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TRS Innermost pair #516979427
details
property
value
status
complete
benchmark
Ex16_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.18520712852 seconds
cpu usage
5.61947505
max memory
4.76377088E8
stage attributes
key
value
output-size
2586
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 96 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(X, X) -> a__f(a, b) a__b -> a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> a__b mark(a) -> a a__f(X1, X2) -> f(X1, X2) a__b -> b The set Q consists of the following terms: a__b mark(f(x0, x1)) mark(b) mark(a) a__f(x0, x1) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [a__b, mark_1] > a__f_2 > [a, b, f_2] Status: a__f_2: [1,2] a: multiset status b: multiset status a__b: multiset status mark_1: [1] f_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__b -> a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> a__b mark(a) -> a a__f(X1, X2) -> f(X1, X2) a__b -> b ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(X, X) -> a__f(a, b) The set Q consists of the following terms: a__b mark(f(x0, x1)) mark(b) mark(a) a__f(x0, x1) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation:
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