5.97/2.65	WORST_CASE(Omega(n^1), O(n^1))
5.97/2.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.97/2.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.97/2.66	
5.97/2.66	
5.97/2.66	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.97/2.66	
5.97/2.66	(0) CpxIntTrs
5.97/2.66	(1) Koat Proof [FINISHED, 925 ms]
5.97/2.66	(2) BOUNDS(1, n^1)
5.97/2.66	(3) Loat Proof [FINISHED, 724 ms]
5.97/2.66	(4) BOUNDS(n^1, INF)
5.97/2.66	
5.97/2.66	
5.97/2.66	----------------------------------------
5.97/2.66	
5.97/2.66	(0)
5.97/2.66	Obligation:
5.97/2.66	Complexity Int TRS consisting of the following rules:
5.97/2.66	eval0(A, B, C, D) -> Com_1(eval1(B, B, 1, D)) :|: TRUE
5.97/2.66	eval1(A, B, C, D) -> Com_1(end(A, B, C, D)) :|: A >= 101
5.97/2.66	eval1(A, B, C, D) -> Com_1(eval3(A, B, C, D)) :|: 100 >= A
5.97/2.66	eval3(A, B, C, D) -> Com_1(eval3(A + 11, B, C + 1, D)) :|: 100 >= A
5.97/2.66	eval3(A, B, C, D) -> Com_1(eval5(A, B, C, D)) :|: A >= 101
5.97/2.66	eval5(A, B, C, D) -> Com_1(eval7(A - 10, B, C - 1, D)) :|: C >= 2
5.97/2.66	eval7(A, B, C, D) -> Com_1(eval5(A, B, C, A - 10)) :|: A >= 101 && C >= 1 && C <= 1
5.97/2.66	eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: 100 >= A
5.97/2.66	eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: 2 >= C
5.97/2.66	eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: C >= 0
5.97/2.66	eval9(A, B, C, D) -> Com_1(eval11(A - 10, B, C - 1, D)) :|: A >= 101
5.97/2.66	eval9(A, B, C, D) -> Com_1(eval11(A, B, C, D)) :|: 100 >= A
5.97/2.66	eval11(A, B, C, D) -> Com_1(eval5(A + 11, B, C + 1, D)) :|: TRUE
5.97/2.66	
5.97/2.66	The start-symbols are:[eval0_4]
5.97/2.66	
5.97/2.66	
5.97/2.66	----------------------------------------
5.97/2.66	
5.97/2.66	(1) Koat Proof (FINISHED)
5.97/2.66	YES(?, 84482*ar_1 + 8492880)
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Initial complexity problem:
5.97/2.66	
5.97/2.66	1:	T:
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval0(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval1(ar_1, ar_1, 1, ar_3))
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval1(ar_0, ar_1, ar_2, ar_3) -> Com_1(end(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval1(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval3(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1, ar_3)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval5(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval5(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval5(ar_0, ar_1, ar_2, ar_0 - 10)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval9(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval9(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval9(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1, ar_3)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval11(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval11(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1, ar_3))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(eval0(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2].
5.97/2.66	
5.97/2.66	We thus obtain the following problem:
5.97/2.66	
5.97/2.66	2:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.97/2.66	
5.97/2.66	3:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	A polynomial rank function with
5.97/2.66	
5.97/2.66		Pol(koat_start) = 1
5.97/2.66	
5.97/2.66		Pol(eval0) = 1
5.97/2.66	
5.97/2.66		Pol(eval11) = 0
5.97/2.66	
5.97/2.66		Pol(eval5) = 0
5.97/2.66	
5.97/2.66		Pol(eval9) = 0
5.97/2.66	
5.97/2.66		Pol(eval7) = 0
5.97/2.66	
5.97/2.66		Pol(eval3) = 1
5.97/2.66	
5.97/2.66		Pol(eval1) = 1
5.97/2.66	
5.97/2.66		Pol(end) = 0
5.97/2.66	
5.97/2.66	orients all transitions weakly and the transition
5.97/2.66	
5.97/2.66		eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66	strictly and produces the following problem:
5.97/2.66	
5.97/2.66	4:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)    eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	A polynomial rank function with
5.97/2.66	
5.97/2.66		Pol(eval3) = -V_1 + 101
5.97/2.66	
5.97/2.66	and size complexities
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]", 0-0) = ar_1 + 111
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-0) = ar_1 + 111
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))", 0-2) = ?
