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TRS Outer 67415 pair #381917997
details
property
value
status
complete
benchmark
ex1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Mixed_outermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.59122991562 seconds
cpu usage
4.120172621
max memory
3.13397248E8
stage attributes
key
value
output-size
12889
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof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, 40 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 26 ms] (6) QTRS (7) AAECC Innermost [EQUIVALENT, 0 ms] (8) QTRS (9) DependencyPairsProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: f(g(a)) -> a f(f(x)) -> b g(x) -> f(g(x)) 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(g(a))) -> up(a) down(f(f(x))) -> up(b) down(g(x)) -> up(f(g(x))) top(up(x)) -> top(down(x)) down(f(a)) -> f_flat(down(a)) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(f(g(f(y6)))) -> f_flat(down(g(f(y6)))) down(f(g(g(y7)))) -> f_flat(down(g(g(y7)))) down(f(g(b))) -> f_flat(down(g(b))) down(f(g(fresh_constant))) -> f_flat(down(g(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(a) = 0 POL(b) = 0 POL(down(x_1)) = 2 + 2*x_1 POL(f(x_1)) = x_1 POL(f_flat(x_1)) = x_1 POL(fresh_constant) = 0 POL(g(x_1)) = x_1 POL(g_flat(x_1)) = 1 + 2*x_1 POL(top(x_1)) = 2*x_1 POL(up(x_1)) = 2 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g_flat(up(x_1)) -> up(g(x_1)) ----------------------------------------
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