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TRS Standard pair #487070018
details
property
value
status
complete
benchmark
Ex23_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.6979 seconds
cpu usage
3.71323
user time
3.54335
system time
0.169883
max virtual memory
1.8610432E7
max residence set size
267900.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 21 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(f(a))) -> mark(c(f(g(f(a))))) active(f(X)) -> f(active(X)) active(g(X)) -> g(active(X)) f(mark(X)) -> mark(f(X)) g(mark(X)) -> mark(g(X)) proper(f(X)) -> f(proper(X)) proper(a) -> ok(a) proper(c(X)) -> c(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(X)) c(ok(X)) -> ok(c(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a'(f(f(active(x)))) -> a'(f(g(f(c(mark(x)))))) f(active(X)) -> active(f(X)) g(active(X)) -> active(g(X)) mark(f(X)) -> f(mark(X)) mark(g(X)) -> g(mark(X)) f(proper(X)) -> proper(f(X)) a'(proper(x)) -> a'(ok(x)) c(proper(X)) -> proper(c(X)) g(proper(X)) -> proper(g(X)) ok(f(X)) -> f(ok(X)) ok(c(X)) -> c(ok(X)) ok(g(X)) -> g(ok(X)) mark(top(X)) -> proper(top(X)) ok(top(X)) -> active(top(X)) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 6. This implies Q-termination of R. The following rules were used to construct the certificate: a'(f(f(active(x)))) -> a'(f(g(f(c(mark(x)))))) f(active(X)) -> active(f(X)) g(active(X)) -> active(g(X)) mark(f(X)) -> f(mark(X)) mark(g(X)) -> g(mark(X)) f(proper(X)) -> proper(f(X)) a'(proper(x)) -> a'(ok(x)) c(proper(X)) -> proper(c(X)) g(proper(X)) -> proper(g(X)) ok(f(X)) -> f(ok(X)) ok(c(X)) -> c(ok(X)) ok(g(X)) -> g(ok(X)) mark(top(X)) -> proper(top(X)) ok(top(X)) -> active(top(X)) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 65, 66, 75, 76, 81, 83, 89, 90, 94, 95, 97, 98 Node 21 is start node and node 22 is final node. Those nodes are connected through the following edges: * 21 to 23 labelled a'_1(0), f_1(0), c_1(0), g_1(0)* 21 to 28 labelled active_1(0), proper_1(0)* 21 to 27 labelled f_1(0), g_1(0)* 21 to 33 labelled active_1(1), proper_1(1)* 21 to 37 labelled a'_1(1)* 21 to 56 labelled a'_1(2)* 22 to 22 labelled #_1(0)* 23 to 24 labelled f_1(0)* 23 to 22 labelled ok_1(0)* 23 to 29 labelled f_1(1), c_1(1), g_1(1)* 23 to 30 labelled active_1(1)* 23 to 35 labelled active_1(2)* 23 to 45 labelled proper_1(1)* 24 to 25 labelled g_1(0)* 24 to 42 labelled proper_1(1)* 25 to 26 labelled f_1(0)* 25 to 36 labelled proper_1(1)* 26 to 27 labelled c_1(0)* 26 to 34 labelled proper_1(1)* 27 to 22 labelled mark_1(0)* 27 to 31 labelled f_1(1), g_1(1)* 27 to 30 labelled proper_1(1)* 27 to 35 labelled proper_1(2)* 28 to 22 labelled f_1(0), g_1(0), c_1(0), top_1(0)* 28 to 32 labelled active_1(1), proper_1(1)* 29 to 22 labelled ok_1(1)* 29 to 29 labelled f_1(1), c_1(1), g_1(1)* 29 to 30 labelled active_1(1)* 29 to 35 labelled active_1(2)* 30 to 22 labelled top_1(1)* 31 to 22 labelled mark_1(1)* 31 to 31 labelled f_1(1), g_1(1)* 31 to 30 labelled proper_1(1)* 31 to 35 labelled proper_1(2)* 32 to 22 labelled f_1(1), g_1(1), c_1(1)* 32 to 32 labelled active_1(1), proper_1(1)* 33 to 30 labelled f_1(1), g_1(1)* 