5.06/2.31	WORST_CASE(NON_POLY, ?)
5.06/2.32	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.06/2.32	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.06/2.32	
5.06/2.32	
5.06/2.32	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
5.06/2.32	
5.06/2.32	(0) CpxIntTrs
5.06/2.32	(1) Loat Proof [FINISHED, 630 ms]
5.06/2.32	(2) BOUNDS(INF, INF)
5.06/2.32	
5.06/2.32	
5.06/2.32	----------------------------------------
5.06/2.32	
5.06/2.32	(0)
5.06/2.32	Obligation:
5.06/2.32	Complexity Int TRS consisting of the following rules:
5.06/2.32	f11(A, B, C, D, E) -> Com_1(f11(A - 1, B - 1, C + 1, F, E)) :|: A >= 1 && F >= 1
5.06/2.32	f11(A, B, C, D, E) -> Com_1(f11(A - 1, B, C, F, E)) :|: 0 >= F && A >= 1 && A >= B + 1
5.06/2.32	f21(A, B, C, D, E) -> Com_1(f21(A, B, C, D, E)) :|: TRUE
5.06/2.32	f23(A, B, C, D, E) -> Com_1(f26(A, B, C, D, E)) :|: TRUE
5.06/2.32	f11(A, B, C, D, E) -> Com_1(f21(A, B, C, D, E)) :|: 0 >= A
5.06/2.32	f0(A, B, C, D, E) -> Com_1(f11(8, F, 0, D, 8)) :|: F >= 1
5.06/2.32	
5.06/2.32	The start-symbols are:[f0_5]
5.06/2.32	
5.06/2.32	
5.06/2.32	----------------------------------------
5.06/2.32	
5.06/2.32	(1) Loat Proof (FINISHED)
5.06/2.32	
5.06/2.32	
5.06/2.32	### Pre-processing the ITS problem ###
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Initial linear ITS problem
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	      0: f11 -> f11 : A'=-1+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
5.06/2.32	
5.06/2.32	      1: f11 -> f11 : A'=-1+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
5.06/2.32	
5.06/2.32	      4: f11 -> f21 : [ 0>=A ], cost: 1
5.06/2.32	
5.06/2.32	      2: f21 -> f21 : [], cost: 1
5.06/2.32	
5.06/2.32	      3: f23 -> f26 : [], cost: 1
5.06/2.32	
5.06/2.32	      5: f0 -> f11 : A'=8, B'=free_2, C'=0, E'=8, [ free_2>=1 ], cost: 1
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Removed unreachable and leaf rules:
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	      0: f11 -> f11 : A'=-1+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
5.06/2.32	
5.06/2.32	      1: f11 -> f11 : A'=-1+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
5.06/2.32	
5.06/2.32	      4: f11 -> f21 : [ 0>=A ], cost: 1
5.06/2.32	
5.06/2.32	      2: f21 -> f21 : [], cost: 1
5.06/2.32	
5.06/2.32	      5: f0 -> f11 : A'=8, B'=free_2, C'=0, E'=8, [ free_2>=1 ], cost: 1
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	### Simplification by acceleration and chaining ###
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Accelerating simple loops of location 0.
5.06/2.32	
5.06/2.32	   Accelerating the following rules:
5.06/2.32	
5.06/2.32	      0: f11 -> f11 : A'=-1+A, B'=-1+B, C'=1+C, D'=free, [ A>=1 && free>=1 ], cost: 1
5.06/2.32	
5.06/2.32	      1: f11 -> f11 : A'=-1+A, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B ], cost: 1
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	   Accelerated rule 0 with metering function A, yielding the new rule 6.
5.06/2.32	
5.06/2.32	   Accelerated rule 1 with backward acceleration, yielding the new rule 7.
5.06/2.32	
5.06/2.32	   Accelerated rule 1 with backward acceleration, yielding the new rule 8.
5.06/2.32	
5.06/2.32	   Removing the simple loops: 0 1.
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Accelerating simple loops of location 1.
5.06/2.32	
5.06/2.32	   Accelerating the following rules:
5.06/2.32	
5.06/2.32	      2: f21 -> f21 : [], cost: 1
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	   Accelerated rule 2 with NONTERM, yielding the new rule 9.
5.06/2.32	
5.06/2.32	   Removing the simple loops: 2.
