6.65/3.02	WORST_CASE(Omega(n^1), O(n^1))
6.65/3.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.65/3.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.65/3.03	
6.65/3.03	
6.65/3.03	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
6.65/3.03	
6.65/3.03	(0) CpxIntTrs
6.65/3.03	(1) Koat Proof [FINISHED, 544 ms]
6.65/3.03	(2) BOUNDS(1, n^1)
6.65/3.03	(3) Loat Proof [FINISHED, 1301 ms]
6.65/3.03	(4) BOUNDS(n^1, INF)
6.65/3.03	
6.65/3.03	
6.65/3.03	----------------------------------------
6.65/3.03	
6.65/3.03	(0)
6.65/3.03	Obligation:
6.65/3.03	Complexity Int TRS consisting of the following rules:
6.65/3.03	evalfstart(A, B, C, D) -> Com_1(evalfentryin(A, B, C, D)) :|: TRUE
6.65/3.03	evalfentryin(A, B, C, D) -> Com_1(evalfbb5in(B, B, C, D)) :|: TRUE
6.65/3.03	evalfbb5in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: B >= 2
6.65/3.03	evalfbb5in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: 1 >= B
6.65/3.03	evalfbbin(A, B, C, D) -> Com_1(evalfbb2in(A, B, B - 1, A + B - 1)) :|: TRUE
6.65/3.03	evalfbb2in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: C >= D + 1
6.65/3.03	evalfbb2in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C, D)) :|: D >= C
6.65/3.03	evalfbb3in(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: 0 >= E + 1
6.65/3.03	evalfbb3in(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: E >= 1
6.65/3.03	evalfbb3in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: TRUE
6.65/3.03	evalfbb1in(A, B, C, D) -> Com_1(evalfbb2in(A, B, C, D - 1)) :|: TRUE
6.65/3.03	evalfbb4in(A, B, C, D) -> Com_1(evalfbb5in(D - C + 1, C - 1, C, D)) :|: TRUE
6.65/3.03	evalfreturnin(A, B, C, D) -> Com_1(evalfstop(A, B, C, D)) :|: TRUE
6.65/3.03	
6.65/3.03	The start-symbols are:[evalfstart_4]
6.65/3.03	
6.65/3.03	
6.65/3.03	----------------------------------------
6.65/3.03	
6.65/3.03	(1) Koat Proof (FINISHED)
6.65/3.03	YES(?, 32*ar_1 + 14)
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Initial complexity problem:
6.65/3.03	
6.65/3.03	1:	T:
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Repeatedly propagating knowledge in problem 1 produces the following problem:
6.65/3.03	
6.65/3.03	2:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	A polynomial rank function with
6.65/3.03	
6.65/3.03		Pol(evalfstart) = 2
6.65/3.03	
6.65/3.03		Pol(evalfentryin) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbb5in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbbin) = 2
6.65/3.03	
6.65/3.03		Pol(evalfreturnin) = 1
6.65/3.03	
6.65/3.03		Pol(evalfbb2in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbb4in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbb3in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbb1in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfstop) = 0
6.65/3.03	
6.65/3.03		Pol(koat_start) = 2
6.65/3.03	
6.65/3.03	orients all transitions weakly and the transitions
6.65/3.03	
6.65/3.03		evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03	strictly and produces the following problem:
6.65/3.03	
6.65/3.03	3:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	A polynomial rank function with
6.65/3.03	
6.65/3.03		Pol(evalfstart) = V_2 + 1
6.65/3.03	
6.65/3.03		Pol(evalfentryin) = V_2 + 1
6.65/3.03	
6.65/3.03		Pol(evalfbb5in) = V_2 + 1
6.65/3.03	
6.65/3.03		Pol(evalfbbin) = V_2 - 1
6.65/3.03	
6.65/3.03		Pol(evalfreturnin) = V_2
6.65/3.03	
6.65/3.03		Pol(evalfbb2in) = V_3
6.65/3.03	
6.65/3.03		Pol(evalfbb4in) = V_3
6.65/3.03	
6.65/3.03		Pol(evalfbb3in) = V_3
6.65/3.03	
6.65/3.03		Pol(evalfbb1in) = V_3
6.65/3.03	
6.65/3.03		Pol(evalfstop) = V_2
6.65/3.03	
6.65/3.03		Pol(koat_start) = V_2 + 1
6.65/3.03	
6.65/3.03	orients all transitions weakly and the transition
6.65/3.03	
6.65/3.03		evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03	strictly and produces the following problem:
6.65/3.03	