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.97/2.66	
5.97/2.66	orients the transitions
5.97/2.66	
5.97/2.66		eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66	weakly and the transition
5.97/2.66	
5.97/2.66		eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66	strictly and produces the following problem:
5.97/2.66	
5.97/2.66	5:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	A polynomial rank function with
5.97/2.66	
5.97/2.66		Pol(eval9) = V_3
5.97/2.66	
5.97/2.66		Pol(eval11) = V_3
5.97/2.66	
5.97/2.66		Pol(eval7) = V_3
5.97/2.66	
5.97/2.66		Pol(eval5) = V_3 - 1
5.97/2.66	
5.97/2.66	and size complexities
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]", 0-0) = ar_1 + 111
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]", 0-2) = ar_1 + 102
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-0) = ar_1 + 111
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]", 0-2) = ar_1 + 102
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))", 0-2) = ?
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.97/2.66	
5.97/2.66	orients the transitions
5.97/2.66	
5.97/2.66		eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66		eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66		eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66		eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))
5.97/2.66	
5.97/2.66	weakly and the transition
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66	strictly and produces the following problem:
5.97/2.66	
5.97/2.66	6:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1))
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Applied AI with 'oct' on problem 6 to obtain the following invariants:
5.97/2.66	
5.97/2.66	  For symbol eval1: -X_3 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0
5.97/2.66	
5.97/2.66	  For symbol eval11: X_3 >= 0 /\ -X_2 + X_3 + 100 >= 0 /\ X_1 + X_3 - 91 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0
5.97/2.66	
5.97/2.66	  For symbol eval3: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 >= 0
5.97/2.66	
5.97/2.66	  For symbol eval5: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 102 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 101 >= 0
5.97/2.66	
5.97/2.66	  For symbol eval7: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0
5.97/2.66	
5.97/2.66	  For symbol eval9: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	This yielded the following problem:
5.97/2.66	
5.97/2.66	7:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)    eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)             eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)             eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	A polynomial rank function with
5.97/2.66	
5.97/2.66		Pol(eval0) = -20*V_2 + 2010
5.97/2.66	
5.97/2.66		Pol(eval1) = -20*V_2 + 2010
5.97/2.66	
5.97/2.66		Pol(end) = -20*V_2
5.97/2.66	
5.97/2.66		Pol(eval3) = -20*V_1 + 220*V_3 + 1790
5.97/2.66	
5.97/2.66		Pol(eval5) = -22*V_1 + 220*V_3 + 1992
5.97/2.66	
5.97/2.66		Pol(eval7) = -22*V_1 + 220*V_3 + 1992
5.97/2.66	
5.97/2.66		Pol(eval9) = -22*V_1 + 220*V_3 + 1981
5.97/2.66	
5.97/2.66		Pol(eval11) = -22*V_1 + 220*V_3 + 1970
5.97/2.66	
5.97/2.66		Pol(koat_start) = -20*V_2 + 2010
5.97/2.66	
5.97/2.66	orients all transitions weakly and the transitions
5.97/2.66	
5.97/2.66		eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66	strictly and produces the following problem:
5.97/2.66	
5.97/2.66	8:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)        eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)        eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)                 koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	By chaining the transition eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 ] with all transitions in problem 8, the following new transition is obtained:
5.97/2.66	
5.97/2.66		eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 ]
5.97/2.66	
5.97/2.66	We thus obtain the following problem:
5.97/2.66	
5.97/2.66	9:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                 eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)        eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)        eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)                 koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	By chaining the transition eval3(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 ] with all transitions in problem 9, the following new transition is obtained:
5.97/2.66	
5.97/2.66		eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66	We thus obtain the following problem:
5.97/2.66	
5.97/2.66	10:	T:
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                 eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                 eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)        eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)        eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)                 koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	By chaining the transition eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ] with all transitions in problem 10, the following new transition is obtained:
