details

property	value
status	complete
benchmark	Ex6_GM04_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.565 seconds
cpu usage	312.809
user time	309.959
system time	2.85028
max virtual memory	5.6829356E7
max residence set size	5174700.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 42 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 13 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: a__c -> a__f(g(c)) a__f(g(X)) -> g(X) mark(c) -> a__c mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) a__c -> c a__f(X) -> f(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(g(x_1)) -> g(encArg(x_1)) encArg(c) -> c encArg(f(x_1)) -> f(encArg(x_1)) encArg(cons_a__c) -> a__c encArg(cons_a__f(x_1)) -> a__f(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__c -> a__c encode_a__f(x_1) -> a__f(encArg(x_1)) encode_g(x_1) -> g(encArg(x_1)) encode_c -> c encode_mark(x_1) -> mark(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: a__c -> a__f(g(c)) a__f(g(X)) -> g(X) mark(c) -> a__c mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) a__c -> c a__f(X) -> f(X) The (relative) TRS S consists of the following rules: encArg(g(x_1)) -> g(encArg(x_1)) encArg(c) -> c encArg(f(x_1)) -> f(encArg(x_1)) encArg(cons_a__c) -> a__c encArg(cons_a__f(x_1)) -> a__f(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__c -> a__c encode_a__f(x_1) -> a__f(encArg(x_1)) encode_g(x_1) -> g(encArg(x_1)) encode_c -> c encode_mark(x_1) -> mark(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). popout

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actions

all output return to Derivational Complexity: TRS