6.65/3.03	4:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)           evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)           evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)           evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)           evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Repeatedly propagating knowledge in problem 4 produces the following problem:
6.65/3.03	
6.65/3.03	5:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)           evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)           evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)    evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)           evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)           evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)           evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	A polynomial rank function with
6.65/3.03	
6.65/3.03		Pol(evalfbb4in) = 1
6.65/3.03	
6.65/3.03		Pol(evalfbb5in) = 0
6.65/3.03	
6.65/3.03		Pol(evalfbb3in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbb1in) = 2
6.65/3.03	
6.65/3.03		Pol(evalfbb2in) = 2
6.65/3.03	
6.65/3.03	and size complexities
6.65/3.03	
6.65/3.03		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
6.65/3.03	
6.65/3.03		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
6.65/3.03	
6.65/3.03		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
6.65/3.03	
6.65/3.03		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
6.65/3.03	
6.65/3.03		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]", 0-0) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]", 0-1) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]", 0-2) = ?
6.65/3.03	
6.65/3.03		S("evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]", 0-3) = ?
6.65/3.03	
6.65/3.03		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))", 0-0) = ar_1
6.65/3.03	
6.65/3.03		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.65/3.03	
6.65/3.03		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.65/3.03	
6.65/3.03		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.65/3.03	
6.65/3.03		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.65/3.03	
6.65/3.03		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.65/3.03	
6.65/3.03		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.65/3.03	
6.65/3.03		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.65/3.03	
6.65/3.03	orients the transitions
6.65/3.03	
6.65/3.03		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03		evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03	weakly and the transitions
6.65/3.03	
6.65/3.03		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03	strictly and produces the following problem:
6.65/3.03	
6.65/3.03	6:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)             evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)             evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)      evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)             evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)      evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1))
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)             evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Applied AI with 'oct' on problem 6 to obtain the following invariants:
6.65/3.03	
6.65/3.03	  For symbol evalfbb1in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0
6.65/3.03	
6.65/3.03	  For symbol evalfbb2in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0
6.65/3.03	
6.65/3.03	  For symbol evalfbb3in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0
6.65/3.03	
6.65/3.03	  For symbol evalfbb4in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0
6.65/3.03	
6.65/3.03	  For symbol evalfbbin: X_2 - 2 >= 0
6.65/3.03	
6.65/3.03	  For symbol evalfreturnin: -X_2 + 1 >= 0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	This yielded the following problem:
6.65/3.03	