33 to 35 labelled f_1(1), g_1(1)* 33 to 45 labelled f_1(1), c_1(1), g_1(1)* 34 to 30 labelled c_1(1)* 34 to 35 labelled c_1(1)* 35 to 30 labelled f_1(2), g_1(2)* 35 to 35 labelled f_1(2), g_1(2)* 36 to 34 labelled f_1(1)* 37 to 38 labelled f_1(1)* 37 to 45 labelled ok_1(1)* 37 to 51 labelled f_1(2)* 37 to 54 labelled proper_1(2)* 38 to 39 labelled g_1(1)* 38 to 52 labelled proper_1(2)* 39 to 40 labelled f_1(1)* 39 to 49 labelled proper_1(2)* 40 to 41 labelled c_1(1)* 40 to 46 labelled proper_1(2)* 41 to 30 labelled mark_1(1)* 41 to 43 labelled proper_1(2)* 41 to 35 labelled mark_1(1)* 41 to 47 labelled f_1(2), g_1(2)* 41 to 53 labelled proper_1(3)* 42 to 36 labelled g_1(1)* 43 to 22 labelled top_1(2)* 45 to 42 labelled f_1(1)* 46 to 43 labelled c_1(2)* 46 to 53 labelled c_1(2)* 47 to 30 labelled mark_1(2)* 47 to 35 labelled mark_1(2)* 47 to 43 labelled proper_1(2)* 47 to 50 labelled f_1(3), g_1(3)* 47 to 53 labelled proper_1(3)* 47 to 57 labelled proper_1(4)* 49 to 46 labelled f_1(2)* 50 to 30 labelled mark_1(3)* 50 to 35 labelled mark_1(3)* 50 to 43 labelled proper_1(2)* 50 to 50 labelled f_1(3), g_1(3)* 50 to 53 labelled proper_1(3)* 50 to 57 labelled proper_1(4)* 51 to 42 labelled ok_1(2)* 51 to 55 labelled g_1(2)* 52 to 49 labelled g_1(2)* 53 to 43 labelled f_1(3), g_1(3)* 53 to 53 labelled f_1(3), g_1(3)* 53 to 57 labelled f_1(3), g_1(3)* 54 to 52 labelled f_1(2)* 55 to 36 labelled ok_1(2)* 55 to 58 labelled f_1(2)* 56 to 54 labelled ok_1(2)* 56 to 65 labelled f_1(3)* 57 to 53 labelled f_1(4), g_1(4)* 57 to 57 labelled f_1(4), g_1(4)* 58 to 34 labelled ok_1(2)* 58 to 66 labelled c_1(2)* 65 to 52 labelled ok_1(3)* 65 to 76 labelled g_1(3)* 66 to 30 labelled ok_1(2)* 66 to 35 labelled ok_1(2)* 66 to 43 labelled active_1(2)* 66 to 75 labelled f_1(3), g_1(3)* 66 to 53 labelled active_1(3)* 66 to 57 labelled active_1(4)* 75 to 30 labelled ok_1(3)* 75 to 35 labelled ok_1(3)* 75 to 43 labelled active_1(2)* 75 to 75 labelled f_1(3), g_1(3)* 75 to 53 labelled active_1(3)* 75 to 57 labelled active_1(4)* 76 to 49 labelled ok_1(3)* 76 to 81 labelled f_1(3)* 81 to 46 labelled ok_1(3)* 81 to 83 labelled c_1(3)* 83 to 43 labelled ok_1(3)* 83 to 53 labelled ok_1(3)* 83 to 89 labelled active_1(3)* 83 to 90 labelled f_1(4), g_1(4)* 83 to 95 labelled active_1(4)* 83 to 97 labelled active_1(5)* 89 to 22 labelled top_1(3)* 90 to 43 labelled ok_1(4)* 90 to 53 labelled ok_1(4)* 90 to 57 labelled ok_1(4)* 90 to 89 labelled active_1(3)* 90 to 90 labelled f_1(4), g_1(4)* 90 to 94 labelled f_1(5), g_1(5)* 90 to 95 labelled active_1(4)* 90 to 97 labelled active_1(5)* 90 to 98 labelled active_1(6)* 94 to 53 labelled ok_1(5)* 94 to 57 labelled ok_1(5)* 94 to 90 labelled f_1(4), g_1(4)* 94 to 94 labelled f_1(5), g_1(5)* 94 to 95 labelled active_1(4)* 94 to 97 labelled active_1(5)* 94 to 98 labelled active_1(6)* 95 to 89 labelled f_1(4), g_1(4)* 97 to 95 labelled f_1(5), g_1(5)* 97 to 97 labelled f_1(5), g_1(5)* 97 to 98 labelled f_1(5), g_1(5)* 98 to 97 labelled f_1(6), g_1(6)* 98 to 98 labelled f_1(6), g_1(6) ----------------------------------------
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