3.89/1.83	WORST_CASE(NON_POLY, ?)
3.89/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.89/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.89/1.84	
3.89/1.84	
3.89/1.84	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.89/1.84	
3.89/1.84	(0) CpxIntTrs
3.89/1.84	(1) Loat Proof [FINISHED, 203 ms]
3.89/1.84	(2) BOUNDS(INF, INF)
3.89/1.84	
3.89/1.84	
3.89/1.84	----------------------------------------
3.89/1.84	
3.89/1.84	(0)
3.89/1.84	Obligation:
3.89/1.84	Complexity Int TRS consisting of the following rules:
3.89/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f1(A, 1 + B, D, O, D, P, B, H, I, J, K, L, M, N)) :|: A >= B + 1 && B >= 0
3.89/1.84	f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, Q, R, U, T, F, G, O, S, V, W, C, M, N)) :|: B >= A && B >= 0 && Q >= O && O >= 2
3.89/1.84	f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(R, S, Q, V, U, F, G, P, T, W, Y, 0, O, N)) :|: 0 >= P && 0 >= X
3.89/1.84	f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f1(P, 2, R, Q, R, F, G, P, R, J, K, L, O, S)) :|: P >= 2
3.89/1.84	f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, Q, R, U, T, F, G, 1, S, V, W, D, O, N)) :|: TRUE
3.89/1.84	
3.89/1.84	The start-symbols are:[f3_14]
3.89/1.84	
3.89/1.84	
3.89/1.84	----------------------------------------
3.89/1.84	
3.89/1.84	(1) Loat Proof (FINISHED)
3.89/1.84	
3.89/1.84	
3.89/1.84	### Pre-processing the ITS problem ###
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Initial linear ITS problem
3.89/1.84	
3.89/1.84	   Start location: f3
3.89/1.84	
3.89/1.84	      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, [ A>=1+B && B>=0 ], cost: 1
3.89/1.84	
3.89/1.84	      1: f1 -> f4 : A'=free_10, B'=free_4, C'=free_9, D'=free_3, E'=free_6, H'=free_7, Q'=free_8, J'=free_2, K'=free_5, L'=C, [ B>=A && B>=0 && free_4>=free_7 && free_7>=2 ], cost: 1
3.89/1.84	
3.89/1.84	      2: f3 -> f4 : A'=free_21, B'=free_14, C'=free_20, D'=free_13, E'=free_16, H'=free_17, Q'=free_19, J'=free_12, K'=free_15, L'=0, M'=free_11, [ 0>=free_17 && 0>=free_18 ], cost: 1
3.89/1.84	
3.89/1.84	      3: f3 -> f1 : A'=free_26, B'=2, C'=free_23, D'=free_25, E'=free_23, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=2 ], cost: 1
3.89/1.84	
3.89/1.84	      4: f3 -> f4 : A'=free_35, B'=free_29, C'=free_34, D'=free_28, E'=free_31, H'=1, Q'=free_32, J'=free_33, K'=free_27, L'=D, M'=free_30, [], cost: 1
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Removed unreachable and leaf rules:
3.89/1.84	
3.89/1.84	   Start location: f3
3.89/1.84	
3.89/1.84	      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, [ A>=1+B && B>=0 ], cost: 1
3.89/1.84	
3.89/1.84	      3: f3 -> f1 : A'=free_26, B'=2, C'=free_23, D'=free_25, E'=free_23, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=2 ], cost: 1
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	### Simplification by acceleration and chaining ###
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Accelerating simple loops of location 0.
3.89/1.84	
3.89/1.84	   Accelerating the following rules:
3.89/1.84	
3.89/1.84	      0: f1 -> f1 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, [ A>=1+B && B>=0 ], cost: 1
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	   Accelerated rule 0 with metering function A-B, yielding the new rule 5.
3.89/1.84	
3.89/1.84	   Removing the simple loops: 0.
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Accelerated all simple loops using metering functions (where possible):
3.89/1.84	
3.89/1.84	   Start location: f3
3.89/1.84	
3.89/1.84	      5: f1 -> f1 : B'=A, C'=free_1, D'=free_1, E'=free_1, F'=free, G'=-1+A, [ A>=1+B && B>=0 ], cost: A-B
3.89/1.84	
3.89/1.84	      3: f3 -> f1 : A'=free_26, B'=2, C'=free_23, D'=free_25, E'=free_23, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=2 ], cost: 1
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Chained accelerated rules (with incoming rules):
3.89/1.84	
3.89/1.84	   Start location: f3
3.89/1.84	
3.89/1.84	      3: f3 -> f1 : A'=free_26, B'=2, C'=free_23, D'=free_25, E'=free_23, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=2 ], cost: 1
3.89/1.84	
3.89/1.84	      6: f3 -> f1 : A'=free_26, B'=free_26, C'=free_1, D'=free_1, E'=free_1, F'=free, G'=-1+free_26, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=3 ], cost: -1+free_26
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Removed unreachable locations (and leaf rules with constant cost):
3.89/1.84	
3.89/1.84	   Start location: f3
3.89/1.84	
3.89/1.84	      6: f3 -> f1 : A'=free_26, B'=free_26, C'=free_1, D'=free_1, E'=free_1, F'=free, G'=-1+free_26, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=3 ], cost: -1+free_26
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	### Computing asymptotic complexity ###
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Fully simplified ITS problem
3.89/1.84	
3.89/1.84	   Start location: f3
3.89/1.84	
3.89/1.84	      6: f3 -> f1 : A'=free_26, B'=free_26, C'=free_1, D'=free_1, E'=free_1, F'=free, G'=-1+free_26, H'=free_26, Q'=free_23, M'=free_22, N'=free_24, [ free_26>=3 ], cost: -1+free_26
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Computing asymptotic complexity for rule 6
3.89/1.84	
3.89/1.84	   Solved the limit problem by the following transformations:
3.89/1.84	
3.89/1.84	      Created initial limit problem:
3.89/1.84	
3.89/1.84	      -1+free_26 (+), -2+free_26 (+/+!) [not solved]
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	      removing all constraints (solved by SMT)
3.89/1.84	
3.89/1.84	      resulting limit problem: [solved]
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	      applying transformation rule (C) using substitution {free_26==n}
3.89/1.84	
3.89/1.84	      resulting limit problem:
3.89/1.84	
3.89/1.84	      [solved]
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	   Solution:
3.89/1.84	
3.89/1.84	      free_26 / n
3.89/1.84	
3.89/1.84	   Resulting cost -1+n has complexity: Unbounded
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Found new complexity Unbounded.
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	Obtained the following overall complexity (w.r.t. the length of the input n):
3.89/1.84	
3.89/1.84	   Complexity:  Unbounded
3.89/1.84	
3.89/1.84	   Cpx degree:  Unbounded
3.89/1.84	
3.89/1.84	   Solved cost: -1+n
3.89/1.84	
3.89/1.84	   Rule cost:   -1+free_26
3.89/1.84	
3.89/1.84	   Rule guard:  [ free_26>=3 ]
3.89/1.84	
3.89/1.84	
3.89/1.84	
3.89/1.84	WORST_CASE(INF,?)
3.89/1.84	
3.89/1.84	
3.89/1.84	----------------------------------------
3.89/1.84	
3.89/1.84	(2)
3.89/1.84	BOUNDS(INF, INF)
4.04/1.87	EOF