|: A >= 1
4.69/2.17	f24(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(A, M, C, L, L, F, G, H, I, J, K)) :|: 0 >= A && 999 + C >= L
4.69/2.17	f24(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(1, M, C, L, L, F, G, H, I, J, K)) :|: 0 >= A && L >= C + 1000
4.69/2.17	f18(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f24(0, B, L, D, E, L, G, H, I, J, K)) :|: A >= 1
4.69/2.17	f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f18(1, B, C, D, E, F, L, M, I, J, K)) :|: 0 >= M
4.69/2.17	f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f18(1, B, C, D, E, F, L, 0, 1, M, M)) :|: M >= 1 && N >= 1
4.69/2.17	f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(1, B, C, D, E, F, L, 0, 1, M, M)) :|: 0 >= M && N >= 1
4.69/2.17	
4.69/2.17	The start-symbols are:[f0_11]
4.69/2.17	
4.69/2.17	
4.69/2.17	----------------------------------------
4.69/2.17	
4.69/2.17	(1) Loat Proof (FINISHED)
4.69/2.17	
4.69/2.17	
4.69/2.17	### Pre-processing the ITS problem ###
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Initial linear ITS problem
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	      0: f18 -> f24 : [ 0>=A ], cost: 1
4.69/2.17	
4.69/2.17	      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      1: f32 -> f32 : [], cost: 1
4.69/2.17	
4.69/2.17	      2: f34 -> f37 : [], cost: 1
4.69/2.17	
4.69/2.17	      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      4: f24 -> f32 : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: 1
4.69/2.17	
4.69/2.17	      5: f24 -> f32 : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: 1
4.69/2.17	
4.69/2.17	      7: f0 -> f18 : A'=1, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 1
4.69/2.17	
4.69/2.17	      8: f0 -> f18 : A'=1, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 && free_10>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      9: f0 -> f32 : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 && free_13>=1 ], cost: 1
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Removed unreachable and leaf rules:
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	      0: f18 -> f24 : [ 0>=A ], cost: 1
4.69/2.17	
4.69/2.17	      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      1: f32 -> f32 : [], cost: 1
4.69/2.17	
4.69/2.17	      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      4: f24 -> f32 : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: 1
4.69/2.17	
4.69/2.17	      5: f24 -> f32 : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: 1
4.69/2.17	
4.69/2.17	      7: f0 -> f18 : A'=1, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 1
4.69/2.17	
4.69/2.17	      8: f0 -> f18 : A'=1, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 && free_10>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      9: f0 -> f32 : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 && free_13>=1 ], cost: 1
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Simplified all rules, resulting in:
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	      0: f18 -> f24 : [ 0>=A ], cost: 1
4.69/2.17	
4.69/2.17	      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      1: f32 -> f32 : [], cost: 1
4.69/2.17	
4.69/2.17	      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      4: f24 -> f32 : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: 1
4.69/2.17	
4.69/2.17	      5: f24 -> f32 : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: 1
4.69/2.17	
4.69/2.17	      7: f0 -> f18 : A'=1, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 1
4.69/2.17	
4.69/2.17	      8: f0 -> f18 : A'=1, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      9: f0 -> f32 : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: 1
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	### Simplification by acceleration and chaining ###
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Accelerating simple loops of location 1.
4.69/2.17	
4.69/2.17	   Accelerating the following rules:
4.69/2.17	
4.69/2.17	      1: f32 -> f32 : [], cost: 1
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	   Accelerated rule 1 with NONTERM, yielding the new rule 10.
4.69/2.17	
4.69/2.17	   Removing the simple loops: 1.
