details

property	value
status	complete
benchmark	dup06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	7.54445815086 seconds
cpu usage	26.641486818
max memory	1.437585408E9

stage attributes

key	value
output-size	8526
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 4 ms] (7) QDP (8) MNOCProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPOrderProof [EQUIVALENT, 54 ms] (11) QDP (12) QDPOrderProof [EQUIVALENT, 28 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) QDPOrderProof [EQUIVALENT, 95 ms] (18) QDP (19) PisEmptyProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: A(a(b(b(x1)))) -> B(b(c(c(a(a(x1)))))) A(a(b(b(x1)))) -> B(c(c(a(a(x1))))) A(a(b(b(x1)))) -> A(a(x1)) A(a(b(b(x1)))) -> A(x1) B(b(c(c(x1)))) -> B(b(b(b(x1)))) B(b(c(c(x1)))) -> B(b(b(x1))) B(b(c(c(x1)))) -> B(b(x1)) B(b(c(c(x1)))) -> B(x1) B(b(a(a(x1)))) -> A(a(c(c(b(b(x1)))))) B(b(a(a(x1)))) -> A(c(c(b(b(x1))))) B(b(a(a(x1)))) -> B(b(x1)) B(b(a(a(x1)))) -> B(x1) The TRS R consists of the following rules: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 4 less nodes. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Q DP problem: The TRS P consists of the following rules: B(b(c(c(x1)))) -> B(b(b(x1))) B(b(c(c(x1)))) -> B(b(b(b(x1)))) B(b(c(c(x1)))) -> B(b(x1)) popout

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