3.68/1.99	WORST_CASE(Omega(n^1), O(n^1))
3.68/2.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.68/2.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.68/2.00	
3.68/2.00	
3.68/2.00	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
3.68/2.00	
3.68/2.00	(0) CpxIntTrs
3.68/2.00	(1) Koat Proof [FINISHED, 9 ms]
3.68/2.00	(2) BOUNDS(1, n^1)
3.68/2.00	(3) Loat Proof [FINISHED, 324 ms]
3.68/2.00	(4) BOUNDS(n^1, INF)
3.68/2.00	
3.68/2.00	
3.68/2.00	----------------------------------------
3.68/2.00	
3.68/2.00	(0)
3.68/2.00	Obligation:
3.68/2.00	Complexity Int TRS consisting of the following rules:
3.68/2.00	evalrandom1dstart(A, B) -> Com_1(evalrandom1dentryin(A, B)) :|: TRUE
3.68/2.00	evalrandom1dentryin(A, B) -> Com_1(evalrandom1dbb5in(A, 1)) :|: A >= 1
3.68/2.00	evalrandom1dentryin(A, B) -> Com_1(evalrandom1dreturnin(A, B)) :|: 0 >= A
3.68/2.00	evalrandom1dbb5in(A, B) -> Com_1(evalrandom1dbb1in(A, B)) :|: A >= B
3.68/2.00	evalrandom1dbb5in(A, B) -> Com_1(evalrandom1dreturnin(A, B)) :|: B >= A + 1
3.68/2.00	evalrandom1dbb1in(A, B) -> Com_1(evalrandom1dbb5in(A, B + 1)) :|: 0 >= C + 1
3.68/2.00	evalrandom1dbb1in(A, B) -> Com_1(evalrandom1dbb5in(A, B + 1)) :|: C >= 1
3.68/2.00	evalrandom1dbb1in(A, B) -> Com_1(evalrandom1dbb5in(A, B + 1)) :|: TRUE
3.68/2.00	evalrandom1dreturnin(A, B) -> Com_1(evalrandom1dstop(A, B)) :|: TRUE
3.68/2.00	
3.68/2.00	The start-symbols are:[evalrandom1dstart_2]
3.68/2.00	
3.68/2.00	
3.68/2.00	----------------------------------------
3.68/2.00	
3.68/2.00	(1) Koat Proof (FINISHED)
3.68/2.00	YES(?, 4*ar_0 + 15)
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Initial complexity problem:
3.68/2.00	
3.68/2.00	1:	T:
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]
3.68/2.00	
3.68/2.00		start location:	koat_start
3.68/2.00	
3.68/2.00		leaf cost:	0
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.68/2.00	
3.68/2.00	2:	T:
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)    evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)    evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)    evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]
3.68/2.00	
3.68/2.00		start location:	koat_start
3.68/2.00	
3.68/2.00		leaf cost:	0
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	A polynomial rank function with
3.68/2.00	
3.68/2.00		Pol(evalrandom1dstart) = 2
3.68/2.00	
3.68/2.00		Pol(evalrandom1dentryin) = 2
3.68/2.00	
3.68/2.00		Pol(evalrandom1dbb5in) = 2
3.68/2.00	
3.68/2.00		Pol(evalrandom1dreturnin) = 1
3.68/2.00	
3.68/2.00		Pol(evalrandom1dbb1in) = 2
3.68/2.00	
3.68/2.00		Pol(evalrandom1dstop) = 0
3.68/2.00	
3.68/2.00		Pol(koat_start) = 2
3.68/2.00	
3.68/2.00	orients all transitions weakly and the transitions
3.68/2.00	
3.68/2.00		evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))
3.68/2.00	
3.68/2.00		evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.68/2.00	
3.68/2.00	strictly and produces the following problem:
3.68/2.00	
3.68/2.00	3:	T:
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)    evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)    evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)    evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00			(Comp: 2, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))
3.68/2.00	
3.68/2.00			(Comp: 2, Cost: 1)    evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]
3.68/2.00	
3.68/2.00		start location:	koat_start
3.68/2.00	
3.68/2.00		leaf cost:	0
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	A polynomial rank function with
3.68/2.00	
3.68/2.00		Pol(evalrandom1dbb5in) = V_1 - V_2 + 1
3.68/2.00	
3.68/2.00		Pol(evalrandom1dbb1in) = V_1 - V_2
3.68/2.00	
3.68/2.00	and size complexities
3.68/2.00	
3.68/2.00		S("koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
3.68/2.00	
3.68/2.00		S("evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))", 0-1) = ?
3.68/2.00	
3.68/2.00		S("evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))", 0-1) = ?
3.68/2.00	
3.68/2.00		S("evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]", 0-1) = ?
3.68/2.00	
3.68/2.00		S("evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]", 0-1) = ?
3.68/2.00	
3.68/2.00		S("evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ?
