details

property	value
status	complete
benchmark	4.51.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n160.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.77798604965 seconds
cpu usage	4.505204199
max memory	2.73084416E8

stage attributes

key	value
output-size	4554
starexec-result	"YES"

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 45 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a) -> g(h(a)) h(g(x)) -> g(h(f(x))) k(x, h(x), a) -> h(x) k(f(x), y, x) -> f(x) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(f(x_1)) = x_1 POL(g(x_1)) = 2*x_1 POL(h(x_1)) = x_1 POL(k(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + x_3 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: k(x, h(x), a) -> h(x) k(f(x), y, x) -> f(x) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a) -> g(h(a)) h(g(x)) -> g(h(f(x))) Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a) -> g(h(a)) h(g(x)) -> g(h(f(x))) The set Q consists of the following terms: f(a) h(g(x0)) ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (6) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard