details

property	value
status	complete
benchmark	#4.35.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.42435 seconds
cpu usage	5.77864
user time	5.49386
system time	0.284779
max virtual memory	1.827736E7
max residence set size	718272.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) DecreasingLoopProof [FINISHED, 352 ms] (10) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: and(true, y) -> y and(false, y) -> false eq(nil, nil) -> true eq(cons(t, l), nil) -> false eq(nil, cons(t, l)) -> false eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l')) eq(var(l), var(l')) -> eq(l, l') eq(var(l), apply(t, s)) -> false eq(var(l), lambda(x, t)) -> false eq(apply(t, s), var(l)) -> false eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s')) eq(apply(t, s), lambda(x, t)) -> false eq(lambda(x, t), var(l)) -> false eq(lambda(x, t), apply(t, s)) -> false eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t')) if(true, var(k), var(l')) -> var(k) if(false, var(k), var(l')) -> var(l') ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l')) ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s)) ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: and(true, y) -> y and(false, y) -> false eq(nil, nil) -> true eq(cons(t, l), nil) -> false eq(nil, cons(t, l)) -> false eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l')) eq(var(l), var(l')) -> eq(l, l') eq(var(l), apply(t, s)) -> false eq(var(l), lambda(x, t)) -> false eq(apply(t, s), var(l)) -> false eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s')) eq(apply(t, s), lambda(x, t)) -> false eq(lambda(x, t), var(l)) -> false eq(lambda(x, t), apply(t, s)) -> false eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t')) if(true, var(k), var(l')) -> var(k) if(false, var(k), var(l')) -> var(l') ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l')) ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s)) ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence eq(lambda(x, t), lambda(x', t')) ->^+ and(eq(x, x'), eq(t, t')) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. popout

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actions

all output return to Runtime Complexity: TRS