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TRS Standard pair #516966690
details
property
value
status
complete
benchmark
2.49.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.17276883125 seconds
cpu usage
5.560803671
max memory
4.762624E8
stage attributes
key
value
output-size
2004
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ----------------------------------------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(d(x))) -> c(x) u(b(d(d(x)))) -> b(x) v(a(a(x))) -> u(v(x)) v(a(c(x))) -> u(b(d(x))) v(c(x)) -> b(x) w(a(a(x))) -> u(w(x)) w(a(c(x))) -> u(b(d(x))) w(c(x)) -> b(x) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. The following rules were used to construct the certificate: a(c(d(x))) -> c(x) u(b(d(d(x)))) -> b(x) v(a(a(x))) -> u(v(x)) v(a(c(x))) -> u(b(d(x))) v(c(x)) -> b(x) w(a(a(x))) -> u(w(x)) w(a(c(x))) -> u(b(d(x))) w(c(x)) -> b(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 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 2 labelled c_1(0), b_1(0), b_1(1)* 1 to 3 labelled u_1(0)* 1 to 4 labelled u_1(0)* 2 to 2 labelled #_1(0)* 3 to 2 labelled v_1(0), w_1(0), b_1(1)* 3 to 6 labelled u_1(1)* 3 to 7 labelled u_1(1)* 4 to 5 labelled b_1(0)* 5 to 2 labelled d_1(0)* 6 to 2 labelled v_1(1), w_1(1), b_1(1)* 6 to 6 labelled u_1(1)* 6 to 7 labelled u_1(1)* 7 to 8 labelled b_1(1)* 8 to 2 labelled d_1(1) ---------------------------------------- (2) YES
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