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	n029.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.90743899345 seconds
cpu usage	6.262901783
max memory	4.7712256E8

stage attributes

key	value
output-size	5632
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 71 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5)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: max/1)YES( L/1)YES( N/2(YES,YES) s/1(YES) Quasi precedence: N_2 > s_1 Status: N_2: multiset status s_1: multiset status 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)))) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard