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SRS Stand 10685 pair #381717252
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
n090.star.cs.uiowa.edu
space
Trafo_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.52173399925 seconds
cpu usage
10.112072712
max memory
9.39425792E8
stage attributes
key
value
output-size
8461
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 16 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) MNOCProof [EQUIVALENT, 5 ms] (9) QDP (10) QDPOrderProof [EQUIVALENT, 29 ms] (11) QDP (12) QDPOrderProof [EQUIVALENT, 10 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) QDPOrderProof [EQUIVALENT, 26 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))
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