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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313301
details
property
value
status
complete
benchmark
wst99.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.618 seconds
cpu usage
357.78
user time
354.478
system time
3.30255
max virtual memory
3.730892E7
max residence set size
6513180.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
357.16/291.45 WORST_CASE(Omega(n^1), O(n^2)) 357.16/291.46 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 357.16/291.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 357.16/291.46 357.16/291.46 357.16/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 357.16/291.46 357.16/291.46 (0) CpxTRS 357.16/291.46 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 15 ms] 357.16/291.46 (2) CdtProblem 357.16/291.46 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 357.16/291.46 (4) CdtProblem 357.16/291.46 (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 357.16/291.46 (6) CdtProblem 357.16/291.46 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 116 ms] 357.16/291.46 (8) CdtProblem 357.16/291.46 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 30 ms] 357.16/291.46 (10) CdtProblem 357.16/291.46 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 28 ms] 357.16/291.46 (12) CdtProblem 357.16/291.46 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 171 ms] 357.16/291.46 (14) CdtProblem 357.16/291.46 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 180 ms] 357.16/291.46 (16) CdtProblem 357.16/291.46 (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 357.16/291.46 (18) BOUNDS(1, 1) 357.16/291.46 (19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 357.16/291.46 (20) TRS for Loop Detection 357.16/291.46 (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 357.16/291.46 (22) BEST 357.16/291.46 (23) proven lower bound 357.16/291.46 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 357.16/291.46 (25) BOUNDS(n^1, INF) 357.16/291.46 (26) TRS for Loop Detection 357.16/291.46 357.16/291.46 357.16/291.46 ---------------------------------------- 357.16/291.46 357.16/291.46 (0) 357.16/291.46 Obligation: 357.16/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 357.16/291.46 357.16/291.46 357.16/291.46 The TRS R consists of the following rules: 357.16/291.46 357.16/291.46 din(der(plus(X, Y))) -> u21(din(der(X)), X, Y) 357.16/291.46 u21(dout(DX), X, Y) -> u22(din(der(Y)), X, Y, DX) 357.16/291.46 u22(dout(DY), X, Y, DX) -> dout(plus(DX, DY)) 357.16/291.46 din(der(times(X, Y))) -> u31(din(der(X)), X, Y) 357.16/291.46 u31(dout(DX), X, Y) -> u32(din(der(Y)), X, Y, DX) 357.16/291.46 u32(dout(DY), X, Y, DX) -> dout(plus(times(X, DY), times(Y, DX))) 357.16/291.46 din(der(der(X))) -> u41(din(der(X)), X) 357.16/291.46 u41(dout(DX), X) -> u42(din(der(DX)), X, DX) 357.16/291.46 u42(dout(DDX), X, DX) -> dout(DDX) 357.16/291.46 357.16/291.46 S is empty. 357.16/291.46 Rewrite Strategy: INNERMOST 357.16/291.46 ---------------------------------------- 357.16/291.46 357.16/291.46 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 357.16/291.46 Converted Cpx (relative) TRS to CDT 357.16/291.46 ---------------------------------------- 357.16/291.46 357.16/291.46 (2) 357.16/291.46 Obligation: 357.16/291.46 Complexity Dependency Tuples Problem 357.16/291.46 357.16/291.46 Rules: 357.16/291.46 din(der(plus(z0, z1))) -> u21(din(der(z0)), z0, z1) 357.16/291.46 din(der(times(z0, z1))) -> u31(din(der(z0)), z0, z1) 357.16/291.46 din(der(der(z0))) -> u41(din(der(z0)), z0) 357.16/291.46 u21(dout(z0), z1, z2) -> u22(din(der(z2)), z1, z2, z0) 357.16/291.46 u22(dout(z0), z1, z2, z3) -> dout(plus(z3, z0)) 357.16/291.46 u31(dout(z0), z1, z2) -> u32(din(der(z2)), z1, z2, z0) 357.16/291.46 u32(dout(z0), z1, z2, z3) -> dout(plus(times(z1, z0), times(z2, z3))) 357.16/291.46 u41(dout(z0), z1) -> u42(din(der(z0)), z1, z0) 357.16/291.46 u42(dout(z0), z1, z2) -> dout(z0) 357.16/291.46 Tuples: 357.16/291.46 DIN(der(plus(z0, z1))) -> c(U21(din(der(z0)), z0, z1), DIN(der(z0))) 357.16/291.46 DIN(der(times(z0, z1))) -> c1(U31(din(der(z0)), z0, z1), DIN(der(z0))) 357.16/291.46 DIN(der(der(z0))) -> c2(U41(din(der(z0)), z0), DIN(der(z0))) 357.16/291.46 U21(dout(z0), z1, z2) -> c3(U22(din(der(z2)), z1, z2, z0), DIN(der(z2))) 357.16/291.46 U22(dout(z0), z1, z2, z3) -> c4 357.16/291.46 U31(dout(z0), z1, z2) -> c5(U32(din(der(z2)), z1, z2, z0), DIN(der(z2))) 357.16/291.46 U32(dout(z0), z1, z2, z3) -> c6 357.16/291.46 U41(dout(z0), z1) -> c7(U42(din(der(z0)), z1, z0), DIN(der(z0))) 357.16/291.46 U42(dout(z0), z1, z2) -> c8 357.16/291.46 S tuples: 357.16/291.46 DIN(der(plus(z0, z1))) -> c(U21(din(der(z0)), z0, z1), DIN(der(z0))) 357.16/291.46 DIN(der(times(z0, z1))) -> c1(U31(din(der(z0)), z0, z1), DIN(der(z0))) 357.16/291.46 DIN(der(der(z0))) -> c2(U41(din(der(z0)), z0), DIN(der(z0))) 357.16/291.46 U21(dout(z0), z1, z2) -> c3(U22(din(der(z2)), z1, z2, z0), DIN(der(z2))) 357.16/291.46 U22(dout(z0), z1, z2, z3) -> c4 357.16/291.46 U31(dout(z0), z1, z2) -> c5(U32(din(der(z2)), z1, z2, z0), DIN(der(z2))) 357.16/291.46 U32(dout(z0), z1, z2, z3) -> c6 357.16/291.46 U41(dout(z0), z1) -> c7(U42(din(der(z0)), z1, z0), DIN(der(z0))) 357.16/291.46 U42(dout(z0), z1, z2) -> c8 357.16/291.46 K tuples:none 357.16/291.46 Defined Rule Symbols: din_1, u21_3, u22_4, u31_3, u32_4, u41_2, u42_3 357.16/291.46
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