2.17/1.40	WORST_CASE(?, O(n^2))
2.17/1.41	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.17/1.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.17/1.41	
2.17/1.41	
2.17/1.41	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.17/1.41	
2.17/1.41	(0) CpxIntTrs
2.17/1.41	(1) Koat Proof [FINISHED, 88 ms]
2.17/1.41	(2) BOUNDS(1, n^2)
2.17/1.41	
2.17/1.41	
2.17/1.41	----------------------------------------
2.17/1.41	
2.17/1.41	(0)
2.17/1.41	Obligation:
2.17/1.41	Complexity Int TRS consisting of the following rules:
2.17/1.41	eval_foo_start(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE
2.17/1.41	eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_c, v_x, v_y)) :|: TRUE
2.17/1.41	eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 < v_.02
2.17/1.41	eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 > v_.02
2.17/1.41	eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 >= v_.02 && v_.01 <= v_.02
2.17/1.41	eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02 + 1, v_c, v_x, v_y)) :|: v_.01 > v_.02
2.17/1.41	eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_.02 + 1, v_c, v_x, v_y)) :|: v_.01 > v_.02 && v_.01 <= v_.02
2.17/1.41	eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 <= v_.02 && v_.01 > v_.02
2.17/1.41	eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_.02, v_c, v_x, v_y)) :|: v_.01 <= v_.02
2.17/1.41	eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE
2.17/1.41	
2.17/1.41	The start-symbols are:[eval_foo_start_5]
2.17/1.41	
2.17/1.41	
2.17/1.41	----------------------------------------
2.17/1.41	
2.17/1.41	(1) Koat Proof (FINISHED)
2.17/1.41	YES(?, 24*ar_1^2 + 56*ar_1*ar_3 + 32*ar_3^2 + 176*ar_1 + 184*ar_3 + 154)
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	Initial complexity problem:
2.17/1.41	
2.17/1.41	1:	T:
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.17/1.41	
2.17/1.41		start location:	koat_start
2.17/1.41	
2.17/1.41		leaf cost:	0
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.17/1.41	
2.17/1.41		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41	We thus obtain the following problem:
2.17/1.41	
2.17/1.41	2:	T:
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.17/1.41	
2.17/1.41		start location:	koat_start
2.17/1.41	
2.17/1.41		leaf cost:	0
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.17/1.41	
2.17/1.41	3:	T:
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.17/1.41	
2.17/1.41		start location:	koat_start
2.17/1.41	
2.17/1.41		leaf cost:	0
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	A polynomial rank function with
2.17/1.41	
2.17/1.41		Pol(evalfoobb3in) = 1
2.17/1.41	
2.17/1.41		Pol(evalfoostop) = 0
2.17/1.41	
2.17/1.41		Pol(evalfoobb2in) = 2
2.17/1.41	
2.17/1.41		Pol(evalfoobb1in) = 2
2.17/1.41	
2.17/1.41		Pol(evalfoobb0in) = 2
2.17/1.41	
2.17/1.41		Pol(evalfoostart) = 2
2.17/1.41	
2.17/1.41		Pol(koat_start) = 2
2.17/1.41	
2.17/1.41	orients all transitions weakly and the transitions
2.17/1.41	
2.17/1.41		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41	strictly and produces the following problem:
2.17/1.41	
2.17/1.41	4:	T:
2.17/1.41	
2.17/1.41			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.17/1.41	
2.17/1.41		start location:	koat_start
2.17/1.41	
2.17/1.41		leaf cost:	0
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	A polynomial rank function with
2.17/1.41	
2.17/1.41		Pol(evalfoobb1in) = -2*V_1 + 2*V_3 + 2
2.17/1.41	
2.17/1.41		Pol(evalfoobb2in) = -2*V_1 + 2*V_3 + 1
2.17/1.41	
2.17/1.41	and size complexities
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-0) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-0) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-2) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.17/1.41	
2.17/1.41	orients the transitions
2.17/1.41	
2.17/1.41		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41	weakly and the transitions
2.17/1.41	
2.17/1.41		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41	strictly and produces the following problem:
2.17/1.41	
2.17/1.41	5:	T:
2.17/1.41	
2.17/1.41			(Comp: 2, Cost: 1)                      evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)                      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: 2, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41			(Comp: ?, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)                      evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.17/1.41	
2.17/1.41		start location:	koat_start
2.17/1.41	
2.17/1.41		leaf cost:	0
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	A polynomial rank function with
2.17/1.41	
2.17/1.41		Pol(evalfoobb2in) = 2*V_1 - 2*V_3 - 1
2.17/1.41	
2.17/1.41		Pol(evalfoobb1in) = 2*V_1 - 2*V_3
2.17/1.41	
2.17/1.41	and size complexities
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.17/1.41	
2.17/1.41		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.17/1.41	
2.17/1.41		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 3*ar_1 + 3*ar_3 + 18
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = 3*ar_1 + 3*ar_3 + 54
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-0) = 3*ar_1 + 3*ar_3 + 162
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-0) = 3*ar_1 + 3*ar_3 + 18
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-2) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = 3*ar_1 + 3*ar_3 + 54
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 3*ar_1 + 3*ar_3 + 486
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.17/1.41	
2.17/1.41		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.17/1.41	
2.17/1.41	orients the transitions
2.17/1.41	
2.17/1.41		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41	weakly and the transitions
2.17/1.41	
2.17/1.41		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41	strictly and produces the following problem:
2.17/1.41	
2.17/1.41	6:	T:
2.17/1.41	
2.17/1.41			(Comp: 2, Cost: 1)                                                                evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 12*ar_1^2 + 28*ar_1*ar_3 + 16*ar_3^2 + 86*ar_1 + 90*ar_3 + 72, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)                                              evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.17/1.41	
2.17/1.41			(Comp: 2, Cost: 1)                                                                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.17/1.41	
2.17/1.41			(Comp: 12*ar_1^2 + 28*ar_1*ar_3 + 16*ar_3^2 + 86*ar_1 + 90*ar_3 + 72, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)                                                                evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 1)                                                                evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.17/1.41	
2.17/1.41			(Comp: 1, Cost: 0)                                                                koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.17/1.41	
2.17/1.41		start location:	koat_start
2.17/1.41	
2.17/1.41		leaf cost:	0
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	Complexity upper bound 24*ar_1^2 + 56*ar_1*ar_3 + 32*ar_3^2 + 176*ar_1 + 184*ar_3 + 154
2.17/1.41	
2.17/1.41	
2.17/1.41	
2.17/1.41	Time: 0.115 sec (SMT: 0.098 sec)
2.17/1.41	
2.17/1.41	
2.17/1.41	----------------------------------------
2.17/1.41	
2.17/1.41	(2)
2.17/1.41	BOUNDS(1, n^2)
2.17/1.42	EOF