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TRS Innermost pair #487524119
details
property
value
status
complete
benchmark
Ex15_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.67361783981 seconds
cpu usage
3.348314363
max memory
2.22265344E8
stage attributes
key
value
output-size
2117
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(X) mark(a) -> a mark(g(X)) -> g(mark(X)) a__f(X) -> f(X) The set Q consists of the following terms: mark(f(x0)) mark(a) mark(g(x0)) a__f(x0) ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(X) mark(a) -> a mark(g(X)) -> g(mark(X)) a__f(X) -> f(X) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6, 13, 14, 15, 16 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled a__f_1(0), f_1(1)* 1 to 2 labelled a__f_1(0), a(0), f_1(0), f_1(1)* 1 to 6 labelled g_1(0)* 1 to 13 labelled a__f_1(1), f_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled g_1(0)* 4 to 5 labelled f_1(0)* 5 to 2 labelled a(0)* 6 to 2 labelled mark_1(0), a__f_1(1), a(1), f_1(2)* 6 to 16 labelled g_1(1)* 6 to 13 labelled a__f_1(1), f_1(2)* 13 to 14 labelled g_1(1)* 14 to 15 labelled f_1(1)* 15 to 2 labelled a(1)* 16 to 2 labelled mark_1(1), a__f_1(1), a(1), f_1(2)* 16 to 16 labelled g_1(1)* 16 to 13 labelled a__f_1(1), f_1(2) ---------------------------------------- (2) YES
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