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TRS Stand 20472 pair #381712566
details
property
value
status
complete
benchmark
24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n079.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.93449807167 seconds
cpu usage
4.580709433
max memory
2.15908352E8
stage attributes
key
value
output-size
5654
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 73 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 16 ms] (4) QTRS (5) Overlay + Local Confluence [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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: max(L(x)) -> x max(N(L(0), L(y))) -> y max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z))))) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(L(x_1)) = x_1 POL(N(x_1, x_2)) = 2*x_1 + 2*x_2 POL(max(x_1)) = x_1 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: max(N(L(0), L(y))) -> y ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: max(L(x)) -> x max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z))))) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(L(x_1)) = x_1 POL(N(x_1, x_2)) = x_1 + x_2 POL(max(x_1)) = x_1 POL(s(x_1)) = 1 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y)))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules:
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