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Derivational Complexity: TRS Innermost pair #487109340
details
property
value
status
complete
benchmark
z29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
3.65152 seconds
cpu usage
11.4697
user time
10.7073
system time
0.762379
max virtual memory
1.8645308E7
max residence set size
2482080.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 168 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 58 ms] (16) CdtProblem (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (18) BOUNDS(1, 1) (19) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRelTRS (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) typed CpxTrs (23) OrderProof [LOWER BOUND(ID), 0 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 298 ms] (26) proven lower bound (27) LowerBoundPropagationProof [FINISHED, 0 ms] (28) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a(lambda(x), y) -> lambda(a(x, 1)) a(lambda(x), y) -> lambda(a(x, a(y, t))) a(a(x, y), z) -> a(x, a(y, z)) lambda(x) -> x a(x, y) -> x a(x, y) -> y 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(1) -> 1 encArg(t) -> t encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(cons_lambda(x_1)) -> lambda(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_lambda(x_1) -> lambda(encArg(x_1)) encode_1 -> 1 encode_t -> t ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a(lambda(x), y) -> lambda(a(x, 1)) a(lambda(x), y) -> lambda(a(x, a(y, t))) a(a(x, y), z) -> a(x, a(y, z)) lambda(x) -> x a(x, y) -> x a(x, y) -> y The (relative) TRS S consists of the following rules: encArg(1) -> 1 encArg(t) -> t encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(cons_lambda(x_1)) -> lambda(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_lambda(x_1) -> lambda(encArg(x_1)) encode_1 -> 1 encode_t -> t Rewrite Strategy: INNERMOST ----------------------------------------
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