details

property	value
status	complete
benchmark	z124.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.12470698357 seconds
cpu usage	5.48362421
max memory	4.727808E8

stage attributes

key	value
output-size	3709
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4)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: q0(a(x1)) -> x(q1(x1)) q1(a(x1)) -> a(q1(x1)) q1(y(x1)) -> y(q1(x1)) a(q1(b(x1))) -> q2(a(y(x1))) a(q2(a(x1))) -> q2(a(a(x1))) a(q2(y(x1))) -> q2(a(y(x1))) y(q1(b(x1))) -> q2(y(y(x1))) y(q2(a(x1))) -> q2(y(a(x1))) y(q2(y(x1))) -> q2(y(y(x1))) q2(x(x1)) -> x(q0(x1)) q0(y(x1)) -> y(q3(x1)) q3(y(x1)) -> y(q3(x1)) q3(bl(x1)) -> bl(q4(x1)) 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(q0(x1)) -> q1(x(x1)) a(q1(x1)) -> q1(a(x1)) y(q1(x1)) -> q1(y(x1)) b(q1(a(x1))) -> y(a(q2(x1))) a(q2(a(x1))) -> a(a(q2(x1))) y(q2(a(x1))) -> y(a(q2(x1))) b(q1(y(x1))) -> y(y(q2(x1))) a(q2(y(x1))) -> a(y(q2(x1))) y(q2(y(x1))) -> y(y(q2(x1))) x(q2(x1)) -> q0(x(x1)) y(q0(x1)) -> q3(y(x1)) y(q3(x1)) -> q3(y(x1)) bl(q3(x1)) -> q4(bl(x1)) Q is empty. ---------------------------------------- (3) 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(q0(x1)) -> q1(x(x1)) a(q1(x1)) -> q1(a(x1)) y(q1(x1)) -> q1(y(x1)) b(q1(a(x1))) -> y(a(q2(x1))) a(q2(a(x1))) -> a(a(q2(x1))) y(q2(a(x1))) -> y(a(q2(x1))) b(q1(y(x1))) -> y(y(q2(x1))) a(q2(y(x1))) -> a(y(q2(x1))) y(q2(y(x1))) -> y(y(q2(x1))) x(q2(x1)) -> q0(x(x1)) y(q0(x1)) -> q3(y(x1)) y(q3(x1)) -> q3(y(x1)) bl(q3(x1)) -> q4(bl(x1)) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23 Node 9 is start node and node 10 is final node. Those nodes are connected through the following edges: * 9 to 11 labelled q1_1(0), q0_1(0), q3_1(0)* 9 to 12 labelled y_1(0), a_1(0)* 9 to 14 labelled y_1(0), a_1(0)* 9 to 16 labelled q4_1(0)* 10 to 10 labelled #_1(0)* 11 to 10 labelled x_1(0), a_1(0), y_1(0)* 11 to 18 labelled q0_1(1), q1_1(1), q3_1(1)* 11 to 19 labelled a_1(1), y_1(1)* 11 to 21 labelled a_1(1), y_1(1)* 12 to 13 labelled a_1(0)* 12 to 19 labelled a_1(1)* 12 to 21 labelled a_1(1)* 13 to 10 labelled q2_1(0)* 14 to 15 labelled y_1(0)* 14 to 19 labelled y_1(1)* 14 to 21 labelled y_1(1)* 15 to 10 labelled q2_1(0)* 16 to 10 labelled bl_1(0)* 16 to 23 labelled q4_1(1)* 18 to 10 labelled x_1(1), a_1(1), y_1(1)* 18 to 18 labelled q0_1(1), q1_1(1), q3_1(1)* 18 to 19 labelled a_1(1), y_1(1)* 18 to 21 labelled a_1(1), y_1(1)* 19 to 20 labelled a_1(1)* 19 to 19 labelled a_1(1)* 19 to 21 labelled a_1(1)* 20 to 10 labelled q2_1(1)* 21 to 22 labelled y_1(1)* 21 to 19 labelled y_1(1)* 21 to 21 labelled y_1(1)* 22 to 10 labelled q2_1(1)* 23 to 10 labelled bl_1(1)* 23 to 23 labelled q4_1(1) popout

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