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Derivational Complexity: TRS pair #487100828
details
property
value
status
complete
benchmark
2.01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.606 seconds
cpu usage
309.126
user time
307.158
system time
1.96761
max virtual memory
3.7446528E7
max residence set size
5116108.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 174 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (16) CdtProblem (17) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 238 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 131 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 511 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 470 ms] (26) CdtProblem (27) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (28) BOUNDS(1, 1) (29) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRelTRS (31) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (32) typed CpxTrs (33) OrderProof [LOWER BOUND(ID), 0 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 202 ms] (36) proven lower bound (37) LowerBoundPropagationProof [FINISHED, 0 ms] (38) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: i(0) -> 0 +(0, y) -> y +(x, 0) -> x i(i(x)) -> x +(i(x), x) -> 0 +(x, i(x)) -> 0 i(+(x, y)) -> +(i(x), i(y)) +(x, +(y, z)) -> +(+(x, y), z) +(+(x, i(y)), y) -> x +(+(x, y), i(y)) -> x S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(cons_i(x_1)) -> i(encArg(x_1)) encArg(cons_+(x_1, x_2)) -> +(encArg(x_1), encArg(x_2)) encode_i(x_1) -> i(encArg(x_1)) encode_0 -> 0 encode_+(x_1, x_2) -> +(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: i(0) -> 0 +(0, y) -> y +(x, 0) -> x i(i(x)) -> x +(i(x), x) -> 0 +(x, i(x)) -> 0 i(+(x, y)) -> +(i(x), i(y)) +(x, +(y, z)) -> +(+(x, y), z)
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