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Derivational Complexity: TRS Innermost pair #487105304
details
property
value
status
complete
benchmark
#4.15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.485 seconds
cpu usage
371.423
user time
368.839
system time
2.58397
max virtual memory
1.9144432E7
max residence set size
5130748.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 192 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 117 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 334 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 315 ms] (22) CdtProblem (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (24) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: f(0, 1, g(x, y), z) -> f(g(x, y), g(x, y), g(x, y), h(x)) g(0, 1) -> 0 g(0, 1) -> 1 h(g(x, y)) -> h(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(1) -> 1 encArg(cons_f(x_1, x_2, x_3, x_4)) -> f(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_h(x_1)) -> h(encArg(x_1)) encode_f(x_1, x_2, x_3, x_4) -> f(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_0 -> 0 encode_1 -> 1 encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_h(x_1) -> h(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: f(0, 1, g(x, y), z) -> f(g(x, y), g(x, y), g(x, y), h(x)) g(0, 1) -> 0 g(0, 1) -> 1 h(g(x, y)) -> h(x) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(1) -> 1 encArg(cons_f(x_1, x_2, x_3, x_4)) -> f(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_h(x_1)) -> h(encArg(x_1)) encode_f(x_1, x_2, x_3, x_4) -> f(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_0 -> 0 encode_1 -> 1 encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_h(x_1) -> h(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ----------------------------------------
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