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TRS Outer 67415 pair #381918062
details
property
value
status
complete
benchmark
cariboo_add2a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
Zantema_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.66734409332 seconds
cpu usage
4.490991594
max memory
3.72928512E8
stage attributes
key
value
output-size
17803
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof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, 19 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 21 ms] (6) QTRS (7) AAECC Innermost [EQUIVALENT, 0 ms] (8) QTRS (9) DependencyPairsProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) AND (13) QDP (14) UsableRulesProof [EQUIVALENT, 0 ms] (15) QDP (16) QReductionProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) QReductionProof [EQUIVALENT, 0 ms] (24) QDP (25) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (26) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: f(h(x)) -> f(i(x)) h(x) -> f(h(x)) i(x) -> h(x) f(i(x)) -> 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(h(x))) -> up(f(i(x))) down(h(x)) -> up(f(h(x))) down(i(x)) -> up(h(x)) down(f(i(x))) -> up(x) top(up(x)) -> top(down(x)) down(f(f(y4))) -> f_flat(down(f(y4))) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) f_flat(up(x_1)) -> up(f(x_1)) h_flat(up(x_1)) -> up(h(x_1)) i_flat(up(x_1)) -> up(i(x_1)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: 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(h(x_1)) = x_1 POL(h_flat(x_1)) = 1 + 2*x_1 POL(i(x_1)) = x_1 POL(i_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:
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