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66	We thus obtain the following problem:
5.97/2.66	
5.97/2.66	11:	T:
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 2)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                 eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                 eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                 eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)        eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)        eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: ?, Cost: 1)                 eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)                 koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	A polynomial rank function with
5.97/2.66	
5.97/2.66		Pol(eval9) = 4*V_1 - 9
5.97/2.66	
5.97/2.66		Pol(eval11) = 4*V_1 + 22
5.97/2.66	
5.97/2.66		Pol(eval7) = 4*V_1
5.97/2.66	
5.97/2.66		Pol(eval5) = 4*V_1 - 31
5.97/2.66	
5.97/2.66	and size complexities
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\\ -ar_1 + ar_2 + 100 >= 0 /\\ ar_0 + ar_2 - 91 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\\ -ar_1 + ar_2 + 100 >= 0 /\\ ar_0 + ar_2 - 91 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\\ -ar_1 + ar_2 + 100 >= 0 /\\ ar_0 + ar_2 - 91 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 100 >= ar_0 ]", 0-0) = 100
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_0 >= 101 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_0 >= 101 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_2 >= 0 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_2 >= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_2 >= 0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 2 >= ar_2 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 2 >= ar_2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 2 >= ar_2 ]", 0-2) = 2
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ ar_0 >= 101 /\\ ar_2 = 1 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 101 >= 0 /\\ ar_2 >= 2 ]", 0-0) = ?
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 101 >= 0 /\\ ar_2 >= 2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 101 >= 0 /\\ ar_2 >= 2 ]", 0-2) = ?
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ 100 >= ar_0 ]", 0-0) = ar_1 + 222
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ 100 >= ar_0 ]", 0-2) = ar_1 + 103
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 101 ]", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 101 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 101 ]", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-0) = ar_1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))", 0-2) = 1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 100 >= ar_0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 ]", 0-0) = ar_1 + 111
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 100 >= ar_0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ 100 >= ar_0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 ]", 0-2) = 2
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 101 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 101 >= 0 /\\ ar_2 >= 2 ]", 0-0) = ar_1 + 222
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 101 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 101 >= 0 /\\ ar_2 >= 2 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 101 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 - 101 >= 0 /\\ ar_2 >= 2 ]", 0-2) = ar_1 + 105
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 100 >= ar_0 ]", 0-0) = 100
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 100 >= ar_0 ]", 0-1) = ar_1
5.97/2.66	
5.97/2.66		S("eval7(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 + 99 >= 0 /\\ ar_0 + ar_2 - 92 >= 0 /\\ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 9 >= 0 /\\ ar_0 - 91 >= 0 /\\ 100 >= ar_0 ]", 0-2) = ?
5.97/2.66	
5.97/2.66	orients the transitions
5.97/2.66	
5.97/2.66		eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66		eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66		eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66	weakly and the transitions
5.97/2.66	
5.97/2.66		eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66		eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66		eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66		eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66	strictly and produces the following problem:
5.97/2.66	
5.97/2.66	12:	T:
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 2)          eval7(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                       eval3(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 101 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 2)                       eval1(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 100 >= ar_0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                       eval0(ar_0, ar_1, ar_2) -> Com_1(eval1(ar_1, ar_1, 1))