3.68/2.00	
3.68/2.00		S("evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]", 0-1) = ?
3.68/2.00	
3.68/2.00		S("evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]", 0-1) = ar_1
3.68/2.00	
3.68/2.00		S("evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]", 0-1) = 1
3.68/2.00	
3.68/2.00		S("evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))", 0-0) = ar_0
3.68/2.00	
3.68/2.00		S("evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))", 0-1) = ar_1
3.68/2.00	
3.68/2.00	orients the transitions
3.68/2.00	
3.68/2.00		evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00		evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]
3.68/2.00	
3.68/2.00		evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]
3.68/2.00	
3.68/2.00		evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))
3.68/2.00	
3.68/2.00	weakly and the transition
3.68/2.00	
3.68/2.00		evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00	strictly and produces the following problem:
3.68/2.00	
3.68/2.00	4:	T:
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)           evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)           evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)           evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]
3.68/2.00	
3.68/2.00			(Comp: ar_0 + 2, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00			(Comp: 2, Cost: 1)           evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)           evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)           evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: ?, Cost: 1)           evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))
3.68/2.00	
3.68/2.00			(Comp: 2, Cost: 1)           evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]
3.68/2.00	
3.68/2.00		start location:	koat_start
3.68/2.00	
3.68/2.00		leaf cost:	0
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Repeatedly propagating knowledge in problem 4 produces the following problem:
3.68/2.00	
3.68/2.00	5:	T:
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)           evalrandom1dstart(ar_0, ar_1) -> Com_1(evalrandom1dentryin(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)           evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, 1)) [ ar_0 >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 1)           evalrandom1dentryin(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ 0 >= ar_0 ]
3.68/2.00	
3.68/2.00			(Comp: ar_0 + 2, Cost: 1)    evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dbb1in(ar_0, ar_1)) [ ar_0 >= ar_1 ]
3.68/2.00	
3.68/2.00			(Comp: 2, Cost: 1)           evalrandom1dbb5in(ar_0, ar_1) -> Com_1(evalrandom1dreturnin(ar_0, ar_1)) [ ar_1 >= ar_0 + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ar_0 + 2, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ 0 >= c + 1 ]
3.68/2.00	
3.68/2.00			(Comp: ar_0 + 2, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1)) [ c >= 1 ]
3.68/2.00	
3.68/2.00			(Comp: ar_0 + 2, Cost: 1)    evalrandom1dbb1in(ar_0, ar_1) -> Com_1(evalrandom1dbb5in(ar_0, ar_1 + 1))
3.68/2.00	
3.68/2.00			(Comp: 2, Cost: 1)           evalrandom1dreturnin(ar_0, ar_1) -> Com_1(evalrandom1dstop(ar_0, ar_1))
3.68/2.00	
3.68/2.00			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1) -> Com_1(evalrandom1dstart(ar_0, ar_1)) [ 0 <= 0 ]
3.68/2.00	
3.68/2.00		start location:	koat_start
3.68/2.00	
3.68/2.00		leaf cost:	0
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Complexity upper bound 4*ar_0 + 15
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Time: 0.076 sec (SMT: 0.069 sec)
3.68/2.00	
3.68/2.00	
3.68/2.00	----------------------------------------
3.68/2.00	
3.68/2.00	(2)
3.68/2.00	BOUNDS(1, n^1)
3.68/2.00	
3.68/2.00	----------------------------------------
3.68/2.00	
3.68/2.00	(3) Loat Proof (FINISHED)
3.68/2.00	
3.68/2.00	
3.68/2.00	### Pre-processing the ITS problem ###
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Initial linear ITS problem
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	      0: evalrandom1dstart -> evalrandom1dentryin : [], cost: 1
3.68/2.00	
3.68/2.00	      1: evalrandom1dentryin -> evalrandom1dbb5in : B'=1, [ A>=1 ], cost: 1
3.68/2.00	
3.68/2.00	      2: evalrandom1dentryin -> evalrandom1dreturnin : [ 0>=A ], cost: 1
3.68/2.00	
3.68/2.00	      3: evalrandom1dbb5in -> evalrandom1dbb1in : [ A>=B ], cost: 1
3.68/2.00	
3.68/2.00	      4: evalrandom1dbb5in -> evalrandom1dreturnin : [ B>=1+A ], cost: 1
3.68/2.00	
3.68/2.00	      5: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [ 0>=1+free ], cost: 1
3.68/2.00	
3.68/2.00	      6: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [ free_1>=1 ], cost: 1
3.68/2.00	
3.68/2.00	      7: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [], cost: 1
3.68/2.00	
3.68/2.00	      8: evalrandom1dreturnin -> evalrandom1dstop : [], cost: 1
