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TRS Innermost pair #487093205
details
property
value
status
complete
benchmark
Ex15_Luc06_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68432 seconds
cpu usage
3.50464
user time
3.3419
system time
0.162743
max virtual memory
1.8279436E7
max residence set size
248268.0
stage attributes
key
value
starexec-result
YES
output
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES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: active(f(f(a))) -> mark(f(g(f(a)))) mark(f(X)) -> active(f(X)) mark(a) -> active(a) mark(g(X)) -> active(g(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) The set Q consists of the following terms: active(f(f(a))) mark(f(x0)) mark(a) mark(g(x0)) f(mark(x0)) f(active(x0)) g(mark(x0)) g(active(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: active(f(f(a))) -> mark(f(g(f(a)))) mark(f(X)) -> active(f(X)) mark(a) -> active(a) mark(g(X)) -> active(g(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) g(mark(X)) -> g(X) g(active(X)) -> g(X) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled mark_1(0)* 1 to 7 labelled active_1(0)* 1 to 6 labelled active_1(0)* 1 to 8 labelled active_1(0)* 1 to 2 labelled f_1(0), g_1(0), f_1(1), g_1(1)* 1 to 10 labelled active_1(1)* 1 to 13 labelled mark_1(1)* 1 to 17 labelled active_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled f_1(0)* 4 to 5 labelled g_1(0)* 5 to 6 labelled f_1(0)* 6 to 2 labelled a(0)* 7 to 2 labelled f_1(0), f_1(1), a(1)* 8 to 9 labelled g_1(0)* 8 to 2 labelled g_1(1)* 8 to 7 labelled g_1(1)* 8 to 11 labelled g_1(1)* 8 to 13 labelled g_1(1)* 8 to 17 labelled g_1(1)* 9 to 2 labelled mark_1(0)* 9 to 7 labelled active_1(1)* 9 to 11 labelled active_1(1)* 9 to 13 labelled mark_1(1)* 9 to 17 labelled active_1(2)* 10 to 4 labelled f_1(1)* 11 to 12 labelled g_1(1)* 11 to 2 labelled g_1(2), g_1(1)* 11 to 7 labelled g_1(2)* 11 to 11 labelled g_1(2)* 11 to 13 labelled g_1(2)* 11 to 17 labelled g_1(2)* 12 to 2 labelled mark_1(1)* 12 to 7 labelled active_1(1)* 12 to 11 labelled active_1(1)* 12 to 13 labelled mark_1(1)* 12 to 17 labelled active_1(2)* 13 to 14 labelled f_1(1)* 14 to 15 labelled g_1(1)* 15 to 16 labelled f_1(1)* 16 to 2 labelled a(1)* 17 to 14 labelled f_1(2) ---------------------------------------- (2) YES
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