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Runti Compl Inner Rewri 22807 pair #381904726
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
n039.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.503777981 seconds
cpu usage
355.651873271
max memory
6.638936064E9
stage attributes
key
value
output-size
27921
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 15 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 123 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 39 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 26 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 150 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 890 ms] (16) CdtProblem (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (18) BOUNDS(1, 1) (19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (20) TRS for Loop Detection (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: din(der(plus(X, Y))) -> u21(din(der(X)), X, Y) u21(dout(DX), X, Y) -> u22(din(der(Y)), X, Y, DX) u22(dout(DY), X, Y, DX) -> dout(plus(DX, DY)) din(der(times(X, Y))) -> u31(din(der(X)), X, Y) u31(dout(DX), X, Y) -> u32(din(der(Y)), X, Y, DX) u32(dout(DY), X, Y, DX) -> dout(plus(times(X, DY), times(Y, DX))) din(der(der(X))) -> u41(din(der(X)), X) u41(dout(DX), X) -> u42(din(der(DX)), X, DX) u42(dout(DDX), X, DX) -> dout(DDX) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: din(der(plus(z0, z1))) -> u21(din(der(z0)), z0, z1) din(der(times(z0, z1))) -> u31(din(der(z0)), z0, z1) din(der(der(z0))) -> u41(din(der(z0)), z0) u21(dout(z0), z1, z2) -> u22(din(der(z2)), z1, z2, z0) u22(dout(z0), z1, z2, z3) -> dout(plus(z3, z0)) u31(dout(z0), z1, z2) -> u32(din(der(z2)), z1, z2, z0) u32(dout(z0), z1, z2, z3) -> dout(plus(times(z1, z0), times(z2, z3))) u41(dout(z0), z1) -> u42(din(der(z0)), z1, z0) u42(dout(z0), z1, z2) -> dout(z0) Tuples: DIN(der(plus(z0, z1))) -> c(U21(din(der(z0)), z0, z1), DIN(der(z0))) DIN(der(times(z0, z1))) -> c1(U31(din(der(z0)), z0, z1), DIN(der(z0))) DIN(der(der(z0))) -> c2(U41(din(der(z0)), z0), DIN(der(z0))) U21(dout(z0), z1, z2) -> c3(U22(din(der(z2)), z1, z2, z0), DIN(der(z2))) U22(dout(z0), z1, z2, z3) -> c4 U31(dout(z0), z1, z2) -> c5(U32(din(der(z2)), z1, z2, z0), DIN(der(z2))) U32(dout(z0), z1, z2, z3) -> c6 U41(dout(z0), z1) -> c7(U42(din(der(z0)), z1, z0), DIN(der(z0))) U42(dout(z0), z1, z2) -> c8 S tuples: DIN(der(plus(z0, z1))) -> c(U21(din(der(z0)), z0, z1), DIN(der(z0))) DIN(der(times(z0, z1))) -> c1(U31(din(der(z0)), z0, z1), DIN(der(z0))) DIN(der(der(z0))) -> c2(U41(din(der(z0)), z0), DIN(der(z0))) U21(dout(z0), z1, z2) -> c3(U22(din(der(z2)), z1, z2, z0), DIN(der(z2))) U22(dout(z0), z1, z2, z3) -> c4 U31(dout(z0), z1, z2) -> c5(U32(din(der(z2)), z1, z2, z0), DIN(der(z2)))
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