6.65/3.03	7:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)             evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_1 + 1 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ?, Cost: 1)             evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)      evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1)) [ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)             evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)      evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)             evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)             evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	A polynomial rank function with
6.65/3.03	
6.65/3.03		Pol(koat_start) = 6*V_2
6.65/3.03	
6.65/3.03		Pol(evalfstart) = 6*V_2
6.65/3.03	
6.65/3.03		Pol(evalfreturnin) = 3*V_1 + 3*V_2
6.65/3.03	
6.65/3.03		Pol(evalfstop) = 3*V_1 + 3*V_2
6.65/3.03	
6.65/3.03		Pol(evalfbb4in) = 3*V_4
6.65/3.03	
6.65/3.03		Pol(evalfbb5in) = 3*V_1 + 3*V_2
6.65/3.03	
6.65/3.03		Pol(evalfbb1in) = 3*V_4 - 1
6.65/3.03	
6.65/3.03		Pol(evalfbb2in) = 3*V_4 + 1
6.65/3.03	
6.65/3.03		Pol(evalfbb3in) = 3*V_4
6.65/3.03	
6.65/3.03		Pol(evalfbbin) = 3*V_1 + 3*V_2 - 2
6.65/3.03	
6.65/3.03		Pol(evalfentryin) = 6*V_2
6.65/3.03	
6.65/3.03	orients all transitions weakly and the transitions
6.65/3.03	
6.65/3.03		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ e >= 1 ]
6.65/3.03	
6.65/3.03		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03		evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03	strictly and produces the following problem:
6.65/3.03	
6.65/3.03	8:	T:
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)             evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_1 + 1 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_3 - ar_2 + 1, ar_2 - 1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 6*ar_1, Cost: 1)        evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 6*ar_1, Cost: 1)        evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ e >= 1 ]
6.65/3.03	
6.65/3.03			(Comp: 6*ar_1, Cost: 1)        evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ -ar_1 + ar_3 + 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= e + 1 ]
6.65/3.03	
6.65/3.03			(Comp: 6*ar_1, Cost: 1)        evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_3 >= ar_2 ]
6.65/3.03	
6.65/3.03			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_1 + ar_2 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_2 >= ar_3 + 1 ]
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)      evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_1 - 1, ar_0 + ar_1 - 1)) [ ar_1 - 2 >= 0 ]
6.65/3.03	
6.65/3.03			(Comp: 2, Cost: 1)             evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_1 ]
6.65/3.03	
6.65/3.03			(Comp: ar_1 + 1, Cost: 1)      evalfbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 2 ]
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)             evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb5in(ar_1, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03			(Comp: 1, Cost: 1)             evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.65/3.03	
6.65/3.03		start location:	koat_start
6.65/3.03	
6.65/3.03		leaf cost:	0
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Complexity upper bound 32*ar_1 + 14
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Time: 0.494 sec (SMT: 0.414 sec)
6.65/3.03	
6.65/3.03	
6.65/3.03	----------------------------------------
6.65/3.03	
6.65/3.03	(2)
6.65/3.03	BOUNDS(1, n^1)
6.65/3.03	
6.65/3.03	----------------------------------------
6.65/3.03	
6.65/3.03	(3) Loat Proof (FINISHED)
6.65/3.03	
6.65/3.03	
6.65/3.03	### Pre-processing the ITS problem ###
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Initial linear ITS problem
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	      0: evalfstart -> evalfentryin : [], cost: 1
6.65/3.03	
6.65/3.03	      1: evalfentryin -> evalfbb5in : A'=B, [], cost: 1
6.65/3.03	
6.65/3.03	      2: evalfbb5in -> evalfbbin : [ B>=2 ], cost: 1
6.65/3.03	
6.65/3.03	      3: evalfbb5in -> evalfreturnin : [ 1>=B ], cost: 1
6.65/3.03	
6.65/3.03	      4: evalfbbin -> evalfbb2in : C'=-1+B, D'=-1+A+B, [], cost: 1
6.65/3.03	
6.65/3.03	      5: evalfbb2in -> evalfbb4in : [ C>=1+D ], cost: 1
