2.23/1.33	WORST_CASE(?, O(n^2))
2.23/1.34	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.23/1.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.23/1.34	
2.23/1.34	
2.23/1.34	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.23/1.34	
2.23/1.34	(0) CpxIntTrs
2.23/1.34	(1) Koat Proof [FINISHED, 75 ms]
2.23/1.34	(2) BOUNDS(1, n^2)
2.23/1.34	
2.23/1.34	
2.23/1.34	----------------------------------------
2.23/1.34	
2.23/1.34	(0)
2.23/1.34	Obligation:
2.23/1.34	Complexity Int TRS consisting of the following rules:
2.23/1.34	eval_jama_ex1_start(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE
2.23/1.34	eval_jama_ex1_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb1_in(1, v_j.0, v_n)) :|: TRUE
2.23/1.34	eval_jama_ex1_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb2_in(v_i.0, 1, v_n)) :|: v_i.0 <= v_n
2.23/1.34	eval_jama_ex1_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n
2.23/1.34	eval_jama_ex1_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_n
2.23/1.34	eval_jama_ex1_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_n
2.23/1.34	eval_jama_ex1_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE
2.23/1.34	eval_jama_ex1_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_bb1_in(v_i.0 + 1, v_j.0, v_n)) :|: TRUE
2.23/1.34	eval_jama_ex1_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex1_stop(v_i.0, v_j.0, v_n)) :|: TRUE
2.23/1.34	
2.23/1.34	The start-symbols are:[eval_jama_ex1_start_3]
2.23/1.34	
2.23/1.34	
2.23/1.34	----------------------------------------
2.23/1.34	
2.23/1.34	(1) Koat Proof (FINISHED)
2.23/1.34	YES(?, 9*ar_1 + 2*ar_1^2 + 6)
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Initial complexity problem:
2.23/1.34	
2.23/1.34	1:	T:
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.23/1.34	
2.23/1.34	2:	T:
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evaljamaex1start) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb0in) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb1in) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb2in) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb5in) = 1
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb3in) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb4in) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1stop) = 0
2.23/1.34	
2.23/1.34		Pol(koat_start) = 2
2.23/1.34	
2.23/1.34	orients all transitions weakly and the transitions
2.23/1.34	
2.23/1.34		evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34		evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	3:	T:
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)    evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evaljamaex1start) = V_2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb0in) = V_2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb1in) = -V_1 + V_2 + 1
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb2in) = -V_1 + V_2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb5in) = -V_1 + V_2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb3in) = -V_1 + V_2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb4in) = -V_1 + V_2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1stop) = -V_1 + V_2
2.23/1.34	
2.23/1.34		Pol(koat_start) = V_2
2.23/1.34	
2.23/1.34	orients all transitions weakly and the transition
2.23/1.34	
2.23/1.34		evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	4:	T:
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)       evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)       evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ar_1, Cost: 1)    evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)       evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)       evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)       evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)       evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)       evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)       evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb4in) = 1
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb1in) = 0
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb3in) = 2
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb2in) = 2
2.23/1.34	
2.23/1.34	and size complexities
2.23/1.34	
2.23/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.23/1.34	
2.23/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.23/1.34	
2.23/1.34		S("evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]", 0-2) = 1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))", 0-0) = 1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))", 0-2) = ar_2
2.23/1.34	
2.23/1.34		S("evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.23/1.34	
2.23/1.34		S("evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.23/1.34	
2.23/1.34	orients the transitions
2.23/1.34	
2.23/1.34		evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34		evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34		evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34		evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34	weakly and the transitions
2.23/1.34	
2.23/1.34		evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34		evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	5:	T:
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)         evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)         evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ar_1, Cost: 1)      evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)         evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)         evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)         evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1, Cost: 1)    evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)         evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb3in) = V_2 - V_3
2.23/1.34	
2.23/1.34		Pol(evaljamaex1bb2in) = V_2 - V_3 + 1
2.23/1.34	
2.23/1.34	and size complexities
2.23/1.34	
2.23/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.23/1.34	
2.23/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.23/1.34	
2.23/1.34		S("evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))", 0-0) = 2*ar_1 + 20
2.23/1.34	
2.23/1.34		S("evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = 2*ar_1 + 4
2.23/1.34	
2.23/1.34		S("evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 2*ar_1 + 4
2.23/1.34	
2.23/1.34		S("evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 4
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = 2*ar_1 + 4
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 10
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]", 0-0) = 2*ar_1 + 4
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]", 0-2) = 1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))", 0-0) = 1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))", 0-2) = ar_2
2.23/1.34	
2.23/1.34		S("evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.23/1.34	
2.23/1.34		S("evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.23/1.34	
2.23/1.34	orients the transitions
2.23/1.34	
2.23/1.34		evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34		evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34	weakly and the transition
2.23/1.34	
2.23/1.34		evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	6:	T:
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                  evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                  evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ar_1, Cost: 1)               evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                  evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ar_1^2 + 2*ar_1, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1, Cost: 1)             evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)                  evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1, Cost: 1)             evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                  evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Repeatedly propagating knowledge in problem 6 produces the following problem:
2.23/1.34	
2.23/1.34	7:	T:
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                  evaljamaex1start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb0in(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                  evaljamaex1bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: ar_1, Cost: 1)               evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, 1)) [ ar_1 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                  evaljamaex1bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ar_1^2 + 2*ar_1, Cost: 1)    evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1, Cost: 1)             evaljamaex1bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ar_1^2 + 2*ar_1, Cost: 1)    evaljamaex1bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb2in(ar_0, ar_1, ar_2 + 1))
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1, Cost: 1)             evaljamaex1bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1bb1in(ar_0 + 1, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                  evaljamaex1bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1stop(ar_0, ar_1, ar_2))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex1start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Complexity upper bound 9*ar_1 + 2*ar_1^2 + 6
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Time: 0.089 sec (SMT: 0.080 sec)
2.23/1.34	
2.23/1.34	
2.23/1.34	----------------------------------------
2.23/1.34	
2.23/1.34	(2)
2.23/1.34	BOUNDS(1, n^2)
2.23/1.36	EOF