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TRS Inner 89993 pair #381733975
details
property
value
status
complete
benchmark
Ex6_GM04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.59753298759 seconds
cpu usage
3.270404224
max memory
2.21802496E8
stage attributes
key
value
output-size
1927
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__c -> a__f(g(c)) a__f(g(X)) -> g(X) mark(c) -> a__c mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) a__c -> c a__f(X) -> f(X) The set Q consists of the following terms: a__c mark(c) mark(f(x0)) 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__c -> a__f(g(c)) a__f(g(X)) -> g(X) mark(c) -> a__c mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) a__c -> c 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 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 g_1(0), a__c(0), a__f_1(0), c(0), f_1(0), c(1), f_1(1), g_1(1)* 1 to 5 labelled a__f_1(1), f_1(2)* 1 to 4 labelled g_1(1)* 1 to 6 labelled g_1(2)* 2 to 2 labelled #_1(0)* 3 to 4 labelled g_1(0)* 4 to 2 labelled c(0)* 5 to 6 labelled g_1(1)* 6 to 2 labelled c(1) ---------------------------------------- (2) YES
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