details

property	value
status	complete
benchmark	wst99.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n064.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.04727602005 seconds
cpu usage	9.031503985
max memory	5.92396288E8

stage attributes

key	value
output-size	11316
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 16 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPQMonotonicMRRProof [EQUIVALENT, 70 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 37 ms] (12) QDP (13) PisEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: din(der(plus(X, Y))) -> u21(din(der(X)), X, Y) u21(dout(DX), X, Y) -> u22(din(der(Y)), X, Y, DX) u22(dout(DY), X, Y, DX) -> dout(plus(DX, DY)) din(der(times(X, Y))) -> u31(din(der(X)), X, Y) u31(dout(DX), X, Y) -> u32(din(der(Y)), X, Y, DX) u32(dout(DY), X, Y, DX) -> dout(plus(times(X, DY), times(Y, DX))) din(der(der(X))) -> u41(din(der(X)), X) u41(dout(DX), X) -> u42(din(der(DX)), X, DX) u42(dout(DDX), X, DX) -> dout(DDX) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: din(der(plus(X, Y))) -> u21(din(der(X)), X, Y) u21(dout(DX), X, Y) -> u22(din(der(Y)), X, Y, DX) u22(dout(DY), X, Y, DX) -> dout(plus(DX, DY)) din(der(times(X, Y))) -> u31(din(der(X)), X, Y) u31(dout(DX), X, Y) -> u32(din(der(Y)), X, Y, DX) u32(dout(DY), X, Y, DX) -> dout(plus(times(X, DY), times(Y, DX))) din(der(der(X))) -> u41(din(der(X)), X) u41(dout(DX), X) -> u42(din(der(DX)), X, DX) u42(dout(DDX), X, DX) -> dout(DDX) The set Q consists of the following terms: din(der(plus(x0, x1))) u21(dout(x0), x1, x2) u22(dout(x0), x1, x2, x3) din(der(times(x0, x1))) u31(dout(x0), x1, x2) u32(dout(x0), x1, x2, x3) din(der(der(x0))) u41(dout(x0), x1) u42(dout(x0), x1, x2) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: DIN(der(plus(X, Y))) -> U21(din(der(X)), X, Y) DIN(der(plus(X, Y))) -> DIN(der(X)) U21(dout(DX), X, Y) -> U22(din(der(Y)), X, Y, DX) U21(dout(DX), X, Y) -> DIN(der(Y)) DIN(der(times(X, Y))) -> U31(din(der(X)), X, Y) DIN(der(times(X, Y))) -> DIN(der(X)) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard