4.56/2.20	WORST_CASE(Omega(n^1), O(n^1))
4.56/2.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.56/2.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.56/2.21	
4.56/2.21	
4.56/2.21	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.56/2.21	
4.56/2.21	(0) CpxIntTrs
4.56/2.21	(1) Koat Proof [FINISHED, 201 ms]
4.56/2.21	(2) BOUNDS(1, n^1)
4.56/2.21	(3) Loat Proof [FINISHED, 531 ms]
4.56/2.21	(4) BOUNDS(n^1, INF)
4.56/2.21	
4.56/2.21	
4.56/2.21	----------------------------------------
4.56/2.21	
4.56/2.21	(0)
4.56/2.21	Obligation:
4.56/2.21	Complexity Int TRS consisting of the following rules:
4.56/2.21	start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F
4.56/2.21	start(A, B, C, D, E, F) -> Com_1(lbl101(A, 2, C, D, 1, F)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F
4.56/2.21	start(A, B, C, D, E, F) -> Com_1(lbl101(A, 2, C, D, -(1), F)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F
4.56/2.21	lbl101(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: E + A >= 0 && A >= 1 && A >= E && B >= A + 1 && B <= A + 1 && D >= A && D <= A
4.56/2.21	lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + B, C, D, 1 + E, F)) :|: A >= B && E + B >= 1 && A + 1 >= B && B >= 2 && B >= E + 1 && D >= A && D <= A
4.56/2.21	lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + B, C, D, E - 1, F)) :|: A >= B && E + B >= 1 && A + 1 >= B && B >= 2 && B >= E + 1 && D >= A && D <= A
4.56/2.21	start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, A, F, F)) :|: TRUE
4.56/2.21	
4.56/2.21	The start-symbols are:[start0_6]
4.56/2.21	
4.56/2.21	
4.56/2.21	----------------------------------------
4.56/2.21	
4.56/2.21	(1) Koat Proof (FINISHED)
4.56/2.21	YES(?, 4*ar_0 + 17)
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Initial complexity problem:
4.56/2.21	
4.56/2.21	1:	T:
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
4.56/2.21	
4.56/2.21		start location:	koat_start
4.56/2.21	
4.56/2.21		leaf cost:	0
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.56/2.21	
4.56/2.21	2:	T:
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
4.56/2.21	
4.56/2.21		start location:	koat_start
4.56/2.21	
4.56/2.21		leaf cost:	0
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	A polynomial rank function with
4.56/2.21	
4.56/2.21		Pol(start) = 1
4.56/2.21	
4.56/2.21		Pol(stop) = 0
4.56/2.21	
4.56/2.21		Pol(lbl101) = 1
4.56/2.21	
4.56/2.21		Pol(start0) = 1
4.56/2.21	
4.56/2.21		Pol(koat_start) = 1
4.56/2.21	
4.56/2.21	orients all transitions weakly and the transition
4.56/2.21	
4.56/2.21		lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21	strictly and produces the following problem:
4.56/2.21	
4.56/2.21	3:	T:
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: ?, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
4.56/2.21	
4.56/2.21		start location:	koat_start
4.56/2.21	
4.56/2.21		leaf cost:	0
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	A polynomial rank function with
4.56/2.21	
4.56/2.21		Pol(lbl101) = V_1 - V_2 + 1
4.56/2.21	
4.56/2.21	and size complexities
4.56/2.21	
4.56/2.21		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_1
4.56/2.21	
4.56/2.21		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_3
4.56/2.21	
4.56/2.21		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-4) = ar_4
4.56/2.21	
4.56/2.21		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-1) = ar_2
4.56/2.21	
4.56/2.21		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-4) = ar_5
4.56/2.21	
4.56/2.21		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-1) = ?
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-4) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-1) = ?
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-4) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\\ ar_4 + ar_1 >= 1 /\\ ar_0 + 1 >= ar_1 /\\ ar_1 >= 2 /\\ ar_1 >= ar_4 + 1 /\\ ar_3 = ar_0 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\\ ar_0 >= 1 /\\ ar_0 >= ar_4 /\\ ar_1 = ar_0 + 1 /\\ ar_3 = ar_0 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\\ ar_0 >= 1 /\\ ar_0 >= ar_4 /\\ ar_1 = ar_0 + 1 /\\ ar_3 = ar_0 ]", 0-1) = ?
