3.65/1.70	WORST_CASE(?, O(1))
3.65/1.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.65/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.65/1.71	
3.65/1.71	
3.65/1.71	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.65/1.71	
3.65/1.71	(0) CpxIntTrs
3.65/1.71	(1) Koat Proof [FINISHED, 24 ms]
3.65/1.71	(2) BOUNDS(1, 1)
3.65/1.71	
3.65/1.71	
3.65/1.71	----------------------------------------
3.65/1.71	
3.65/1.71	(0)
3.65/1.71	Obligation:
3.65/1.71	Complexity Int TRS consisting of the following rules:
3.65/1.71	evaleasy1start(A, B) -> Com_1(evaleasy1entryin(A, B)) :|: TRUE
3.65/1.71	evaleasy1entryin(A, B) -> Com_1(evaleasy1bb3in(0, B)) :|: TRUE
3.65/1.71	evaleasy1bb3in(A, B) -> Com_1(evaleasy1bbin(A, B)) :|: 39 >= A
3.65/1.71	evaleasy1bb3in(A, B) -> Com_1(evaleasy1returnin(A, B)) :|: A >= 40
3.65/1.71	evaleasy1bbin(A, B) -> Com_1(evaleasy1bb1in(A, B)) :|: B >= 0 && B <= 0
3.65/1.71	evaleasy1bbin(A, B) -> Com_1(evaleasy1bb2in(A, B)) :|: 0 >= B + 1
3.65/1.71	evaleasy1bbin(A, B) -> Com_1(evaleasy1bb2in(A, B)) :|: B >= 1
3.65/1.71	evaleasy1bb1in(A, B) -> Com_1(evaleasy1bb3in(A + 1, B)) :|: TRUE
3.65/1.71	evaleasy1bb2in(A, B) -> Com_1(evaleasy1bb3in(A + 2, B)) :|: TRUE
3.65/1.71	evaleasy1returnin(A, B) -> Com_1(evaleasy1stop(A, B)) :|: TRUE
3.65/1.71	
3.65/1.71	The start-symbols are:[evaleasy1start_2]
3.65/1.71	
3.65/1.71	
3.65/1.71	----------------------------------------
3.65/1.71	
3.65/1.71	(1) Koat Proof (FINISHED)
3.65/1.71	YES(?, 286)
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	Initial complexity problem:
3.65/1.71	
3.65/1.71	1:	T:
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1start(ar_0, ar_1) -> Com_1(evaleasy1entryin(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1entryin(ar_0, ar_1) -> Com_1(evaleasy1bb3in(0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1bbin(ar_0, ar_1)) [ 39 >= ar_0 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1returnin(ar_0, ar_1)) [ ar_0 >= 40 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb1in(ar_0, ar_1)) [ ar_1 = 0 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ ar_1 >= 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb1in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 1, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb2in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 2, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1returnin(ar_0, ar_1) -> Com_1(evaleasy1stop(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evaleasy1start(ar_0, ar_1)) [ 0 <= 0 ]
3.65/1.71	
3.65/1.71		start location:	koat_start
3.65/1.71	
3.65/1.71		leaf cost:	0
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.65/1.71	
3.65/1.71	2:	T:
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)    evaleasy1start(ar_0, ar_1) -> Com_1(evaleasy1entryin(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)    evaleasy1entryin(ar_0, ar_1) -> Com_1(evaleasy1bb3in(0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1bbin(ar_0, ar_1)) [ 39 >= ar_0 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1returnin(ar_0, ar_1)) [ ar_0 >= 40 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb1in(ar_0, ar_1)) [ ar_1 = 0 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ ar_1 >= 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb1in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 1, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb2in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 2, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1returnin(ar_0, ar_1) -> Com_1(evaleasy1stop(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evaleasy1start(ar_0, ar_1)) [ 0 <= 0 ]
3.65/1.71	
3.65/1.71		start location:	koat_start
3.65/1.71	
3.65/1.71		leaf cost:	0
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	A polynomial rank function with
3.65/1.71	
3.65/1.71		Pol(evaleasy1start) = 2
3.65/1.71	
3.65/1.71		Pol(evaleasy1entryin) = 2
3.65/1.71	
3.65/1.71		Pol(evaleasy1bb3in) = 2
3.65/1.71	
3.65/1.71		Pol(evaleasy1bbin) = 2
3.65/1.71	
3.65/1.71		Pol(evaleasy1returnin) = 1
3.65/1.71	
3.65/1.71		Pol(evaleasy1bb1in) = 2
3.65/1.71	
3.65/1.71		Pol(evaleasy1bb2in) = 2
3.65/1.71	
3.65/1.71		Pol(evaleasy1stop) = 0
3.65/1.71	
3.65/1.71		Pol(koat_start) = 2
3.65/1.71	
3.65/1.71	orients all transitions weakly and the transitions
3.65/1.71	
3.65/1.71		evaleasy1returnin(ar_0, ar_1) -> Com_1(evaleasy1stop(ar_0, ar_1))
3.65/1.71	
3.65/1.71		evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1returnin(ar_0, ar_1)) [ ar_0 >= 40 ]
3.65/1.71	
3.65/1.71	strictly and produces the following problem:
3.65/1.71	
3.65/1.71	3:	T:
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)    evaleasy1start(ar_0, ar_1) -> Com_1(evaleasy1entryin(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)    evaleasy1entryin(ar_0, ar_1) -> Com_1(evaleasy1bb3in(0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1bbin(ar_0, ar_1)) [ 39 >= ar_0 ]
3.65/1.71	
3.65/1.71			(Comp: 2, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1returnin(ar_0, ar_1)) [ ar_0 >= 40 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb1in(ar_0, ar_1)) [ ar_1 = 0 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ ar_1 >= 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb1in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 1, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)    evaleasy1bb2in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 2, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 2, Cost: 1)    evaleasy1returnin(ar_0, ar_1) -> Com_1(evaleasy1stop(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evaleasy1start(ar_0, ar_1)) [ 0 <= 0 ]
3.65/1.71	
3.65/1.71		start location:	koat_start
3.65/1.71	
3.65/1.71		leaf cost:	0
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	A polynomial rank function with
3.65/1.71	
3.65/1.71		Pol(evaleasy1start) = 40
3.65/1.71	
3.65/1.71		Pol(evaleasy1entryin) = 40
3.65/1.71	
3.65/1.71		Pol(evaleasy1bb3in) = -V_1 + 40
3.65/1.71	
3.65/1.71		Pol(evaleasy1bbin) = -V_1 + 39
3.65/1.71	
3.65/1.71		Pol(evaleasy1returnin) = -V_1
3.65/1.71	
3.65/1.71		Pol(evaleasy1bb1in) = -V_1 + 39
3.65/1.71	
3.65/1.71		Pol(evaleasy1bb2in) = -V_1 + 39
3.65/1.71	
3.65/1.71		Pol(evaleasy1stop) = -V_1
3.65/1.71	
3.65/1.71		Pol(koat_start) = 40
3.65/1.71	
3.65/1.71	orients all transitions weakly and the transition
3.65/1.71	
3.65/1.71		evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1bbin(ar_0, ar_1)) [ 39 >= ar_0 ]
3.65/1.71	
3.65/1.71	strictly and produces the following problem:
3.65/1.71	
3.65/1.71	4:	T:
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)     evaleasy1start(ar_0, ar_1) -> Com_1(evaleasy1entryin(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)     evaleasy1entryin(ar_0, ar_1) -> Com_1(evaleasy1bb3in(0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 40, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1bbin(ar_0, ar_1)) [ 39 >= ar_0 ]
3.65/1.71	
3.65/1.71			(Comp: 2, Cost: 1)     evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1returnin(ar_0, ar_1)) [ ar_0 >= 40 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)     evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb1in(ar_0, ar_1)) [ ar_1 = 0 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)     evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)     evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ ar_1 >= 1 ]
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)     evaleasy1bb1in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 1, ar_1))
3.65/1.71	
3.65/1.71			(Comp: ?, Cost: 1)     evaleasy1bb2in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 2, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 2, Cost: 1)     evaleasy1returnin(ar_0, ar_1) -> Com_1(evaleasy1stop(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1) -> Com_1(evaleasy1start(ar_0, ar_1)) [ 0 <= 0 ]
3.65/1.71	
3.65/1.71		start location:	koat_start
3.65/1.71	
3.65/1.71		leaf cost:	0
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	Repeatedly propagating knowledge in problem 4 produces the following problem:
3.65/1.71	
3.65/1.71	5:	T:
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)     evaleasy1start(ar_0, ar_1) -> Com_1(evaleasy1entryin(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 1)     evaleasy1entryin(ar_0, ar_1) -> Com_1(evaleasy1bb3in(0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 40, Cost: 1)    evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1bbin(ar_0, ar_1)) [ 39 >= ar_0 ]
3.65/1.71	
3.65/1.71			(Comp: 2, Cost: 1)     evaleasy1bb3in(ar_0, ar_1) -> Com_1(evaleasy1returnin(ar_0, ar_1)) [ ar_0 >= 40 ]
3.65/1.71	
3.65/1.71			(Comp: 40, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb1in(ar_0, ar_1)) [ ar_1 = 0 ]
3.65/1.71	
3.65/1.71			(Comp: 40, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
3.65/1.71	
3.65/1.71			(Comp: 40, Cost: 1)    evaleasy1bbin(ar_0, ar_1) -> Com_1(evaleasy1bb2in(ar_0, ar_1)) [ ar_1 >= 1 ]
3.65/1.71	
3.65/1.71			(Comp: 40, Cost: 1)    evaleasy1bb1in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 1, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 80, Cost: 1)    evaleasy1bb2in(ar_0, ar_1) -> Com_1(evaleasy1bb3in(ar_0 + 2, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 2, Cost: 1)     evaleasy1returnin(ar_0, ar_1) -> Com_1(evaleasy1stop(ar_0, ar_1))
3.65/1.71	
3.65/1.71			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1) -> Com_1(evaleasy1start(ar_0, ar_1)) [ 0 <= 0 ]
3.65/1.71	
3.65/1.71		start location:	koat_start
3.65/1.71	
3.65/1.71		leaf cost:	0
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	Complexity upper bound 286
3.65/1.71	
3.65/1.71	
3.65/1.71	
3.65/1.71	Time: 0.082 sec (SMT: 0.076 sec)
3.65/1.71	
3.65/1.71	
3.65/1.71	----------------------------------------
3.65/1.71	
3.65/1.71	(2)
3.65/1.71	BOUNDS(1, 1)
3.70/1.73	EOF