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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313677
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
n128.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.517 seconds
cpu usage
325.595
user time
323.202
system time
2.39281
max virtual memory
1.9149512E7
max residence set size
5379296.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
325.47/291.47 WORST_CASE(Omega(n^1), O(n^2)) 325.53/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 325.53/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 325.53/291.48 325.53/291.48 325.53/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 325.53/291.48 325.53/291.48 (0) CpxTRS 325.53/291.48 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 325.53/291.48 (2) CdtProblem 325.53/291.48 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 325.53/291.48 (4) CdtProblem 325.53/291.48 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 325.53/291.48 (6) CdtProblem 325.53/291.48 (7) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 325.53/291.48 (8) CdtProblem 325.53/291.48 (9) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 325.53/291.48 (10) CdtProblem 325.53/291.48 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 10 ms] 325.53/291.48 (12) CdtProblem 325.53/291.48 (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 325.53/291.48 (14) CdtProblem 325.53/291.48 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 40 ms] 325.53/291.48 (16) CdtProblem 325.53/291.48 (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 49 ms] 325.53/291.48 (18) CdtProblem 325.53/291.48 (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 325.53/291.48 (20) BOUNDS(1, 1) 325.53/291.48 (21) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 325.53/291.48 (22) TRS for Loop Detection 325.53/291.48 (23) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 325.53/291.48 (24) BEST 325.53/291.48 (25) proven lower bound 325.53/291.48 (26) LowerBoundPropagationProof [FINISHED, 0 ms] 325.53/291.48 (27) BOUNDS(n^1, INF) 325.53/291.48 (28) TRS for Loop Detection 325.53/291.48 325.53/291.48 325.53/291.48 ---------------------------------------- 325.53/291.48 325.53/291.48 (0) 325.53/291.48 Obligation: 325.53/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 325.53/291.48 325.53/291.48 325.53/291.48 The TRS R consists of the following rules: 325.53/291.48 325.53/291.48 r(xs, ys, zs, nil) -> xs 325.53/291.48 r(xs, nil, zs, cons(w, ws)) -> r(xs, xs, cons(succ(zero), zs), ws) 325.53/291.48 r(xs, cons(y, ys), nil, cons(w, ws)) -> r(xs, xs, cons(succ(zero), nil), ws) 325.53/291.48 r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) -> r(ys, cons(y, ys), zs, cons(succ(zero), cons(w, ws))) 325.53/291.48 325.53/291.48 S is empty. 325.53/291.48 Rewrite Strategy: INNERMOST 325.53/291.48 ---------------------------------------- 325.53/291.48 325.53/291.48 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 325.53/291.48 Converted Cpx (relative) TRS to CDT 325.53/291.48 ---------------------------------------- 325.53/291.48 325.53/291.48 (2) 325.53/291.48 Obligation: 325.53/291.48 Complexity Dependency Tuples Problem 325.53/291.48 325.53/291.48 Rules: 325.53/291.48 r(z0, z1, z2, nil) -> z0 325.53/291.48 r(z0, nil, z1, cons(z2, z3)) -> r(z0, z0, cons(succ(zero), z1), z3) 325.53/291.48 r(z0, cons(z1, z2), nil, cons(z3, z4)) -> r(z0, z0, cons(succ(zero), nil), z4) 325.53/291.48 r(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> r(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6))) 325.53/291.48 Tuples: 325.53/291.48 R(z0, z1, z2, nil) -> c 325.53/291.48 R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3)) 325.53/291.48 R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4)) 325.53/291.48 R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))) 325.53/291.48 S tuples: 325.53/291.48 R(z0, z1, z2, nil) -> c 325.53/291.48 R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3)) 325.53/291.48 R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4)) 325.53/291.48 R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))) 325.53/291.48 K tuples:none 325.53/291.48 Defined Rule Symbols: r_4 325.53/291.48 325.53/291.48 Defined Pair Symbols: R_4 325.53/291.48 325.53/291.48 Compound Symbols: c, c1_1, c2_1, c3_1 325.53/291.48 325.53/291.48 325.53/291.48 ---------------------------------------- 325.53/291.48 325.53/291.48 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 325.53/291.48 Removed 1 trailing nodes: 325.53/291.48 R(z0, z1, z2, nil) -> c 325.53/291.48 325.53/291.48 ---------------------------------------- 325.53/291.48 325.53/291.48 (4) 325.53/291.48 Obligation: 325.53/291.48 Complexity Dependency Tuples Problem 325.53/291.48 325.53/291.48 Rules:
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40