2.09/1.36	WORST_CASE(?, O(1))
2.09/1.37	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.09/1.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.09/1.37	
2.09/1.37	
2.09/1.37	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.09/1.37	
2.09/1.37	(0) CpxIntTrs
2.09/1.37	(1) Koat Proof [FINISHED, 77 ms]
2.09/1.37	(2) BOUNDS(1, 1)
2.09/1.37	
2.09/1.37	
2.09/1.37	----------------------------------------
2.09/1.37	
2.09/1.37	(0)
2.09/1.37	Obligation:
2.09/1.37	Complexity Int TRS consisting of the following rules:
2.09/1.37	eval_foo_start(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_c, v_i, v_j)) :|: TRUE
2.09/1.37	eval_foo_bb0_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb1_in(0, v_.01, v_c, v_i, v_j)) :|: TRUE
2.09/1.37	eval_foo_bb1_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, 3, v_c, v_i, v_j)) :|: v_.0 < 10
2.09/1.37	eval_foo_bb1_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_c, v_i, v_j)) :|: v_.0 >= 10
2.09/1.37	eval_foo_bb2_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_i, v_j)) :|: v_.01 < 12
2.09/1.37	eval_foo_bb2_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_c, v_i, v_j)) :|: v_.01 >= 12
2.09/1.37	eval_foo_bb3_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 + 1, v_c, v_i, v_j)) :|: TRUE
2.09/1.37	eval_foo_bb4_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_c, v_i, v_j)) :|: TRUE
2.09/1.37	eval_foo_bb5_in(v_.0, v_.01, v_c, v_i, v_j) -> Com_1(eval_foo_stop(v_.0, v_.01, v_c, v_i, v_j)) :|: TRUE
2.09/1.37	
2.09/1.37	The start-symbols are:[eval_foo_start_5]
2.09/1.37	
2.09/1.37	
2.09/1.37	----------------------------------------
2.09/1.37	
2.09/1.37	(1) Koat Proof (FINISHED)
2.09/1.37	YES(?, 356)
2.09/1.37	
2.09/1.37	
2.09/1.37	
2.09/1.37	Initial complexity problem:
2.09/1.37	
2.09/1.37	1:	T:
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.37	
2.09/1.37		start location:	koat_start
2.09/1.37	
2.09/1.37		leaf cost:	0
2.09/1.37	
2.09/1.37	
2.09/1.37	
2.09/1.37	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.09/1.37	
2.09/1.37	2:	T:
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.37	
2.09/1.37		start location:	koat_start
2.09/1.37	
2.09/1.37		leaf cost:	0
2.09/1.37	
2.09/1.37	
2.09/1.37	
2.09/1.37	A polynomial rank function with
2.09/1.37	
2.09/1.37		Pol(evalfoostart) = 2
2.09/1.37	
2.09/1.37		Pol(evalfoobb0in) = 2
2.09/1.37	
2.09/1.37		Pol(evalfoobb1in) = 2
2.09/1.37	
2.09/1.37		Pol(evalfoobb2in) = 2
2.09/1.37	
2.09/1.37		Pol(evalfoobb5in) = 1
2.09/1.37	
2.09/1.37		Pol(evalfoobb3in) = 2
2.09/1.37	
2.09/1.37		Pol(evalfoobb4in) = 2
2.09/1.37	
2.09/1.37		Pol(evalfoostop) = 0
2.09/1.37	
2.09/1.37		Pol(koat_start) = 2
2.09/1.37	
2.09/1.37	orients all transitions weakly and the transitions
2.09/1.37	
2.09/1.37		evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.37	
2.09/1.37		evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.37	
2.09/1.37	strictly and produces the following problem:
2.09/1.37	
2.09/1.37	3:	T:
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.37	
2.09/1.37			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.37	
2.09/1.37			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.37	
2.09/1.37			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.37	
2.09/1.37			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.37	
2.09/1.37		start location:	koat_start
2.09/1.37	
2.09/1.37		leaf cost:	0
2.09/1.37	
2.09/1.37	
2.09/1.37	
2.09/1.37	A polynomial rank function with
2.09/1.37	
2.09/1.37		Pol(evalfoostart) = 10
2.09/1.37	
2.09/1.37		Pol(evalfoobb0in) = 10
2.09/1.38	
2.09/1.38		Pol(evalfoobb1in) = -V_1 + 10
2.09/1.38	
2.09/1.38		Pol(evalfoobb2in) = -V_1 + 9
2.09/1.38	
2.09/1.38		Pol(evalfoobb5in) = -V_1
2.09/1.38	
2.09/1.38		Pol(evalfoobb3in) = -V_1 + 9
2.09/1.38	
2.09/1.38		Pol(evalfoobb4in) = -V_1 + 9
2.09/1.38	
2.09/1.38		Pol(evalfoostop) = -V_1
2.09/1.38	
2.09/1.38		Pol(koat_start) = 10
2.09/1.38	
2.09/1.38	orients all transitions weakly and the transition
2.09/1.38	
2.09/1.38		evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.38	
2.09/1.38	strictly and produces the following problem:
2.09/1.38	
2.09/1.38	4:	T:
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)     evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)     evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 10, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)     evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)     evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)     evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)     evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)     evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.38	
2.09/1.38		start location:	koat_start
2.09/1.38	
2.09/1.38		leaf cost:	0
2.09/1.38	
2.09/1.38	
2.09/1.38	
2.09/1.38	A polynomial rank function with
2.09/1.38	
2.09/1.38		Pol(evalfoobb4in) = 1
2.09/1.38	
2.09/1.38		Pol(evalfoobb1in) = 0
2.09/1.38	
2.09/1.38		Pol(evalfoobb3in) = 2
2.09/1.38	
2.09/1.38		Pol(evalfoobb2in) = 2
2.09/1.38	
2.09/1.38	and size complexities
2.09/1.38	
2.09/1.38		S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
2.09/1.38	
2.09/1.38		S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
2.09/1.38	
2.09/1.38		S("evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]", 0-0) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]", 0-1) = 3
2.09/1.38	
2.09/1.38		S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))", 0-0) = 0
2.09/1.38	
