2.26/1.37	WORST_CASE(?, O(n^2))
2.26/1.38	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.26/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.26/1.38	
2.26/1.38	
2.26/1.38	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.26/1.38	
2.26/1.38	(0) CpxIntTrs
2.26/1.38	(1) Koat Proof [FINISHED, 75 ms]
2.26/1.38	(2) BOUNDS(1, n^2)
2.26/1.38	
2.26/1.38	
2.26/1.38	----------------------------------------
2.26/1.38	
2.26/1.38	(0)
2.26/1.38	Obligation:
2.26/1.38	Complexity Int TRS consisting of the following rules:
2.26/1.38	eval_jama_ex5_start(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE
2.26/1.38	eval_jama_ex5_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb1_in(0, v_j.0, v_n)) :|: TRUE
2.26/1.38	eval_jama_ex5_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 <= v_n
2.26/1.38	eval_jama_ex5_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n
2.26/1.38	eval_jama_ex5_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_n
2.26/1.38	eval_jama_ex5_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_n
2.26/1.38	eval_jama_ex5_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb2_in(v_i.0, v_j.0 + 2, v_n)) :|: TRUE
2.26/1.38	eval_jama_ex5_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_bb1_in(v_i.0 + 2, v_j.0, v_n)) :|: TRUE
2.26/1.38	eval_jama_ex5_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex5_stop(v_i.0, v_j.0, v_n)) :|: TRUE
2.26/1.38	
2.26/1.38	The start-symbols are:[eval_jama_ex5_start_3]
2.26/1.38	
2.26/1.38	
2.26/1.38	----------------------------------------
2.26/1.38	
2.26/1.38	(1) Koat Proof (FINISHED)
2.26/1.38	YES(?, 13*ar_1 + 2*ar_1^2 + 24)
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Initial complexity problem:
2.26/1.38	
2.26/1.38	1:	T:
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.26/1.38	
2.26/1.38	2:	T:
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	A polynomial rank function with
2.26/1.38	
2.26/1.38		Pol(evaljamaex5start) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb0in) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb1in) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb2in) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb5in) = 1
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb3in) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb4in) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5stop) = 0
2.26/1.38	
2.26/1.38		Pol(koat_start) = 2
2.26/1.38	
2.26/1.38	orients all transitions weakly and the transitions
2.26/1.38	
2.26/1.38		evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38		evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38	strictly and produces the following problem:
2.26/1.38	
2.26/1.38	3:	T:
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)    evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)    evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)    evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	A polynomial rank function with
2.26/1.38	
2.26/1.38		Pol(evaljamaex5start) = V_2 + 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb0in) = V_2 + 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb1in) = -V_1 + V_2 + 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb2in) = -V_1 + V_2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb5in) = -V_1 + V_2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb3in) = -V_1 + V_2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb4in) = -V_1 + V_2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5stop) = -V_1 + V_2
2.26/1.38	
2.26/1.38		Pol(koat_start) = V_2 + 2
2.26/1.38	
2.26/1.38	orients all transitions weakly and the transition
2.26/1.38	
2.26/1.38		evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38	strictly and produces the following problem:
2.26/1.38	
2.26/1.38	4:	T:
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)           evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)           evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ar_1 + 2, Cost: 1)    evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)           evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)           evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)           evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)           evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)           evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)           evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	A polynomial rank function with
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb4in) = 1
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb1in) = 0
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb3in) = 2
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb2in) = 2
2.26/1.38	
2.26/1.38	and size complexities
2.26/1.38	
2.26/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.26/1.38	
2.26/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.26/1.38	
2.26/1.38		S("evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]", 0-0) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]", 0-2) = 0
2.26/1.38	
2.26/1.38		S("evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))", 0-0) = 0
2.26/1.38	
2.26/1.38		S("evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))", 0-2) = ar_2
2.26/1.38	
2.26/1.38		S("evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.26/1.38	
2.26/1.38		S("evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.26/1.38	
2.26/1.38	orients the transitions
2.26/1.38	
2.26/1.38		evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38		evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38		evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38		evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38	weakly and the transitions
2.26/1.38	
2.26/1.38		evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38		evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38	strictly and produces the following problem:
2.26/1.38	
2.26/1.38	5:	T:
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)             evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)             evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ar_1 + 2, Cost: 1)      evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)             evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)             evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: 2*ar_1 + 4, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)             evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: 2*ar_1 + 4, Cost: 1)    evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)             evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	A polynomial rank function with
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb3in) = V_2 - V_3
2.26/1.38	
2.26/1.38		Pol(evaljamaex5bb2in) = V_2 - V_3 + 2
2.26/1.38	
2.26/1.38	and size complexities
2.26/1.38	
2.26/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.26/1.38	
2.26/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.26/1.38	
2.26/1.38		S("evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))", 0-0) = 4*ar_1 + 2048
2.26/1.38	
2.26/1.38		S("evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))", 0-0) = 4*ar_1 + 128
2.26/1.38	
2.26/1.38		S("evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))", 0-0) = 4*ar_1 + 128
2.26/1.38	
2.26/1.38		S("evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = 4*ar_1 + 128
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = 4*ar_1 + 128
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 4*ar_1 + 512
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]", 0-0) = 4*ar_1 + 128
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]", 0-2) = 0
2.26/1.38	
2.26/1.38		S("evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))", 0-0) = 0
2.26/1.38	
2.26/1.38		S("evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))", 0-2) = ar_2
2.26/1.38	
2.26/1.38		S("evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.26/1.38	
2.26/1.38		S("evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.26/1.38	
2.26/1.38		S("evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.26/1.38	
2.26/1.38	orients the transitions
2.26/1.38	
2.26/1.38		evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38		evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38	weakly and the transition
2.26/1.38	
2.26/1.38		evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38	strictly and produces the following problem:
2.26/1.38	
2.26/1.38	6:	T:
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                      evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                      evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ar_1 + 2, Cost: 1)               evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                      evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1^2 + 4*ar_1 + 4, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: 2*ar_1 + 4, Cost: 1)             evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ?, Cost: 1)                      evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: 2*ar_1 + 4, Cost: 1)             evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                      evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.26/1.38	
2.26/1.38	7:	T:
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                      evaljamaex5start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb0in(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 1)                      evaljamaex5bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: ar_1 + 2, Cost: 1)               evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 ]
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                      evaljamaex5bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1^2 + 4*ar_1 + 4, Cost: 1)    evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.26/1.38	
2.26/1.38			(Comp: 2*ar_1 + 4, Cost: 1)             evaljamaex5bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.26/1.38	
2.26/1.38			(Comp: ar_1^2 + 4*ar_1 + 4, Cost: 1)    evaljamaex5bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb2in(ar_0, ar_1, ar_2 + 2))
2.26/1.38	
2.26/1.38			(Comp: 2*ar_1 + 4, Cost: 1)             evaljamaex5bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5bb1in(ar_0 + 2, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 2, Cost: 1)                      evaljamaex5bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5stop(ar_0, ar_1, ar_2))
2.26/1.38	
2.26/1.38			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex5start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.26/1.38	
2.26/1.38		start location:	koat_start
2.26/1.38	
2.26/1.38		leaf cost:	0
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Complexity upper bound 13*ar_1 + 2*ar_1^2 + 24
2.26/1.38	
2.26/1.38	
2.26/1.38	
2.26/1.38	Time: 0.091 sec (SMT: 0.082 sec)
2.26/1.38	
2.26/1.38	
2.26/1.38	----------------------------------------
2.26/1.38	
2.26/1.38	(2)
2.26/1.38	BOUNDS(1, n^2)
2.26/1.40	EOF