3.47/1.81	WORST_CASE(NON_POLY, ?)
3.47/1.82	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.47/1.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.47/1.82	
3.47/1.82	
3.47/1.82	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).
3.47/1.82	
3.47/1.82	(0) CpxIntTrs
3.47/1.82	(1) Loat Proof [FINISHED, 109 ms]
3.47/1.82	(2) BOUNDS(INF, INF)
3.47/1.82	
3.47/1.82	
3.47/1.82	----------------------------------------
3.47/1.82	
3.47/1.82	(0)
3.47/1.82	Obligation:
3.47/1.82	Complexity Int TRS consisting of the following rules:
3.47/1.82	f0(A, B) -> Com_1(f4(C, 0)) :|: TRUE
3.47/1.82	f4(A, B) -> Com_1(f4(A, B + 1)) :|: 0 >= C + 1
3.47/1.82	f4(A, B) -> Com_1(f4(A, B + 1)) :|: TRUE
3.47/1.82	f4(A, B) -> Com_1(f14(A, B)) :|: A >= 0 && B >= A + 1
3.47/1.82	f4(A, B) -> Com_1(f14(A, B)) :|: 0 >= A + 1
3.47/1.82	f4(A, B) -> Com_1(f14(A, B)) :|: A >= 0 && A >= B
3.47/1.82	f4(A, B) -> Com_1(f14(A, B)) :|: 0 >= C + 1 && A >= 0 && B >= A + 1
3.47/1.82	
3.47/1.82	The start-symbols are:[f0_2]
3.47/1.82	
3.47/1.82	
3.47/1.82	----------------------------------------
3.47/1.82	
3.47/1.82	(1) Loat Proof (FINISHED)
3.47/1.82	
3.47/1.82	
3.47/1.82	### Pre-processing the ITS problem ###
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Initial linear ITS problem
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      0: f0 -> f4 : A'=free, B'=0, [], cost: 1
3.47/1.82	
3.47/1.82	      1: f4 -> f4 : B'=1+B, [ 0>=1+free_1 ], cost: 1
3.47/1.82	
3.47/1.82	      2: f4 -> f4 : B'=1+B, [], cost: 1
3.47/1.82	
3.47/1.82	      3: f4 -> f14 : [ A>=0 && B>=1+A ], cost: 1
3.47/1.82	
3.47/1.82	      4: f4 -> f14 : [ 0>=1+A ], cost: 1
3.47/1.82	
3.47/1.82	      5: f4 -> f14 : [ A>=0 && A>=B ], cost: 1
3.47/1.82	
3.47/1.82	      6: f4 -> f14 : [ 0>=1+free_2 && A>=0 && B>=1+A ], cost: 1
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Removed unreachable and leaf rules:
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      0: f0 -> f4 : A'=free, B'=0, [], cost: 1
3.47/1.82	
3.47/1.82	      1: f4 -> f4 : B'=1+B, [ 0>=1+free_1 ], cost: 1
3.47/1.82	
3.47/1.82	      2: f4 -> f4 : B'=1+B, [], cost: 1
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Simplified all rules, resulting in:
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      0: f0 -> f4 : A'=free, B'=0, [], cost: 1
3.47/1.82	
3.47/1.82	      2: f4 -> f4 : B'=1+B, [], cost: 1
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	### Simplification by acceleration and chaining ###
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Accelerating simple loops of location 1.
3.47/1.82	
3.47/1.82	   Accelerating the following rules:
3.47/1.82	
3.47/1.82	      2: f4 -> f4 : B'=1+B, [], cost: 1
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	   Accelerated rule 2 with NONTERM, yielding the new rule 7.
3.47/1.82	
3.47/1.82	   Removing the simple loops: 2.
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Accelerated all simple loops using metering functions (where possible):
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      0: f0 -> f4 : A'=free, B'=0, [], cost: 1
3.47/1.82	
3.47/1.82	      7: f4 -> [3] : [], cost: INF
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Chained accelerated rules (with incoming rules):
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      0: f0 -> f4 : A'=free, B'=0, [], cost: 1
3.47/1.82	
3.47/1.82	      8: f0 -> [3] : A'=free, B'=0, [], cost: INF
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Removed unreachable locations (and leaf rules with constant cost):
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      8: f0 -> [3] : A'=free, B'=0, [], cost: INF
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	### Computing asymptotic complexity ###
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Fully simplified ITS problem
3.47/1.82	
3.47/1.82	   Start location: f0
3.47/1.82	
3.47/1.82	      8: f0 -> [3] : A'=free, B'=0, [], cost: INF
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Computing asymptotic complexity for rule 8
3.47/1.82	
3.47/1.82	   Resulting cost INF has complexity: Nonterm
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Found new complexity Nonterm.
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	Obtained the following overall complexity (w.r.t. the length of the input n):
3.47/1.82	
3.47/1.82	   Complexity:  Nonterm
3.47/1.82	
3.47/1.82	   Cpx degree:  Nonterm
3.47/1.82	
3.47/1.82	   Solved cost: INF
3.47/1.82	
3.47/1.82	   Rule cost:   INF
3.47/1.82	
3.47/1.82	   Rule guard:  []
3.47/1.82	
3.47/1.82	
3.47/1.82	
3.47/1.82	NO
3.47/1.82	
3.47/1.82	
3.47/1.82	----------------------------------------
3.47/1.82	
3.47/1.82	(2)
3.47/1.82	BOUNDS(INF, INF)
3.47/1.84	EOF