3.56/1.73	WORST_CASE(NON_POLY, ?)
3.56/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.56/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.56/1.74	
3.56/1.74	
3.56/1.74	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.56/1.74	
3.56/1.74	(0) CpxIntTrs
3.56/1.74	(1) Loat Proof [FINISHED, 117 ms]
3.56/1.74	(2) BOUNDS(INF, INF)
3.56/1.74	
3.56/1.74	
3.56/1.74	----------------------------------------
3.56/1.74	
3.56/1.74	(0)
3.56/1.74	Obligation:
3.56/1.74	Complexity Int TRS consisting of the following rules:
3.56/1.74	f2(A, B, C, D, E, F, G, H, I, J) -> Com_1(f2(A, B, K, L, M, F, G, H, I, J)) :|: B >= 1 + A
3.56/1.74	f2(A, B, C, D, E, F, G, H, I, J) -> Com_1(f300(A, B, K, L, E, M, G, H, I, J)) :|: A >= B
3.56/1.74	f1(A, B, C, D, E, F, G, H, I, J) -> Com_1(f2(A, B, C, D, E, F, K, L, L, K)) :|: TRUE
3.56/1.74	
3.56/1.74	The start-symbols are:[f1_10]
3.56/1.74	
3.56/1.74	
3.56/1.74	----------------------------------------
3.56/1.74	
3.56/1.74	(1) Loat Proof (FINISHED)
3.56/1.74	
3.56/1.74	
3.56/1.74	### Pre-processing the ITS problem ###
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Initial linear ITS problem
3.56/1.74	
3.56/1.74	   Start location: f1
3.56/1.74	
3.56/1.74	      0: f2 -> f2 : C'=free_2, D'=free, E'=free_1, [ A>=1+B ], cost: 1
3.56/1.74	
3.56/1.74	      1: f2 -> f300 : C'=free_5, D'=free_3, F'=free_4, [ B>=A ], cost: 1
3.56/1.74	
3.56/1.74	      2: f1 -> f2 : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [], cost: 1
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Removed unreachable and leaf rules:
3.56/1.74	
3.56/1.74	   Start location: f1
3.56/1.74	
3.56/1.74	      0: f2 -> f2 : C'=free_2, D'=free, E'=free_1, [ A>=1+B ], cost: 1
3.56/1.74	
3.56/1.74	      2: f1 -> f2 : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [], cost: 1
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	### Simplification by acceleration and chaining ###
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Accelerating simple loops of location 0.
3.56/1.74	
3.56/1.74	   Accelerating the following rules:
3.56/1.74	
3.56/1.74	      0: f2 -> f2 : C'=free_2, D'=free, E'=free_1, [ A>=1+B ], cost: 1
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	   Accelerated rule 0 with NONTERM, yielding the new rule 3.
3.56/1.74	
3.56/1.74	   Removing the simple loops: 0.
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Accelerated all simple loops using metering functions (where possible):
3.56/1.74	
3.56/1.74	   Start location: f1
3.56/1.74	
3.56/1.74	      3: f2 -> [3] : [ A>=1+B ], cost: INF
3.56/1.74	
3.56/1.74	      2: f1 -> f2 : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [], cost: 1
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Chained accelerated rules (with incoming rules):
3.56/1.74	
3.56/1.74	   Start location: f1
3.56/1.74	
3.56/1.74	      2: f1 -> f2 : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [], cost: 1
3.56/1.74	
3.56/1.74	      4: f1 -> [3] : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [ A>=1+B ], cost: INF
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Removed unreachable locations (and leaf rules with constant cost):
3.56/1.74	
3.56/1.74	   Start location: f1
3.56/1.74	
3.56/1.74	      4: f1 -> [3] : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [ A>=1+B ], cost: INF
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	### Computing asymptotic complexity ###
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Fully simplified ITS problem
3.56/1.74	
3.56/1.74	   Start location: f1
3.56/1.74	
3.56/1.74	      4: f1 -> [3] : G'=free_7, H'=free_6, Q'=free_6, J'=free_7, [ A>=1+B ], cost: INF
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Computing asymptotic complexity for rule 4
3.56/1.74	
3.56/1.74	   Resulting cost INF has complexity: Nonterm
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Found new complexity Nonterm.
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	Obtained the following overall complexity (w.r.t. the length of the input n):
3.56/1.74	
3.56/1.74	   Complexity:  Nonterm
3.56/1.74	
3.56/1.74	   Cpx degree:  Nonterm
3.56/1.74	
3.56/1.74	   Solved cost: INF
3.56/1.74	
3.56/1.74	   Rule cost:   INF
3.56/1.74	
3.56/1.74	   Rule guard:  [ A>=1+B ]
3.56/1.74	
3.56/1.74	
3.56/1.74	
3.56/1.74	NO
3.56/1.74	
3.56/1.74	
3.56/1.74	----------------------------------------
3.56/1.74	
3.56/1.74	(2)
3.56/1.74	BOUNDS(INF, INF)
3.56/1.76	EOF