details

property	value
status	complete
benchmark	sizeChange.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	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.514 seconds
cpu usage	321.499
user time	319.137
system time	2.36222
max virtual memory	1.9078288E7
max residence set size	5372544.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (10) CdtProblem (11) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 11 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 66 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 33 ms] (18) CdtProblem (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (20) BOUNDS(1, 1) (21) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTRS (23) SlicingProof [LOWER BOUND(ID), 0 ms] (24) CpxTRS (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) typed CpxTrs (27) OrderProof [LOWER BOUND(ID), 0 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 347 ms] (30) proven lower bound (31) LowerBoundPropagationProof [FINISHED, 0 ms] (32) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: r(xs, ys, zs, nil) -> xs r(xs, nil, zs, cons(w, ws)) -> r(xs, xs, cons(succ(zero), zs), ws) r(xs, cons(y, ys), nil, cons(w, ws)) -> r(xs, xs, cons(succ(zero), nil), ws) r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) -> r(ys, cons(y, ys), zs, cons(succ(zero), cons(w, ws))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: r(z0, z1, z2, nil) -> z0 r(z0, nil, z1, cons(z2, z3)) -> r(z0, z0, cons(succ(zero), z1), z3) r(z0, cons(z1, z2), nil, cons(z3, z4)) -> r(z0, z0, cons(succ(zero), nil), z4) r(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> r(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6))) Tuples: R(z0, z1, z2, nil) -> c R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3)) R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4)) R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))) S tuples: R(z0, z1, z2, nil) -> c R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3)) R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4)) R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))) K tuples:none Defined Rule Symbols: r_4 Defined Pair Symbols: R_4 Compound Symbols: c, c1_1, c2_1, c3_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: R(z0, z1, z2, nil) -> c ---------------------------------------- (4) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS Innermost