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TRS Inner 89993 pair #381734077
details
property
value
status
complete
benchmark
Ex18_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.56708407402 seconds
cpu usage
3.537762099
max memory
2.619392E8
stage attributes
key
value
output-size
6641
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 11 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(f(a))) -> mark(f(g(f(a)))) active(f(X)) -> f(active(X)) f(mark(X)) -> mark(f(X)) proper(f(X)) -> f(proper(X)) proper(a) -> ok(a) 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)) The set Q consists of the following terms: active(f(x0)) f(mark(x0)) proper(f(x0)) proper(a) proper(g(x0)) f(ok(x0)) g(ok(x0)) top(mark(x0)) top(ok(x0)) ---------------------------------------- (1) QTRS Reverse (SOUND) 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(mark(x))))) f(active(X)) -> active(f(X)) mark(f(X)) -> f(mark(X)) f(proper(X)) -> proper(f(X)) a'(proper(x)) -> a'(ok(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 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(mark(x))))) f(active(X)) -> active(f(X)) mark(f(X)) -> f(mark(X)) f(proper(X)) -> proper(f(X)) a'(proper(x)) -> a'(ok(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: 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 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, 88, 89 Node 37 is start node and node 38 is final node. Those nodes are connected through the following edges:
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