6.65/3.03	
6.65/3.03	      6: evalfbb2in -> evalfbb3in : [ D>=C ], cost: 1
6.65/3.03	
6.65/3.03	      7: evalfbb3in -> evalfbb1in : [ 0>=1+free ], cost: 1
6.65/3.03	
6.65/3.03	      8: evalfbb3in -> evalfbb1in : [ free_1>=1 ], cost: 1
6.65/3.03	
6.65/3.03	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.65/3.03	
6.65/3.03	     10: evalfbb1in -> evalfbb2in : D'=-1+D, [], cost: 1
6.65/3.03	
6.65/3.03	     11: evalfbb4in -> evalfbb5in : A'=1-C+D, B'=-1+C, [], cost: 1
6.65/3.03	
6.65/3.03	     12: evalfreturnin -> evalfstop : [], cost: 1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Removed unreachable and leaf rules:
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	      0: evalfstart -> evalfentryin : [], cost: 1
6.65/3.03	
6.65/3.03	      1: evalfentryin -> evalfbb5in : A'=B, [], cost: 1
6.65/3.03	
6.65/3.03	      2: evalfbb5in -> evalfbbin : [ B>=2 ], cost: 1
6.65/3.03	
6.65/3.03	      4: evalfbbin -> evalfbb2in : C'=-1+B, D'=-1+A+B, [], cost: 1
6.65/3.03	
6.65/3.03	      5: evalfbb2in -> evalfbb4in : [ C>=1+D ], cost: 1
6.65/3.03	
6.65/3.03	      6: evalfbb2in -> evalfbb3in : [ D>=C ], cost: 1
6.65/3.03	
6.65/3.03	      7: evalfbb3in -> evalfbb1in : [ 0>=1+free ], cost: 1
6.65/3.03	
6.65/3.03	      8: evalfbb3in -> evalfbb1in : [ free_1>=1 ], cost: 1
6.65/3.03	
6.65/3.03	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.65/3.03	
6.65/3.03	     10: evalfbb1in -> evalfbb2in : D'=-1+D, [], cost: 1
6.65/3.03	
6.65/3.03	     11: evalfbb4in -> evalfbb5in : A'=1-C+D, B'=-1+C, [], cost: 1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Simplified all rules, resulting in:
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	      0: evalfstart -> evalfentryin : [], cost: 1
6.65/3.03	
6.65/3.03	      1: evalfentryin -> evalfbb5in : A'=B, [], cost: 1
6.65/3.03	
6.65/3.03	      2: evalfbb5in -> evalfbbin : [ B>=2 ], cost: 1
6.65/3.03	
6.65/3.03	      4: evalfbbin -> evalfbb2in : C'=-1+B, D'=-1+A+B, [], cost: 1
6.65/3.03	
6.65/3.03	      5: evalfbb2in -> evalfbb4in : [ C>=1+D ], cost: 1
6.65/3.03	
6.65/3.03	      6: evalfbb2in -> evalfbb3in : [ D>=C ], cost: 1
6.65/3.03	
6.65/3.03	      8: evalfbb3in -> evalfbb1in : [], cost: 1
6.65/3.03	
6.65/3.03	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.65/3.03	
6.65/3.03	     10: evalfbb1in -> evalfbb2in : D'=-1+D, [], cost: 1
6.65/3.03	
6.65/3.03	     11: evalfbb4in -> evalfbb5in : A'=1-C+D, B'=-1+C, [], cost: 1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	### Simplification by acceleration and chaining ###
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Eliminated locations (on linear paths):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     14: evalfbb5in -> evalfbb2in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2
6.65/3.03	
6.65/3.03	      5: evalfbb2in -> evalfbb4in : [ C>=1+D ], cost: 1
6.65/3.03	
6.65/3.03	      6: evalfbb2in -> evalfbb3in : [ D>=C ], cost: 1
6.65/3.03	
6.65/3.03	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.65/3.03	
6.65/3.03	     15: evalfbb3in -> evalfbb2in : D'=-1+D, [], cost: 2
6.65/3.03	
6.65/3.03	     11: evalfbb4in -> evalfbb5in : A'=1-C+D, B'=-1+C, [], cost: 1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Eliminated locations (on tree-shaped paths):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     14: evalfbb5in -> evalfbb2in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2
6.65/3.03	
6.65/3.03	     17: evalfbb2in -> evalfbb2in : D'=-1+D, [ D>=C ], cost: 3
6.65/3.03	
6.65/3.03	     18: evalfbb2in -> evalfbb5in : A'=1-C+D, B'=-1+C, [ C>=1+D ], cost: 2
6.65/3.03	
6.65/3.03	     19: evalfbb2in -> evalfbb5in : A'=1-C+D, B'=-1+C, [ D>=C ], cost: 3
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Accelerating simple loops of location 4.
6.65/3.03	
6.65/3.03	   Accelerating the following rules:
6.65/3.03	
6.65/3.03	     17: evalfbb2in -> evalfbb2in : D'=-1+D, [ D>=C ], cost: 3
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Accelerated rule 17 with metering function 1-C+D, yielding the new rule 20.