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Accelerated all simple loops using metering functions (where possible):
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	      0: f18 -> f24 : [ 0>=A ], cost: 1
4.69/2.17	
4.69/2.17	      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	     10: f32 -> [6] : [], cost: INF
4.69/2.17	
4.69/2.17	      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      4: f24 -> f32 : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: 1
4.69/2.17	
4.69/2.17	      5: f24 -> f32 : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: 1
4.69/2.17	
4.69/2.17	      7: f0 -> f18 : A'=1, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 1
4.69/2.17	
4.69/2.17	      8: f0 -> f18 : A'=1, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      9: f0 -> f32 : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: 1
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Chained accelerated rules (with incoming rules):
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	      0: f18 -> f24 : [ 0>=A ], cost: 1
4.69/2.17	
4.69/2.17	      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      4: f24 -> f32 : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: 1
4.69/2.17	
4.69/2.17	      5: f24 -> f32 : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: 1
4.69/2.17	
4.69/2.17	     11: f24 -> [6] : B'=free, [ A>=1 ], cost: INF
4.69/2.17	
4.69/2.17	     12: f24 -> [6] : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     13: f24 -> [6] : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: INF
4.69/2.17	
4.69/2.17	      7: f0 -> f18 : A'=1, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 1
4.69/2.17	
4.69/2.17	      8: f0 -> f18 : A'=1, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 ], cost: 1
4.69/2.17	
4.69/2.17	      9: f0 -> f32 : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: 1
4.69/2.17	
4.69/2.17	     14: f0 -> [6] : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: INF
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Removed unreachable locations (and leaf rules with constant cost):
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	      0: f18 -> f24 : [ 0>=A ], cost: 1
4.69/2.17	
4.69/2.17	      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1
4.69/2.17	
4.69/2.17	     11: f24 -> [6] : B'=free, [ A>=1 ], cost: INF
4.69/2.17	
4.69/2.17	     12: f24 -> [6] : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     13: f24 -> [6] : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: INF
4.69/2.17	
4.69/2.17	      7: f0 -> f18 : A'=1, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 1
4.69/2.17	
4.69/2.17	      8: f0 -> f18 : A'=1, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 ], cost: 1
4.69/2.17	
4.69/2.17	     14: f0 -> [6] : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: INF
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Eliminated locations (on tree-shaped paths):
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	     11: f24 -> [6] : B'=free, [ A>=1 ], cost: INF
4.69/2.17	
4.69/2.17	     12: f24 -> [6] : B'=free_1, D'=free_2, E'=free_2, [ 0>=A && 999+C>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     13: f24 -> [6] : A'=1, B'=free_3, D'=free_4, E'=free_4, [ 0>=A && free_4>=1000+C ], cost: INF
4.69/2.17	
4.69/2.17	     14: f0 -> [6] : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: INF
4.69/2.17	
4.69/2.17	     15: f0 -> f24 : A'=0, C'=free_5, F'=free_5, G'=free_6, H'=free_7, [ 0>=free_7 ], cost: 2
4.69/2.17	
4.69/2.17	     16: f0 -> f24 : A'=0, C'=free_5, F'=free_5, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 ], cost: 2
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Eliminated locations (on tree-shaped paths):
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	     14: f0 -> [6] : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: INF
4.69/2.17	
4.69/2.17	     17: f0 -> [6] : A'=0, B'=free_1, C'=free_5, D'=free_2, E'=free_2, F'=free_5, G'=free_6, H'=free_7, [ 0>=free_7 && 999+free_5>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     18: f0 -> [6] : A'=1, B'=free_3, C'=free_5, D'=free_4, E'=free_4, F'=free_5, G'=free_6, H'=free_7, [ 0>=free_7 && free_4>=1000+free_5 ], cost: INF
4.69/2.17	
4.69/2.17	     19: f0 -> [6] : A'=0, B'=free_1, C'=free_5, D'=free_2, E'=free_2, F'=free_5, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 && 999+free_5>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     20: f0 -> [6] : A'=1, B'=free_3, C'=free_5, D'=free_4, E'=free_4, F'=free_5, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 && free_4>=1000+free_5 ], cost: INF
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	### Computing asymptotic complexity ###
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Fully simplified ITS problem
4.69/2.17	
4.69/2.17	   Start location: f0
4.69/2.17	
4.69/2.17	     14: f0 -> [6] : A'=1, G'=free_11, H'=0, Q'=1, J'=free_12, K'=free_12, [ 0>=free_12 ], cost: INF
4.69/2.17	
4.69/2.17	     17: f0 -> [6] : A'=0, B'=free_1, C'=free_5, D'=free_2, E'=free_2, F'=free_5, G'=free_6, H'=free_7, [ 0>=free_7 && 999+free_5>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     18: f0 -> [6] : A'=1, B'=free_3, C'=free_5, D'=free_4, E'=free_4, F'=free_5, G'=free_6, H'=free_7, [ 0>=free_7 && free_4>=1000+free_5 ], cost: INF
4.69/2.17	
4.69/2.17	     19: f0 -> [6] : A'=0, B'=free_1, C'=free_5, D'=free_2, E'=free_2, F'=free_5, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 && 999+free_5>=free_2 ], cost: INF
4.69/2.17	
4.69/2.17	     20: f0 -> [6] : A'=1, B'=free_3, C'=free_5, D'=free_4, E'=free_4, F'=free_5, G'=free_8, H'=0, Q'=1, J'=free_9, K'=free_9, [ free_9>=1 && free_4>=1000+free_5 ], cost: INF
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Computing asymptotic complexity for rule 14
4.69/2.17	
4.69/2.17	   Resulting cost INF has complexity: Nonterm
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Found new complexity Nonterm.
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	Obtained the following overall complexity (w.r.t. the length of the input n):
4.69/2.17	
4.69/2.17	   Complexity:  Nonterm
4.69/2.17	
4.69/2.17	   Cpx degree:  Nonterm
4.69/2.17	
4.69/2.17	   Solved cost: INF
4.69/2.17	
4.69/2.17	   Rule cost:   INF
4.69/2.17	
4.69/2.17	   Rule guard:  [ 0>=free_12 ]
4.69/2.17	
4.69/2.17	
4.69/2.17	
4.69/2.17	NO
4.69/2.17	
4.69/2.17	
4.69/2.17	----------------------------------------
4.69/2.17	
4.69/2.17	(2)
4.69/2.17	BOUNDS(INF, INF)
4.69/2.18	EOF