Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Outer 67415 pair #381918082
details
property
value
status
complete
benchmark
g_2_const.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
Zantema_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.49202108383 seconds
cpu usage
3.639750597
max memory
2.668544E8
stage attributes
key
value
output-size
9250
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 45 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QReductionProof [EQUIVALENT, 0 ms] (14) QDP (15) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: f(x) -> g(f(x)) g(g(x)) -> c Outermost Strategy. ---------------------------------------- (1) Raffelsieper-Zantema-Transformation (SOUND) We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: down(f(x)) -> up(g(f(x))) down(g(g(x))) -> up(c) top(up(x)) -> top(down(x)) down(g(f(y3))) -> g_flat(down(f(y3))) down(g(c)) -> g_flat(down(c)) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(c) = 0 POL(down(x_1)) = 2*x_1 POL(f(x_1)) = x_1 POL(f_flat(x_1)) = 2 + x_1 POL(fresh_constant) = 0 POL(g(x_1)) = x_1 POL(g_flat(x_1)) = x_1 POL(top(x_1)) = 2*x_1 POL(up(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f_flat(up(x_1)) -> up(f(x_1)) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: down(f(x)) -> up(g(f(x))) down(g(g(x))) -> up(c) top(up(x)) -> top(down(x))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Outer 67415