details

property	value
status	complete
benchmark	Ex6_GM04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.71572685242 seconds
cpu usage	3.794060156
max memory	2.05897728E8

stage attributes

key	value
output-size	5665
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(c) -> mark(f(g(c))) active(f(g(X))) -> mark(g(X)) proper(c) -> ok(c) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) f(ok(X)) -> ok(f(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: c'(active(x)) -> c'(g(f(mark(x)))) g(f(active(X))) -> g(mark(X)) c'(proper(x)) -> c'(ok(x)) f(proper(X)) -> proper(f(X)) g(proper(X)) -> proper(g(X)) ok(f(X)) -> f(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 5. This implies Q-termination of R. The following rules were used to construct the certificate: c'(active(x)) -> c'(g(f(mark(x)))) g(f(active(X))) -> g(mark(X)) c'(proper(x)) -> c'(ok(x)) f(proper(X)) -> proper(f(X)) g(proper(X)) -> proper(g(X)) ok(f(X)) -> f(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: 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 84, 85 Node 24 is start node and node 25 is final node. Those nodes are connected through the following edges: * 24 to 26 labelled c'_1(0), f_1(0), g_1(0)* 24 to 28 labelled g_1(0)* 24 to 29 labelled proper_1(0), active_1(0)* 24 to 51 labelled c'_1(1)* 24 to 54 labelled proper_1(1)* 24 to 53 labelled g_1(1)* 24 to 60 labelled proper_1(2)* 24 to 65 labelled c'_1(2)* 24 to 79 labelled c'_1(3)* 25 to 25 labelled #_1(0)* 26 to 27 labelled g_1(0)* 26 to 25 labelled ok_1(0)* 26 to 30 labelled f_1(1), g_1(1)* 26 to 31 labelled active_1(1)* 26 to 56 labelled proper_1(1)* 26 to 59 labelled g_1(2)* 26 to 62 labelled proper_1(3)* 26 to 66 labelled proper_1(2)* 27 to 28 labelled f_1(0)* 27 to 55 labelled proper_1(1)* 28 to 25 labelled mark_1(0)* 28 to 31 labelled proper_1(1)* 29 to 25 labelled f_1(0), g_1(0), top_1(0)* 29 to 32 labelled proper_1(1)* 29 to 33 labelled g_1(1)* 29 to 57 labelled proper_1(2)* 30 to 25 labelled ok_1(1)* 30 to 30 labelled f_1(1), g_1(1)* 30 to 31 labelled active_1(1)* 30 to 59 labelled g_1(2)* 30 to 62 labelled proper_1(3)* 30 to 66 labelled proper_1(2)* 31 to 25 labelled top_1(1)* 32 to 25 labelled f_1(1), g_1(1)* 32 to 32 labelled proper_1(1)* 32 to 33 labelled g_1(1)* 32 to 57 labelled proper_1(2)* 33 to 25 labelled mark_1(1)* 33 to 31 labelled proper_1(1)* 51 to 52 labelled g_1(1)* 51 to 56 labelled ok_1(1)* 51 to 63 labelled proper_1(2)* 51 to 64 labelled g_1(2)* 51 to 62 labelled ok_1(1)* 51 to 66 labelled ok_1(1)* 51 to 69 labelled f_1(2), g_1(2)* 51 to 72 labelled g_1(3)* 51 to 75 labelled proper_1(4)* 52 to 53 labelled f_1(1)* 52 to 61 labelled proper_1(2)* 53 to 31 labelled mark_1(1)* 53 to 58 labelled proper_1(2)* 54 to 31 labelled g_1(1)* 54 to 56 labelled f_1(1), g_1(1)* 54 to 62 labelled f_1(1), g_1(1)* 54 to 66 labelled f_1(1), g_1(1)* 55 to 31 labelled f_1(1)* 56 to 55 labelled g_1(1)* 57 to 31 labelled g_1(2)* 58 to 25 labelled top_1(2)* 59 to 31 labelled mark_1(2)* 59 to 58 labelled proper_1(2)* 60 to 58 labelled g_1(2)* 61 to 58 labelled f_1(2)* 62 to 58 labelled g_1(3)* 63 to 61 labelled g_1(2)* 64 to 55 labelled ok_1(2)* 64 to 67 labelled f_1(2)* 64 to 58 labelled ok_1(2)* 64 to 71 labelled active_1(3)* 65 to 63 labelled ok_1(2)* 65 to 68 labelled g_1(3)* 65 to 76 labelled g_1(4)* 65 to 75 labelled ok_1(2)* 65 to 78 labelled proper_1(5)* 66 to 62 labelled f_1(2), g_1(2)* 66 to 66 labelled f_1(2), g_1(2)* 67 to 31 labelled ok_1(2)* 67 to 58 labelled active_1(2)* 68 to 61 labelled ok_1(3)* 68 to 70 labelled f_1(3)* 68 to 71 labelled ok_1(3)* 68 to 77 labelled active_1(4)* 69 to 62 labelled ok_1(2)* 69 to 66 labelled ok_1(2)* 69 to 70 labelled g_1(3)* 69 to 73 labelled f_1(3), g_1(3)* 70 to 58 labelled ok_1(3)* 70 to 71 labelled active_1(3)* 71 to 25 labelled top_1(3)* 72 to 58 labelled mark_1(3)* 72 to 71 labelled proper_1(3)* 73 to 62 labelled ok_1(3)* 73 to 66 labelled ok_1(3)* 73 to 74 labelled g_1(4)* 73 to 73 labelled f_1(3), g_1(3)* 74 to 58 labelled ok_1(4)* 74 to 71 labelled active_1(3)* 75 to 71 labelled g_1(4)* 76 to 71 labelled mark_1(4)* 76 to 77 labelled proper_1(4)* 77 to 25 labelled top_1(4)* 78 to 77 labelled g_1(5)* 79 to 78 labelled ok_1(3)* 79 to 84 labelled g_1(4)* 84 to 77 labelled ok_1(4)* 84 to 85 labelled active_1(5)* 85 to 25 labelled top_1(5) ---------------------------------------- (4) YES popout

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job log

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actions

all output return to TRS Stand 20472