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\\ ar_0 >= 1 /\\ ar_0 >= ar_4 /\\ ar_1 = ar_0 + 1 /\\ ar_3 = ar_0 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\\ ar_0 >= 1 /\\ ar_0 >= ar_4 /\\ ar_1 = ar_0 + 1 /\\ ar_3 = ar_0 ]", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\\ ar_0 >= 1 /\\ ar_0 >= ar_4 /\\ ar_1 = ar_0 + 1 /\\ ar_3 = ar_0 ]", 0-4) = ar_0 + 2
4.56/2.21	
4.56/2.21		S("lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\\ ar_0 >= 1 /\\ ar_0 >= ar_4 /\\ ar_1 = ar_0 + 1 /\\ ar_3 = ar_0 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-1) = 2
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-4) = 1
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-1) = 2
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-4) = 1
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-0) = ar_0
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-1) = ar_2
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-2) = ar_2
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-3) = ar_0
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-4) = ar_5
4.56/2.21	
4.56/2.21		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-5) = ar_5
4.56/2.21	
4.56/2.21	orients the transitions
4.56/2.21	
4.56/2.21		lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21		lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21	weakly and the transitions
4.56/2.21	
4.56/2.21		lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21		lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21	strictly and produces the following problem:
4.56/2.21	
4.56/2.21	4:	T:
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)             lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: 2*ar_0 + 6, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: 2*ar_0 + 6, Cost: 1)    lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ]
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 1)             start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))
4.56/2.21	
4.56/2.21			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
4.56/2.21	
4.56/2.21		start location:	koat_start
4.56/2.21	
4.56/2.21		leaf cost:	0
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Complexity upper bound 4*ar_0 + 17
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Time: 0.181 sec (SMT: 0.160 sec)
4.56/2.21	
4.56/2.21	
4.56/2.21	----------------------------------------
4.56/2.21	
4.56/2.21	(2)
4.56/2.21	BOUNDS(1, n^1)
4.56/2.21	
4.56/2.21	----------------------------------------
4.56/2.21	
4.56/2.21	(3) Loat Proof (FINISHED)
4.56/2.21	
4.56/2.21	
4.56/2.21	### Pre-processing the ITS problem ###
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Initial linear ITS problem
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	      0: start -> stop : [ 0>=A && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      1: start -> lbl101 : B'=2, E'=1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      2: start -> lbl101 : B'=2, E'=-1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      3: lbl101 -> stop : [ A+E>=0 && A>=1 && A>=E && B==1+A && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      4: lbl101 -> lbl101 : B'=1+B, E'=1+E, [ A>=B && E+B>=1 && 1+A>=B && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      5: lbl101 -> lbl101 : B'=1+B, E'=-1+E, [ A>=B && E+B>=1 && 1+A>=B && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      6: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Removed unreachable and leaf rules:
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	      1: start -> lbl101 : B'=2, E'=1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      2: start -> lbl101 : B'=2, E'=-1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      4: lbl101 -> lbl101 : B'=1+B, E'=1+E, [ A>=B && E+B>=1 && 1+A>=B && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      5: lbl101 -> lbl101 : B'=1+B, E'=-1+E, [ A>=B && E+B>=1 && 1+A>=B && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      6: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Simplified all rules, resulting in:
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	      1: start -> lbl101 : B'=2, E'=1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      2: start -> lbl101 : B'=2, E'=-1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      4: lbl101 -> lbl101 : B'=1+B, E'=1+E, [ A>=B && E+B>=1 && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      5: lbl101 -> lbl101 : B'=1+B, E'=-1+E, [ A>=B && E+B>=1 && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      6: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	### Simplification by acceleration and chaining ###
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Accelerating simple loops of location 1.
4.56/2.21	
4.56/2.21	   Accelerating the following rules:
4.56/2.21	
4.56/2.21	      4: lbl101 -> lbl101 : B'=1+B, E'=1+E, [ A>=B && E+B>=1 && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	      5: lbl101 -> lbl101 : B'=1+B, E'=-1+E, [ A>=B && E+B>=1 && B>=2 && B>=1+E && D==A ], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	   Accelerated rule 4 with metering function 1+A-B, yielding the new rule 7.
4.56/2.21	
4.56/2.21	   Accelerated rule 5 with metering function 1+A-B, yielding the new rule 8.
4.56/2.21	
4.56/2.21	   Removing the simple loops: 4 5.
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Accelerated all simple loops using metering functions (where possible):
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	      1: start -> lbl101 : B'=2, E'=1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      2: start -> lbl101 : B'=2, E'=-1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      7: lbl101 -> lbl101 : B'=1+A, E'=1+A+E-B, [ A>=B && E+B>=1 && B>=2 && B>=1+E && D==A ], cost: 1+A-B
4.56/2.21	
4.56/2.21	      8: lbl101 -> lbl101 : B'=1+A, E'=-1-A+E+B, [ A>=B && E+B>=1 && B>=2 && B>=1+E && D==A ], cost: 1+A-B
4.56/2.21	
4.56/2.21	      6: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Chained accelerated rules (with incoming rules):
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	      1: start -> lbl101 : B'=2, E'=1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      2: start -> lbl101 : B'=2, E'=-1, [ A>=1 && B==C && D==A && E==F ], cost: 1
4.56/2.21	
4.56/2.21	      9: start -> lbl101 : B'=1+A, E'=A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	     10: start -> lbl101 : B'=1+A, E'=-2+A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	     11: start -> lbl101 : B'=1+A, E'=2-A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	     12: start -> lbl101 : B'=1+A, E'=-A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	      6: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Removed unreachable locations (and leaf rules with constant cost):
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	      9: start -> lbl101 : B'=1+A, E'=A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	     10: start -> lbl101 : B'=1+A, E'=-2+A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	     11: start -> lbl101 : B'=1+A, E'=2-A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	     12: start -> lbl101 : B'=1+A, E'=-A, [ B==C && D==A && E==F && A>=2 ], cost: A
4.56/2.21	
4.56/2.21	      6: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Eliminated locations (on tree-shaped paths):
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	     13: start0 -> lbl101 : B'=1+A, D'=A, E'=A, [ A>=2 ], cost: 1+A
4.56/2.21	
4.56/2.21	     14: start0 -> lbl101 : B'=1+A, D'=A, E'=-2+A, [ A>=2 ], cost: 1+A
4.56/2.21	
4.56/2.21	     15: start0 -> lbl101 : B'=1+A, D'=A, E'=2-A, [ A>=2 ], cost: 1+A
4.56/2.21	
4.56/2.21	     16: start0 -> lbl101 : B'=1+A, D'=A, E'=-A, [ A>=2 ], cost: 1+A
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	### Computing asymptotic complexity ###
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Fully simplified ITS problem
4.56/2.21	
4.56/2.21	   Start location: start0
4.56/2.21	
4.56/2.21	     16: start0 -> lbl101 : B'=1+A, D'=A, E'=-A, [ A>=2 ], cost: 1+A
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Computing asymptotic complexity for rule 16
4.56/2.21	
4.56/2.21	   Solved the limit problem by the following transformations:
4.56/2.21	
4.56/2.21	      Created initial limit problem:
4.56/2.21	
4.56/2.21	      -1+A (+/+!), 1+A (+) [not solved]
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	      removing all constraints (solved by SMT)
4.56/2.21	
4.56/2.21	      resulting limit problem: [solved]
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	      applying transformation rule (C) using substitution {A==n}
4.56/2.21	
4.56/2.21	      resulting limit problem:
4.56/2.21	
4.56/2.21	      [solved]
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	   Solution:
4.56/2.21	
4.56/2.21	      A / n
4.56/2.21	
4.56/2.21	   Resulting cost 1+n has complexity: Poly(n^1)
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Found new complexity Poly(n^1).
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	Obtained the following overall complexity (w.r.t. the length of the input n):
4.56/2.21	
4.56/2.21	   Complexity:  Poly(n^1)
4.56/2.21	
4.56/2.21	   Cpx degree:  1
4.56/2.21	
4.56/2.21	   Solved cost: 1+n
4.56/2.21	
4.56/2.21	   Rule cost:   1+A
4.56/2.21	
4.56/2.21	   Rule guard:  [ A>=2 ]
4.56/2.21	
4.56/2.21	
4.56/2.21	
4.56/2.21	WORST_CASE(Omega(n^1),?)
4.56/2.21	
4.56/2.21	
4.56/2.21	----------------------------------------
4.56/2.21	
4.56/2.21	(4)
4.56/2.21	BOUNDS(n^1, INF)
4.56/2.22	EOF