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TRS Standard pair #516967630
details
property
value
status
complete
benchmark
#4.37a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n010.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.29586315155 seconds
cpu usage
6.059904742
max memory
4.75549696E8
stage attributes
key
value
output-size
7789
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 77 ms] (2) QTRS (3) AAECC Innermost [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) MRRProof [EQUIVALENT, 0 ms] (15) QDP (16) PisEmptyProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) MRRProof [EQUIVALENT, 0 ms] (24) QDP (25) PisEmptyProof [EQUIVALENT, 0 ms] (26) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(c(s(x), y)) -> f(c(x, s(y))) g(c(x, s(y))) -> g(c(s(x), y)) g(s(f(x))) -> g(f(x)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(c(x_1, x_2)) = 2*x_1 + 2*x_2 POL(f(x_1)) = 2*x_1 POL(g(x_1)) = 2*x_1 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(s(f(x))) -> g(f(x)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(c(s(x), y)) -> f(c(x, s(y))) g(c(x, s(y))) -> g(c(s(x), y)) Q is empty. ---------------------------------------- (3) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none The TRS R 2 is f(c(s(x), y)) -> f(c(x, s(y))) g(c(x, s(y))) -> g(c(s(x), y)) The signature Sigma is {f_1, g_1} ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules:
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