3.99/1.83	WORST_CASE(NON_POLY, ?)
3.99/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.99/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.99/1.84	
3.99/1.84	
3.99/1.84	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.99/1.84	
3.99/1.84	(0) CpxIntTrs
3.99/1.84	(1) Loat Proof [FINISHED, 200 ms]
3.99/1.84	(2) BOUNDS(INF, INF)
3.99/1.84	
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(0)
3.99/1.84	Obligation:
3.99/1.84	Complexity Int TRS consisting of the following rules:
3.99/1.84	f300(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(S, T, U, V, W, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: TRUE
3.99/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, 256, S, T, U, V, W, Y, O, P, Q, R)) :|: G >= 1 + F && X >= 1 && H >= 256 && H <= 256
3.99/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, H, S, T, U, V, W, N, O, P, Q, R)) :|: G >= 1 + F && 0 >= H
3.99/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f3(A, B, C, D, E, F, G, H, S, T, K, L, M, N, 0, 0, 0, R)) :|: F >= G
3.99/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f2(A, B, C, D, E, F, G, H, S, T, U, V, W, Y, H, H, H, X)) :|: H >= 1 && G >= 1 + F && H >= 257
3.99/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f2(A, B, C, D, E, F, G, H, S, T, U, V, W, Y, H, H, H, X)) :|: H >= 1 && G >= 1 + F && 255 >= H
3.99/1.84	
3.99/1.84	The start-symbols are:[f300_18]
3.99/1.84	
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(1) Loat Proof (FINISHED)
3.99/1.84	
3.99/1.84	
3.99/1.84	### Pre-processing the ITS problem ###
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Initial linear ITS problem
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1
3.99/1.84	
3.99/1.84	      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && free_10>=1 && H==256 ], cost: 1
3.99/1.84	
3.99/1.84	      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1
3.99/1.84	
3.99/1.84	      3: f1 -> f3 : Q'=free_17, J'=free_18, O'=0, P'=0, Q_1'=0, [ G>=F ], cost: 1
3.99/1.84	
3.99/1.84	      4: f1 -> f2 : Q'=free_21, J'=free_23, K'=free_25, L'=free_20, M'=free_22, N'=free_19, O'=H, P'=H, Q_1'=H, R'=free_24, [ H>=1 && F>=1+G && H>=257 ], cost: 1
3.99/1.84	
3.99/1.84	      5: f1 -> f2 : Q'=free_28, J'=free_30, K'=free_32, L'=free_27, M'=free_29, N'=free_26, O'=H, P'=H, Q_1'=H, R'=free_31, [ H>=1 && F>=1+G && 255>=H ], cost: 1
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Removed unreachable and leaf rules:
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1
3.99/1.84	
3.99/1.84	      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && free_10>=1 && H==256 ], cost: 1
3.99/1.84	
3.99/1.84	      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Simplified all rules, resulting in:
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1
3.99/1.84	
3.99/1.84	      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && H==256 ], cost: 1
3.99/1.84	
3.99/1.84	      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	### Simplification by acceleration and chaining ###
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Accelerating simple loops of location 1.
3.99/1.84	
3.99/1.84	   Accelerating the following rules:
3.99/1.84	
3.99/1.84	      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && H==256 ], cost: 1
3.99/1.84	
3.99/1.84	      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	   Accelerated rule 1 with NONTERM, yielding the new rule 6.
3.99/1.84	
3.99/1.84	   Accelerated rule 2 with NONTERM, yielding the new rule 7.
3.99/1.84	
3.99/1.84	   Removing the simple loops: 1 2.
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Accelerated all simple loops using metering functions (where possible):
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1
3.99/1.84	
3.99/1.84	      6: f1 -> [4] : [ F>=1+G && H==256 ], cost: INF
3.99/1.84	
3.99/1.84	      7: f1 -> [4] : [ F>=1+G && 0>=H ], cost: INF
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Chained accelerated rules (with incoming rules):
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1
3.99/1.84	
3.99/1.84	      8: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && H==256 ], cost: INF
3.99/1.84	
3.99/1.84	      9: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && 0>=H ], cost: INF
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Removed unreachable locations (and leaf rules with constant cost):
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      8: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && H==256 ], cost: INF
3.99/1.84	
3.99/1.84	      9: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && 0>=H ], cost: INF
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	### Computing asymptotic complexity ###
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Fully simplified ITS problem
3.99/1.84	
3.99/1.84	   Start location: f300
3.99/1.84	
3.99/1.84	      8: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && H==256 ], cost: INF
3.99/1.84	
3.99/1.84	      9: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && 0>=H ], cost: INF
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Computing asymptotic complexity for rule 8
3.99/1.84	
3.99/1.84	   Resulting cost INF has complexity: Nonterm
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Found new complexity Nonterm.
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	Obtained the following overall complexity (w.r.t. the length of the input n):
3.99/1.84	
3.99/1.84	   Complexity:  Nonterm
3.99/1.84	
3.99/1.84	   Cpx degree:  Nonterm
3.99/1.84	
3.99/1.84	   Solved cost: INF
3.99/1.84	
3.99/1.84	   Rule cost:   INF
3.99/1.84	
3.99/1.84	   Rule guard:  [ F>=1+G && H==256 ]
3.99/1.84	
3.99/1.84	
3.99/1.84	
3.99/1.84	NO
3.99/1.84	
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(2)
3.99/1.84	BOUNDS(INF, INF)
3.99/1.87	EOF