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 1)                       eval1(ar_0, ar_1, ar_2) -> Com_1(end(ar_0, ar_1, ar_2)) [ -ar_2 + 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 101, Cost: 1)              eval3(ar_0, ar_1, ar_2) -> Com_1(eval3(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 16884*ar_1 + 1697328, Cost: 1)    eval5(ar_0, ar_1, ar_2) -> Com_1(eval7(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 - 101 >= 0 /\ ar_2 >= 2 ]
5.97/2.66	
5.97/2.66			(Comp: ar_1 + 103, Cost: 1)              eval7(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 /\ ar_2 = 1 ]
5.97/2.66	
5.97/2.66			(Comp: 16884*ar_1 + 1697328, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 2 >= ar_2 ]
5.97/2.66	
5.97/2.66			(Comp: 16884*ar_1 + 1697328, Cost: 1)    eval7(ar_0, ar_1, ar_2) -> Com_1(eval9(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_2 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 16884*ar_1 + 1697328, Cost: 1)    eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ ar_0 >= 101 ]
5.97/2.66	
5.97/2.66			(Comp: 20*ar_1 + 2010, Cost: 1)          eval9(ar_0, ar_1, ar_2) -> Com_1(eval11(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ -ar_1 + ar_2 + 99 >= 0 /\ ar_0 + ar_2 - 92 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 /\ 100 >= ar_0 ]
5.97/2.66	
5.97/2.66			(Comp: 16884*ar_1 + 1697328, Cost: 1)    eval11(ar_0, ar_1, ar_2) -> Com_1(eval5(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 >= 0 /\ -ar_1 + ar_2 + 100 >= 0 /\ ar_0 + ar_2 - 91 >= 0 /\ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 9 >= 0 /\ ar_0 - 91 >= 0 ]
5.97/2.66	
5.97/2.66			(Comp: 1, Cost: 0)                       koat_start(ar_0, ar_1, ar_2) -> Com_1(eval0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.97/2.66	
5.97/2.66		start location:	koat_start
5.97/2.66	
5.97/2.66		leaf cost:	0
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Complexity upper bound 84482*ar_1 + 8492880
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Time: 0.956 sec (SMT: 0.800 sec)
5.97/2.66	
5.97/2.66	
5.97/2.66	----------------------------------------
5.97/2.66	
5.97/2.66	(2)
5.97/2.66	BOUNDS(1, n^1)
5.97/2.66	
5.97/2.66	----------------------------------------
5.97/2.66	
5.97/2.66	(3) Loat Proof (FINISHED)
5.97/2.66	
5.97/2.66	
5.97/2.66	### Pre-processing the ITS problem ###
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Initial linear ITS problem
5.97/2.66	
5.97/2.66	   Start location: eval0
5.97/2.66	
5.97/2.66	      0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1
5.97/2.66	
5.97/2.66	      1: eval1 -> end : [ A>=101 ], cost: 1
5.97/2.66	
5.97/2.66	      2: eval1 -> eval3 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      3: eval3 -> eval3 : A'=11+A, C'=1+C, [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.66	
5.97/2.66	      5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1
5.97/2.66	
5.97/2.66	      6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1
5.97/2.66	
5.97/2.66	      7: eval7 -> eval9 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      8: eval7 -> eval9 : [ 2>=C ], cost: 1
5.97/2.66	
5.97/2.66	      9: eval7 -> eval9 : [ C>=0 ], cost: 1
5.97/2.66	
5.97/2.66	     10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1
5.97/2.66	
5.97/2.66	     11: eval9 -> eval11 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	     12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Removed unreachable and leaf rules:
5.97/2.66	
5.97/2.66	   Start location: eval0
5.97/2.66	
5.97/2.66	      0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1
5.97/2.66	
5.97/2.66	      2: eval1 -> eval3 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      3: eval3 -> eval3 : A'=11+A, C'=1+C, [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.66	
5.97/2.66	      5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1
5.97/2.66	
5.97/2.66	      6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1
5.97/2.66	
5.97/2.66	      7: eval7 -> eval9 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      8: eval7 -> eval9 : [ 2>=C ], cost: 1
5.97/2.66	
5.97/2.66	      9: eval7 -> eval9 : [ C>=0 ], cost: 1
5.97/2.66	
5.97/2.66	     10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1
5.97/2.66	
5.97/2.66	     11: eval9 -> eval11 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	     12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	### Simplification by acceleration and chaining ###
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Accelerating simple loops of location 2.
5.97/2.66	
5.97/2.66	   Accelerating the following rules:
5.97/2.66	
5.97/2.66	      3: eval3 -> eval3 : A'=11+A, C'=1+C, [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	   Accelerated rule 3 with metering function meter (where 11*meter==100-A), yielding the new rule 13.
5.97/2.66	
5.97/2.66	   Removing the simple loops: 3.