2.09/1.38		S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))", 0-1) = ar_1
2.09/1.38	
2.09/1.38		S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-0) = ar_0
2.09/1.38	
2.09/1.38		S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-1) = ar_1
2.09/1.38	
2.09/1.38	orients the transitions
2.09/1.38	
2.09/1.38		evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.38	
2.09/1.38		evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.38	
2.09/1.38		evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.38	
2.09/1.38		evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38	weakly and the transitions
2.09/1.38	
2.09/1.38		evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.38	
2.09/1.38		evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.38	
2.09/1.38	strictly and produces the following problem:
2.09/1.38	
2.09/1.38	5:	T:
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)     evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)     evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 10, Cost: 1)    evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)     evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38			(Comp: 20, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)     evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.38	
2.09/1.38			(Comp: 20, Cost: 1)    evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)     evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.38	
2.09/1.38		start location:	koat_start
2.09/1.38	
2.09/1.38		leaf cost:	0
2.09/1.38	
2.09/1.38	
2.09/1.38	
2.09/1.38	A polynomial rank function with
2.09/1.38	
2.09/1.38		Pol(evalfoobb3in) = -V_2 + 11
2.09/1.38	
2.09/1.38		Pol(evalfoobb2in) = -V_2 + 12
2.09/1.38	
2.09/1.38	and size complexities
2.09/1.38	
2.09/1.38		S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
2.09/1.38	
2.09/1.38		S("koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
2.09/1.38	
2.09/1.38		S("evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]", 0-1) = ?
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]", 0-0) = 20
2.09/1.38	
2.09/1.38		S("evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]", 0-1) = 3
2.09/1.38	
2.09/1.38		S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))", 0-0) = 0
2.09/1.38	
2.09/1.38		S("evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))", 0-1) = ar_1
2.09/1.38	
2.09/1.38		S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-0) = ar_0
2.09/1.38	
2.09/1.38		S("evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))", 0-1) = ar_1
2.09/1.38	
2.09/1.38	orients the transitions
2.09/1.38	
2.09/1.38		evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.38	
2.09/1.38		evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38	weakly and the transition
2.09/1.38	
2.09/1.38		evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38	strictly and produces the following problem:
2.09/1.38	
2.09/1.38	6:	T:
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)      evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)      evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 10, Cost: 1)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)      evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.38	
2.09/1.38			(Comp: 150, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38			(Comp: 20, Cost: 1)     evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.38	
2.09/1.38			(Comp: ?, Cost: 1)      evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.38	
2.09/1.38			(Comp: 20, Cost: 1)     evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)      evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 0)      koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.38	
2.09/1.38		start location:	koat_start
2.09/1.38	
2.09/1.38		leaf cost:	0
2.09/1.38	
2.09/1.38	
2.09/1.38	
2.09/1.38	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.09/1.38	
2.09/1.38	7:	T:
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)      evalfoostart(ar_0, ar_1) -> Com_1(evalfoobb0in(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 1)      evalfoobb0in(ar_0, ar_1) -> Com_1(evalfoobb1in(0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 10, Cost: 1)     evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, 3)) [ 9 >= ar_0 ]
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)      evalfoobb1in(ar_0, ar_1) -> Com_1(evalfoobb5in(ar_0, ar_1)) [ ar_0 >= 10 ]
2.09/1.38	
2.09/1.38			(Comp: 150, Cost: 1)    evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb3in(ar_0, ar_1)) [ 11 >= ar_1 ]
2.09/1.38	
2.09/1.38			(Comp: 20, Cost: 1)     evalfoobb2in(ar_0, ar_1) -> Com_1(evalfoobb4in(ar_0, ar_1)) [ ar_1 >= 12 ]
2.09/1.38	
2.09/1.38			(Comp: 150, Cost: 1)    evalfoobb3in(ar_0, ar_1) -> Com_1(evalfoobb2in(ar_0, ar_1 + 1))
2.09/1.38	
2.09/1.38			(Comp: 20, Cost: 1)     evalfoobb4in(ar_0, ar_1) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 2, Cost: 1)      evalfoobb5in(ar_0, ar_1) -> Com_1(evalfoostop(ar_0, ar_1))
2.09/1.38	
2.09/1.38			(Comp: 1, Cost: 0)      koat_start(ar_0, ar_1) -> Com_1(evalfoostart(ar_0, ar_1)) [ 0 <= 0 ]
2.09/1.38	
2.09/1.38		start location:	koat_start
2.09/1.38	
2.09/1.38		leaf cost:	0
2.09/1.38	
2.09/1.38	
2.09/1.38	
2.09/1.38	Complexity upper bound 356
2.09/1.38	
2.09/1.38	
2.09/1.38	
2.09/1.38	Time: 0.078 sec (SMT: 0.069 sec)
2.09/1.38	
2.09/1.38	
2.09/1.38	----------------------------------------
2.09/1.38	
2.09/1.38	(2)
2.09/1.38	BOUNDS(1, 1)
2.09/1.39	EOF