6.65/3.03	
6.65/3.03	   Removing the simple loops: 17.
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Accelerated all simple loops using metering functions (where possible):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     14: evalfbb5in -> evalfbb2in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2
6.65/3.03	
6.65/3.03	     18: evalfbb2in -> evalfbb5in : A'=1-C+D, B'=-1+C, [ C>=1+D ], cost: 2
6.65/3.03	
6.65/3.03	     19: evalfbb2in -> evalfbb5in : A'=1-C+D, B'=-1+C, [ D>=C ], cost: 3
6.65/3.03	
6.65/3.03	     20: evalfbb2in -> evalfbb2in : D'=-1+C, [ D>=C ], cost: 3-3*C+3*D
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Chained accelerated rules (with incoming rules):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     14: evalfbb5in -> evalfbb2in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2
6.65/3.03	
6.65/3.03	     21: evalfbb5in -> evalfbb2in : C'=-1+B, D'=-2+B, [ B>=2 && -1+A+B>=-1+B ], cost: 5+3*A
6.65/3.03	
6.65/3.03	     18: evalfbb2in -> evalfbb5in : A'=1-C+D, B'=-1+C, [ C>=1+D ], cost: 2
6.65/3.03	
6.65/3.03	     19: evalfbb2in -> evalfbb5in : A'=1-C+D, B'=-1+C, [ D>=C ], cost: 3
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Eliminated locations (on tree-shaped paths):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     22: evalfbb5in -> evalfbb5in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+B>=A+B ], cost: 4
6.65/3.03	
6.65/3.03	     23: evalfbb5in -> evalfbb5in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+A+B>=-1+B ], cost: 5
6.65/3.03	
6.65/3.03	     24: evalfbb5in -> evalfbb5in : A'=0, B'=-2+B, C'=-1+B, D'=-2+B, [ B>=2 && -1+A+B>=-1+B ], cost: 7+3*A
6.65/3.03	
6.65/3.03	     25: evalfbb5in -> [11] : [ B>=2 && -1+A+B>=-1+B ], cost: 5+3*A
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Accelerating simple loops of location 2.
6.65/3.03	
6.65/3.03	   Accelerating the following rules:
6.65/3.03	
6.65/3.03	     22: evalfbb5in -> evalfbb5in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+B>=A+B ], cost: 4
6.65/3.03	
6.65/3.03	     23: evalfbb5in -> evalfbb5in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+A+B>=-1+B ], cost: 5
6.65/3.03	
6.65/3.03	     24: evalfbb5in -> evalfbb5in : A'=0, B'=-2+B, C'=-1+B, D'=-2+B, [ B>=2 && -1+A+B>=-1+B ], cost: 7+3*A
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Accelerated rule 22 with NONTERM (after adding A>=B), yielding the new rule 26.
6.65/3.03	
6.65/3.03	   Accelerated rule 22 with backward acceleration, yielding the new rule 27.
6.65/3.03	
6.65/3.03	   Accelerated rule 23 with metering function meter (where 2*meter==-1+B), yielding the new rule 28.
6.65/3.03	
6.65/3.03	   Accelerated rule 24 with metering function meter_1 (where 2*meter_1==-1+B), yielding the new rule 29.
6.65/3.03	
6.65/3.03	      During metering: Instantiating temporary variables by {meter==1}
6.65/3.03	
6.65/3.03	      During metering: Instantiating temporary variables by {meter_1==1}
6.65/3.03	
6.65/3.03	   Removing the simple loops: 22 23 24.