5.97/2.66	
5.97/2.66	
5.97/2.66	
5.97/2.66	Accelerated all simple loops using metering functions (where possible):
5.97/2.66	
5.97/2.66	   Start location: eval0
5.97/2.66	
5.97/2.66	      0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1
5.97/2.66	
5.97/2.66	      2: eval1 -> eval3 : [ 100>=A ], cost: 1
5.97/2.66	
5.97/2.66	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.66	
5.97/2.66	     13: eval3 -> eval3 : A'=11*meter+A, C'=meter+C, [ 100>=A && 11*meter==100-A && meter>=1 ], cost: meter
5.97/2.67	
5.97/2.67	      5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1
5.97/2.67	
5.97/2.67	      6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1
5.97/2.67	
5.97/2.67	      7: eval7 -> eval9 : [ 100>=A ], cost: 1
5.97/2.67	
5.97/2.67	      8: eval7 -> eval9 : [ 2>=C ], cost: 1
5.97/2.67	
5.97/2.67	      9: eval7 -> eval9 : [ C>=0 ], cost: 1
5.97/2.67	
5.97/2.67	     10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1
5.97/2.67	
5.97/2.67	     11: eval9 -> eval11 : [ 100>=A ], cost: 1
5.97/2.67	
5.97/2.67	     12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Chained accelerated rules (with incoming rules):
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	      0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1
5.97/2.67	
5.97/2.67	      2: eval1 -> eval3 : [ 100>=A ], cost: 1
5.97/2.67	
5.97/2.67	     14: eval1 -> eval3 : A'=11*meter+A, C'=meter+C, [ 100>=A && 11*meter==100-A && meter>=1 ], cost: 1+meter
5.97/2.67	
5.97/2.67	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.67	
5.97/2.67	      5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1
5.97/2.67	
5.97/2.67	      6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1
5.97/2.67	
5.97/2.67	      7: eval7 -> eval9 : [ 100>=A ], cost: 1
5.97/2.67	
5.97/2.67	      8: eval7 -> eval9 : [ 2>=C ], cost: 1
5.97/2.67	
5.97/2.67	      9: eval7 -> eval9 : [ C>=0 ], cost: 1
5.97/2.67	
5.97/2.67	     10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1
5.97/2.67	
5.97/2.67	     11: eval9 -> eval11 : [ 100>=A ], cost: 1
5.97/2.67	
5.97/2.67	     12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Eliminated locations (on tree-shaped paths):
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	     15: eval0 -> eval3 : A'=B, C'=1, [ 100>=B ], cost: 2
5.97/2.67	
5.97/2.67	     16: eval0 -> eval3 : A'=11*meter+B, C'=1+meter, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.67	
5.97/2.67	     17: eval5 -> eval5 : A'=-10+A, C'=-1+C, D'=-20+A, [ -10+A>=101 && -1+C==1 ], cost: 2
5.97/2.67	
5.97/2.67	     18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2
5.97/2.67	
5.97/2.67	     19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2
5.97/2.67	
5.97/2.67	     20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2
5.97/2.67	
5.97/2.67	     21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2
5.97/2.67	
5.97/2.67	     22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Accelerating simple loops of location 3.
5.97/2.67	
5.97/2.67	   Accelerating the following rules:
5.97/2.67	
5.97/2.67	     17: eval5 -> eval5 : A'=-10+A, C'=-1+C, D'=-20+A, [ -10+A>=101 && -1+C==1 ], cost: 2
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	   Accelerated rule 17 with metering function -2+C, yielding the new rule 23.
5.97/2.67	
5.97/2.67	   Removing the simple loops: 17.