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Accelerated all simple loops using metering functions (where possible):
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	      4: f11 -> f21 : [ 0>=A ], cost: 1
5.06/2.32	
5.06/2.32	      6: f11 -> f11 : A'=0, B'=-A+B, C'=C+A, D'=free, [ A>=1 && free>=1 ], cost: A
5.06/2.32	
5.06/2.32	      7: f11 -> f11 : A'=0, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B && 1>=1+B ], cost: A
5.06/2.32	
5.06/2.32	      8: f11 -> f11 : A'=B, D'=free_1, [ 0>=free_1 && A>=1 && A>=1+B && 1+B>=1 ], cost: A-B
5.06/2.32	
5.06/2.32	      9: f21 -> [6] : [], cost: INF
5.06/2.32	
5.06/2.32	      5: f0 -> f11 : A'=8, B'=free_2, C'=0, E'=8, [ free_2>=1 ], cost: 1
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Chained accelerated rules (with incoming rules):
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	      4: f11 -> f21 : [ 0>=A ], cost: 1
5.06/2.32	
5.06/2.32	     12: f11 -> [6] : [ 0>=A ], cost: INF
5.06/2.32	
5.06/2.32	      5: f0 -> f11 : A'=8, B'=free_2, C'=0, E'=8, [ free_2>=1 ], cost: 1
5.06/2.32	
5.06/2.32	     10: f0 -> f11 : A'=0, B'=-8+free_2, C'=8, D'=free, E'=8, [ free_2>=1 && free>=1 ], cost: 9
5.06/2.32	
5.06/2.32	     11: f0 -> f11 : A'=free_2, B'=free_2, C'=0, D'=free_1, E'=8, [ free_2>=1 && 0>=free_1 && 8>=1+free_2 ], cost: 9-free_2
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Removed unreachable locations (and leaf rules with constant cost):
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	     12: f11 -> [6] : [ 0>=A ], cost: INF
5.06/2.32	
5.06/2.32	      5: f0 -> f11 : A'=8, B'=free_2, C'=0, E'=8, [ free_2>=1 ], cost: 1
5.06/2.32	
5.06/2.32	     10: f0 -> f11 : A'=0, B'=-8+free_2, C'=8, D'=free, E'=8, [ free_2>=1 && free>=1 ], cost: 9
5.06/2.32	
5.06/2.32	     11: f0 -> f11 : A'=free_2, B'=free_2, C'=0, D'=free_1, E'=8, [ free_2>=1 && 0>=free_1 && 8>=1+free_2 ], cost: 9-free_2
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Eliminated locations (on tree-shaped paths):
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	     13: f0 -> [6] : A'=0, B'=-8+free_2, C'=8, D'=free, E'=8, [ free_2>=1 && free>=1 ], cost: INF
5.06/2.32	
5.06/2.32	     14: f0 -> [7] : [ free_2>=1 && 0>=free_1 && 8>=1+free_2 ], cost: 9-free_2
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	### Computing asymptotic complexity ###
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Fully simplified ITS problem
5.06/2.32	
5.06/2.32	   Start location: f0
5.06/2.32	
5.06/2.32	     13: f0 -> [6] : A'=0, B'=-8+free_2, C'=8, D'=free, E'=8, [ free_2>=1 && free>=1 ], cost: INF
5.06/2.32	
5.06/2.32	     14: f0 -> [7] : [ free_2>=1 && 0>=free_1 && 8>=1+free_2 ], cost: 9-free_2
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Computing asymptotic complexity for rule 13
5.06/2.32	
5.06/2.32	   Resulting cost INF has complexity: Nonterm
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Found new complexity Nonterm.
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	Obtained the following overall complexity (w.r.t. the length of the input n):
5.06/2.32	
5.06/2.32	   Complexity:  Nonterm
5.06/2.32	
5.06/2.32	   Cpx degree:  Nonterm
5.06/2.32	
5.06/2.32	   Solved cost: INF
5.06/2.32	
5.06/2.32	   Rule cost:   INF
5.06/2.32	
5.06/2.32	   Rule guard:  [ free_2>=1 && free>=1 ]
5.06/2.32	
5.06/2.32	
5.06/2.32	
5.06/2.32	NO
5.06/2.32	
5.06/2.32	
5.06/2.32	----------------------------------------
5.06/2.32	
5.06/2.32	(2)
5.06/2.32	BOUNDS(INF, INF)
5.25/2.34	EOF