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Accelerated all simple loops using metering functions (where possible):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     25: evalfbb5in -> [11] : [ B>=2 && -1+A+B>=-1+B ], cost: 5+3*A
6.65/3.03	
6.65/3.03	     26: evalfbb5in -> [12] : [ B>=2 && -1+B>=A+B && A>=B ], cost: INF
6.65/3.03	
6.65/3.03	     27: evalfbb5in -> evalfbb5in : A'=k+A, B'=-2*k+B, C'=1-2*k+B, D'=-k+A+B, [ B>=2 && -1+B>=A+B && k>0 && 2-2*k+B>=2 && 1-2*k+B>=1-k+A+B ], cost: 4*k
6.65/3.03	
6.65/3.03	     28: evalfbb5in -> evalfbb5in : A'=A+meter, B'=-2*meter+B, C'=1-2*meter+B, D'=A-meter+B, [ B>=2 && -1+A+B>=-1+B && 2*meter==-1+B && meter>=1 ], cost: 5*meter
6.65/3.03	
6.65/3.03	     29: evalfbb5in -> evalfbb5in : A'=0, B'=-2*meter_1+B, C'=1-2*meter_1+B, D'=-2*meter_1+B, [ B>=2 && -1+A+B>=-1+B && 2*meter_1==-1+B && meter_1>=1 ], cost: 7*meter_1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Chained accelerated rules (with incoming rules):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     30: evalfstart -> evalfbb5in : A'=meter+B, B'=-2*meter+B, C'=1-2*meter+B, D'=-meter+2*B, [ B>=2 && 2*meter==-1+B && meter>=1 ], cost: 2+5*meter
6.65/3.03	
6.65/3.03	     31: evalfstart -> evalfbb5in : A'=0, B'=-2*meter_1+B, C'=1-2*meter_1+B, D'=-2*meter_1+B, [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+7*meter_1
6.65/3.03	
6.65/3.03	     25: evalfbb5in -> [11] : [ B>=2 && -1+A+B>=-1+B ], cost: 5+3*A
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Removed unreachable locations (and leaf rules with constant cost):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     13: evalfstart -> evalfbb5in : A'=B, [], cost: 2
6.65/3.03	
6.65/3.03	     30: evalfstart -> evalfbb5in : A'=meter+B, B'=-2*meter+B, C'=1-2*meter+B, D'=-meter+2*B, [ B>=2 && 2*meter==-1+B && meter>=1 ], cost: 2+5*meter
6.65/3.03	
6.65/3.03	     31: evalfstart -> evalfbb5in : A'=0, B'=-2*meter_1+B, C'=1-2*meter_1+B, D'=-2*meter_1+B, [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+7*meter_1
6.65/3.03	
6.65/3.03	     25: evalfbb5in -> [11] : [ B>=2 && -1+A+B>=-1+B ], cost: 5+3*A
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Eliminated locations (on tree-shaped paths):
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     32: evalfstart -> [11] : A'=B, [ B>=2 ], cost: 7+3*B
6.65/3.03	
6.65/3.03	     33: evalfstart -> [13] : [ B>=2 && 2*meter==-1+B && meter>=1 ], cost: 2+5*meter
6.65/3.03	
6.65/3.03	     34: evalfstart -> [13] : [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+7*meter_1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	### Computing asymptotic complexity ###
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Fully simplified ITS problem
6.65/3.03	
6.65/3.03	   Start location: evalfstart
6.65/3.03	
6.65/3.03	     32: evalfstart -> [11] : A'=B, [ B>=2 ], cost: 7+3*B
6.65/3.03	
6.65/3.03	     33: evalfstart -> [13] : [ B>=2 && 2*meter==-1+B && meter>=1 ], cost: 2+5*meter
6.65/3.03	
6.65/3.03	     34: evalfstart -> [13] : [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+7*meter_1
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Computing asymptotic complexity for rule 32
6.65/3.03	
6.65/3.03	   Solved the limit problem by the following transformations:
6.65/3.03	
6.65/3.03	      Created initial limit problem:
6.65/3.03	
6.65/3.03	      7+3*B (+), -1+B (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      removing all constraints (solved by SMT)
6.65/3.03	
6.65/3.03	      resulting limit problem: [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {B==n}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Solution:
6.65/3.03	
6.65/3.03	      B / n
6.65/3.03	
6.65/3.03	   Resulting cost 7+3*n has complexity: Poly(n^1)
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Found new complexity Poly(n^1).
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Computing asymptotic complexity for rule 33
6.65/3.03	
6.65/3.03	   Solved the limit problem by the following transformations:
6.65/3.03	
6.65/3.03	      Created initial limit problem:
6.65/3.03	
6.65/3.03	      2+2*meter-B (+/+!), -1+B (+/+!), -2*meter+B (+/+!), 2+5*meter (+) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {B==1+2*meter}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      1 (+/+!), 2*meter (+/+!), 2+5*meter (+) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (B), deleting 1 (+/+!)
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      2*meter (+/+!), 2+5*meter (+) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      removing all constraints (solved by SMT)
6.65/3.03	
6.65/3.03	      resulting limit problem: [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {meter==n}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Solved the limit problem by the following transformations:
6.65/3.03	
6.65/3.03	      Created initial limit problem:
6.65/3.03	
6.65/3.03	      2+2*meter-B (+/+!), -1+B (+/+!), -2*meter+B (+/+!), 2+5*meter (+) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {B==1+2*meter}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      1 (+/+!), 2*meter (+/+!), 2+5*meter (+) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (B), deleting 1 (+/+!)
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      2*meter (+/+!), 2+5*meter (+) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      removing all constraints (solved by SMT)
6.65/3.03	
6.65/3.03	      resulting limit problem: [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {meter==n}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Solution:
6.65/3.03	
6.65/3.03	      meter / n
6.65/3.03	
6.65/3.03	      B / 1+2*n
6.65/3.03	
6.65/3.03	   Resulting cost 2+5*n has complexity: Poly(n^1)
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Computing asymptotic complexity for rule 34
6.65/3.03	
6.65/3.03	   Solved the limit problem by the following transformations:
6.65/3.03	
6.65/3.03	      Created initial limit problem:
6.65/3.03	
6.65/3.03	      -2*meter_1+B (+/+!), 2+2*meter_1-B (+/+!), 2+7*meter_1 (+), -1+B (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {B==1+2*meter_1}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      1 (+/+!), 2+7*meter_1 (+), 2*meter_1 (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (B), deleting 1 (+/+!)
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      2+7*meter_1 (+), 2*meter_1 (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      removing all constraints (solved by SMT)
6.65/3.03	
6.65/3.03	      resulting limit problem: [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {meter_1==n}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Solved the limit problem by the following transformations:
6.65/3.03	
6.65/3.03	      Created initial limit problem:
6.65/3.03	
6.65/3.03	      -2*meter_1+B (+/+!), 2+2*meter_1-B (+/+!), 2+7*meter_1 (+), -1+B (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {B==1+2*meter_1}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      1 (+/+!), 2+7*meter_1 (+), 2*meter_1 (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (B), deleting 1 (+/+!)
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      2+7*meter_1 (+), 2*meter_1 (+/+!) [not solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      removing all constraints (solved by SMT)
6.65/3.03	
6.65/3.03	      resulting limit problem: [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	      applying transformation rule (C) using substitution {meter_1==n}
6.65/3.03	
6.65/3.03	      resulting limit problem:
6.65/3.03	
6.65/3.03	      [solved]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	   Solution:
6.65/3.03	
6.65/3.03	      meter_1 / n
6.65/3.03	
6.65/3.03	      B / 1+2*n
6.65/3.03	
6.65/3.03	   Resulting cost 2+7*n has complexity: Poly(n^1)
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	Obtained the following overall complexity (w.r.t. the length of the input n):
6.65/3.03	
6.65/3.03	   Complexity:  Poly(n^1)
6.65/3.03	
6.65/3.03	   Cpx degree:  1
6.65/3.03	
6.65/3.03	   Solved cost: 7+3*n
6.65/3.03	
6.65/3.03	   Rule cost:   7+3*B
6.65/3.03	
6.65/3.03	   Rule guard:  [ B>=2 ]
6.65/3.03	
6.65/3.03	
6.65/3.03	
6.65/3.03	WORST_CASE(Omega(n^1),?)
6.65/3.03	
6.65/3.03	
6.65/3.03	----------------------------------------
6.65/3.03	
6.65/3.03	(4)
6.65/3.03	BOUNDS(n^1, INF)
6.65/3.05	EOF