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TRS Standard pair #516965515
details
property
value
status
complete
benchmark
z26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n076.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
3.31471705437 seconds
cpu usage
9.35936349
max memory
5.54565632E8
stage attributes
key
value
output-size
6753
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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) QDP (5) MRRProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 36 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y)))))) f(a(x), a(y)) -> a(f(x, y)) f(b(x), b(y)) -> b(f(x, y)) 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(f(x, y))) -> F(a(b(a(b(a(x))))), a(b(a(b(a(y)))))) A(a(f(x, y))) -> A(b(a(b(a(x))))) A(a(f(x, y))) -> A(b(a(x))) A(a(f(x, y))) -> A(x) A(a(f(x, y))) -> A(b(a(b(a(y))))) A(a(f(x, y))) -> A(b(a(y))) A(a(f(x, y))) -> A(y) F(a(x), a(y)) -> A(f(x, y)) F(a(x), a(y)) -> F(x, y) F(b(x), b(y)) -> F(x, y) The TRS R consists of the following rules: a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y)))))) f(a(x), a(y)) -> a(f(x, y)) f(b(x), b(y)) -> b(f(x, y)) 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 1 SCC with 4 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(a(x), a(y)) -> A(f(x, y)) A(a(f(x, y))) -> F(a(b(a(b(a(x))))), a(b(a(b(a(y)))))) F(a(x), a(y)) -> F(x, y) F(b(x), b(y)) -> F(x, y) A(a(f(x, y))) -> A(x) A(a(f(x, y))) -> A(y) The TRS R consists of the following rules: a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y)))))) f(a(x), a(y)) -> a(f(x, y)) f(b(x), b(y)) -> b(f(x, y)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ----------------------------------------
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