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Accelerated all simple loops using metering functions (where possible):
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	     15: eval0 -> eval3 : A'=B, C'=1, [ 100>=B ], cost: 2
5.97/2.67	
5.97/2.67	     16: eval0 -> eval3 : A'=11*meter+B, C'=1+meter, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.67	
5.97/2.67	     18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2
5.97/2.67	
5.97/2.67	     19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2
5.97/2.67	
5.97/2.67	     20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2
5.97/2.67	
5.97/2.67	     23: eval5 -> eval5 : A'=20-10*C+A, C'=2, D'=10-10*C+A, [ -10+A>=101 && -1+C==1 && -2+C>=1 ], cost: -4+2*C
5.97/2.67	
5.97/2.67	     21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2
5.97/2.67	
5.97/2.67	     22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Chained accelerated rules (with incoming rules):
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	     15: eval0 -> eval3 : A'=B, C'=1, [ 100>=B ], cost: 2
5.97/2.67	
5.97/2.67	     16: eval0 -> eval3 : A'=11*meter+B, C'=1+meter, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	      4: eval3 -> eval5 : [ A>=101 ], cost: 1
5.97/2.67	
5.97/2.67	     18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2
5.97/2.67	
5.97/2.67	     19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2
5.97/2.67	
5.97/2.67	     20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2
5.97/2.67	
5.97/2.67	     21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2
5.97/2.67	
5.97/2.67	     22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Eliminated locations (on tree-shaped paths):
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	     24: eval0 -> [10] : [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	     18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2
5.97/2.67	
5.97/2.67	     19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2
5.97/2.67	
5.97/2.67	     20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2
5.97/2.67	
5.97/2.67	     21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2
5.97/2.67	
5.97/2.67	     22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Applied pruning (of leafs and parallel rules):
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	     24: eval0 -> [10] : [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	### Computing asymptotic complexity ###
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Fully simplified ITS problem
5.97/2.67	
5.97/2.67	   Start location: eval0
5.97/2.67	
5.97/2.67	     24: eval0 -> [10] : [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Computing asymptotic complexity for rule 24
5.97/2.67	
5.97/2.67	   Simplified the guard:
5.97/2.67	
5.97/2.67	     24: eval0 -> [10] : [ 11*meter==100-B && meter>=1 ], cost: 2+meter
5.97/2.67	
5.97/2.67	   Solved the limit problem by the following transformations:
5.97/2.67	
5.97/2.67	      Created initial limit problem:
5.97/2.67	
5.97/2.67	      meter (+/+!), -99+11*meter+B (+/+!), 101-11*meter-B (+/+!), 2+meter (+) [not solved]
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	      applying transformation rule (C) using substitution {B==100-11*meter}
5.97/2.67	
5.97/2.67	      resulting limit problem:
5.97/2.67	
5.97/2.67	      1 (+/+!), meter (+/+!), 2+meter (+) [not solved]
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	      applying transformation rule (B), deleting 1 (+/+!)
5.97/2.67	
5.97/2.67	      resulting limit problem:
5.97/2.67	
5.97/2.67	      meter (+/+!), 2+meter (+) [not solved]
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	      removing all constraints (solved by SMT)
5.97/2.67	
5.97/2.67	      resulting limit problem: [solved]
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	      applying transformation rule (C) using substitution {meter==n}
5.97/2.67	
5.97/2.67	      resulting limit problem:
5.97/2.67	
5.97/2.67	      [solved]
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	   Solution:
5.97/2.67	
5.97/2.67	      meter / n
5.97/2.67	
5.97/2.67	      B / 100-11*n
5.97/2.67	
5.97/2.67	   Resulting cost 2+n has complexity: Poly(n^1)
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Found new complexity Poly(n^1).
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	Obtained the following overall complexity (w.r.t. the length of the input n):
5.97/2.67	
5.97/2.67	   Complexity:  Poly(n^1)
5.97/2.67	
5.97/2.67	   Cpx degree:  1
5.97/2.67	
5.97/2.67	   Solved cost: 2+n
5.97/2.67	
5.97/2.67	   Rule cost:   2+meter
5.97/2.67	
5.97/2.67	   Rule guard:  [ 11*meter==100-B && meter>=1 ]
5.97/2.67	
5.97/2.67	
5.97/2.67	
5.97/2.67	WORST_CASE(Omega(n^1),?)
5.97/2.67	
5.97/2.67	
5.97/2.67	----------------------------------------
5.97/2.67	
5.97/2.67	(4)
5.97/2.67	BOUNDS(n^1, INF)
5.97/2.70	EOF