2.18/1.33	WORST_CASE(?, O(n^1))
2.18/1.34	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.18/1.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.18/1.34	
2.18/1.34	
2.18/1.34	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.18/1.34	
2.18/1.34	(0) CpxIntTrs
2.18/1.34	(1) Koat Proof [FINISHED, 77 ms]
2.18/1.34	(2) BOUNDS(1, n^1)
2.18/1.34	
2.18/1.34	
2.18/1.34	----------------------------------------
2.18/1.34	
2.18/1.34	(0)
2.18/1.34	Obligation:
2.18/1.34	Complexity Int TRS consisting of the following rules:
2.18/1.34	eval_wcet2_start(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb0_in(v_.0, v_i, v_j.0)) :|: TRUE
2.18/1.34	eval_wcet2_bb0_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb1_in(v_i, v_i, v_j.0)) :|: TRUE
2.18/1.34	eval_wcet2_bb1_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb2_in(v_.0, v_i, 0)) :|: v_.0 < 5
2.18/1.34	eval_wcet2_bb1_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb5_in(v_.0, v_i, v_j.0)) :|: v_.0 >= 5
2.18/1.34	eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb3_in(v_.0, v_i, v_j.0)) :|: v_.0 > 2 && v_j.0 <= 9
2.18/1.34	eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb4_in(v_.0, v_i, v_j.0)) :|: v_.0 <= 2
2.18/1.34	eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb4_in(v_.0, v_i, v_j.0)) :|: v_j.0 > 9
2.18/1.34	eval_wcet2_bb3_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb2_in(v_.0, v_i, v_j.0 + 1)) :|: TRUE
2.18/1.34	eval_wcet2_bb4_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb1_in(v_.0 + 1, v_i, v_j.0)) :|: TRUE
2.18/1.34	eval_wcet2_bb5_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_stop(v_.0, v_i, v_j.0)) :|: TRUE
2.18/1.34	
2.18/1.34	The start-symbols are:[eval_wcet2_start_3]
2.18/1.34	
2.18/1.34	
2.18/1.34	----------------------------------------
2.18/1.34	
2.18/1.34	(1) Koat Proof (FINISHED)
2.18/1.34	YES(?, 56*ar_1 + 258)
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	Initial complexity problem:
2.18/1.34	
2.18/1.34	1:	T:
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.18/1.34	
2.18/1.34	2:	T:
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)    evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)    evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	A polynomial rank function with
2.18/1.34	
2.18/1.34		Pol(evalwcet2start) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb0in) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb1in) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb2in) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb5in) = 1
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb3in) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb4in) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2stop) = 0
2.18/1.34	
2.18/1.34		Pol(koat_start) = 2
2.18/1.34	
2.18/1.34	orients all transitions weakly and the transitions
2.18/1.34	
2.18/1.34		evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34		evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34	strictly and produces the following problem:
2.18/1.34	
2.18/1.34	3:	T:
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)    evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)    evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)    evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	A polynomial rank function with
2.18/1.34	
2.18/1.34		Pol(evalwcet2start) = -2*V_2 + 9
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb0in) = -2*V_2 + 9
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb1in) = -2*V_1 + 9
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb2in) = -2*V_1 + 8
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb5in) = -2*V_1
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb3in) = -2*V_1 + 8
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb4in) = -2*V_1 + 7
2.18/1.34	
2.18/1.34		Pol(evalwcet2stop) = -2*V_1
2.18/1.34	
2.18/1.34		Pol(koat_start) = -2*V_2 + 9
2.18/1.34	
2.18/1.34	orients all transitions weakly and the transitions
2.18/1.34	
2.18/1.34		evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34		evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34	strictly and produces the following problem:
2.18/1.34	
2.18/1.34	4:	T:
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)             evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)             evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)    evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)             evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)             evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)             evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)             evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)             evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)             evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	A polynomial rank function with
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb4in) = 1
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb1in) = 0
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb3in) = 2
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb2in) = 2
2.18/1.34	
2.18/1.34	and size complexities
2.18/1.34	
2.18/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.18/1.34	
2.18/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.18/1.34	
2.18/1.34		S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-0) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-2) = 0
2.18/1.34	
2.18/1.34		S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.18/1.34	
2.18/1.34		S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.18/1.34	
2.18/1.34		S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.18/1.34	
2.18/1.34	orients the transitions
2.18/1.34	
2.18/1.34		evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34		evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34		evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34		evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34	weakly and the transitions
2.18/1.34	
2.18/1.34		evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34		evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34	strictly and produces the following problem:
2.18/1.34	
2.18/1.34	5:	T:
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)              evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)              evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)     evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)              evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)              evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)     evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 6*ar_1 + 27, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)              evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: 6*ar_1 + 27, Cost: 1)    evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)              evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	A polynomial rank function with
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb3in) = -V_3 + 9
2.18/1.34	
2.18/1.34		Pol(evalwcet2bb2in) = -V_3 + 10
2.18/1.34	
2.18/1.34	and size complexities
2.18/1.34	
2.18/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.18/1.34	
2.18/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.18/1.34	
2.18/1.34		S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-0) = 7*ar_1 + 64827
2.18/1.34	
2.18/1.34		S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = 7*ar_1 + 1323
2.18/1.34	
2.18/1.34		S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 7*ar_1 + 1323
2.18/1.34	
2.18/1.34		S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-0) = 7*ar_1 + 1323
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-0) = 7*ar_1 + 1323
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = 7*ar_1 + 1323
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-0) = 7*ar_1 + 9261
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-2) = ?
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-0) = 7*ar_1 + 1323
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-2) = 0
2.18/1.34	
2.18/1.34		S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2
2.18/1.34	
2.18/1.34		S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.18/1.34	
2.18/1.34		S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.18/1.34	
2.18/1.34		S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.18/1.34	
2.18/1.34	orients the transitions
2.18/1.34	
2.18/1.34		evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34		evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34	weakly and the transition
2.18/1.34	
2.18/1.34		evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34	strictly and produces the following problem:
2.18/1.34	
2.18/1.34	6:	T:
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)               evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)               evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: 20*ar_1 + 90, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 6*ar_1 + 27, Cost: 1)     evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: ?, Cost: 1)               evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: 6*ar_1 + 27, Cost: 1)     evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.18/1.34	
2.18/1.34	7:	T:
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)               evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 1)               evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)               evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]
2.18/1.34	
2.18/1.34			(Comp: 20*ar_1 + 90, Cost: 1)    evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ]
2.18/1.34	
2.18/1.34			(Comp: 2*ar_1 + 9, Cost: 1)      evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]
2.18/1.34	
2.18/1.34			(Comp: 6*ar_1 + 27, Cost: 1)     evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]
2.18/1.34	
2.18/1.34			(Comp: 20*ar_1 + 90, Cost: 1)    evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))
2.18/1.34	
2.18/1.34			(Comp: 6*ar_1 + 27, Cost: 1)     evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 2, Cost: 1)               evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))
2.18/1.34	
2.18/1.34			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.18/1.34	
2.18/1.34		start location:	koat_start
2.18/1.34	
2.18/1.34		leaf cost:	0
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	Complexity upper bound 56*ar_1 + 258
2.18/1.34	
2.18/1.34	
2.18/1.34	
2.18/1.34	Time: 0.104 sec (SMT: 0.089 sec)
2.18/1.34	
2.18/1.34	
2.18/1.34	----------------------------------------
2.18/1.34	
2.18/1.34	(2)
2.18/1.34	BOUNDS(1, n^1)
2.18/1.37	EOF