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Removed unreachable and leaf rules:
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	      0: evalrandom1dstart -> evalrandom1dentryin : [], cost: 1
3.68/2.00	
3.68/2.00	      1: evalrandom1dentryin -> evalrandom1dbb5in : B'=1, [ A>=1 ], cost: 1
3.68/2.00	
3.68/2.00	      3: evalrandom1dbb5in -> evalrandom1dbb1in : [ A>=B ], cost: 1
3.68/2.00	
3.68/2.00	      5: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [ 0>=1+free ], cost: 1
3.68/2.00	
3.68/2.00	      6: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [ free_1>=1 ], cost: 1
3.68/2.00	
3.68/2.00	      7: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [], cost: 1
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Simplified all rules, resulting in:
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	      0: evalrandom1dstart -> evalrandom1dentryin : [], cost: 1
3.68/2.00	
3.68/2.00	      1: evalrandom1dentryin -> evalrandom1dbb5in : B'=1, [ A>=1 ], cost: 1
3.68/2.00	
3.68/2.00	      3: evalrandom1dbb5in -> evalrandom1dbb1in : [ A>=B ], cost: 1
3.68/2.00	
3.68/2.00	      7: evalrandom1dbb1in -> evalrandom1dbb5in : B'=1+B, [], cost: 1
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	### Simplification by acceleration and chaining ###
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Eliminated locations (on linear paths):
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	      9: evalrandom1dstart -> evalrandom1dbb5in : B'=1, [ A>=1 ], cost: 2
3.68/2.00	
3.68/2.00	     10: evalrandom1dbb5in -> evalrandom1dbb5in : B'=1+B, [ A>=B ], cost: 2
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Accelerating simple loops of location 2.
3.68/2.00	
3.68/2.00	   Accelerating the following rules:
3.68/2.00	
3.68/2.00	     10: evalrandom1dbb5in -> evalrandom1dbb5in : B'=1+B, [ A>=B ], cost: 2
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	   Accelerated rule 10 with metering function 1+A-B, yielding the new rule 11.
3.68/2.00	
3.68/2.00	   Removing the simple loops: 10.
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Accelerated all simple loops using metering functions (where possible):
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	      9: evalrandom1dstart -> evalrandom1dbb5in : B'=1, [ A>=1 ], cost: 2
3.68/2.00	
3.68/2.00	     11: evalrandom1dbb5in -> evalrandom1dbb5in : B'=1+A, [ A>=B ], cost: 2+2*A-2*B
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Chained accelerated rules (with incoming rules):
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	      9: evalrandom1dstart -> evalrandom1dbb5in : B'=1, [ A>=1 ], cost: 2
3.68/2.00	
3.68/2.00	     12: evalrandom1dstart -> evalrandom1dbb5in : B'=1+A, [ A>=1 ], cost: 2+2*A
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Removed unreachable locations (and leaf rules with constant cost):
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	     12: evalrandom1dstart -> evalrandom1dbb5in : B'=1+A, [ A>=1 ], cost: 2+2*A
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	### Computing asymptotic complexity ###
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Fully simplified ITS problem
3.68/2.00	
3.68/2.00	   Start location: evalrandom1dstart
3.68/2.00	
3.68/2.00	     12: evalrandom1dstart -> evalrandom1dbb5in : B'=1+A, [ A>=1 ], cost: 2+2*A
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Computing asymptotic complexity for rule 12
3.68/2.00	
3.68/2.00	   Solved the limit problem by the following transformations:
3.68/2.00	
3.68/2.00	      Created initial limit problem:
3.68/2.00	
3.68/2.00	      A (+/+!), 2+2*A (+) [not solved]
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	      removing all constraints (solved by SMT)
3.68/2.00	
3.68/2.00	      resulting limit problem: [solved]
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	      applying transformation rule (C) using substitution {A==n}
3.68/2.00	
3.68/2.00	      resulting limit problem:
3.68/2.00	
3.68/2.00	      [solved]
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	   Solution:
3.68/2.00	
3.68/2.00	      A / n
3.68/2.00	
3.68/2.00	   Resulting cost 2+2*n has complexity: Poly(n^1)
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Found new complexity Poly(n^1).
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	Obtained the following overall complexity (w.r.t. the length of the input n):
3.68/2.00	
3.68/2.00	   Complexity:  Poly(n^1)
3.68/2.00	
3.68/2.00	   Cpx degree:  1
3.68/2.00	
3.68/2.00	   Solved cost: 2+2*n
3.68/2.00	
3.68/2.00	   Rule cost:   2+2*A
3.68/2.00	
3.68/2.00	   Rule guard:  [ A>=1 ]
3.68/2.00	
3.68/2.00	
3.68/2.00	
3.68/2.00	WORST_CASE(Omega(n^1),?)
3.68/2.00	
3.68/2.00	
3.68/2.00	----------------------------------------
3.68/2.00	
3.68/2.00	(4)
3.68/2.00	BOUNDS(n^1, INF)
3.68/2.02	EOF