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TRS Equational pair #487092824
details
property
value
status
complete
benchmark
BAG_nosorts-noand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.48765 seconds
cpu usage
6.0873
user time
5.87801
system time
0.209287
max virtual memory
1.8343376E7
max residence set size
354028.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 221 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 121 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 67 ms] (6) ETRS (7) RRRPoloETRSProof [EQUIVALENT, 38 ms] (8) ETRS (9) RRRPoloETRSProof [EQUIVALENT, 24 ms] (10) ETRS (11) RRRPoloETRSProof [EQUIVALENT, 0 ms] (12) ETRS (13) RisEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: union(X, empty) -> X union(empty, X) -> X 0(z) -> z U11(tt, X, Y) -> U12(tt, X, Y) U12(tt, X, Y) -> 0(mult(X, Y)) U21(tt, X, Y) -> U22(tt, X, Y) U22(tt, X, Y) -> plus(0(mult(X, Y)), Y) U31(tt, X, Y) -> U32(tt, X, Y) U32(tt, X, Y) -> 0(plus(X, Y)) U41(tt, X, Y) -> U42(tt, X, Y) U42(tt, X, Y) -> 1(plus(X, Y)) U51(tt, X, Y) -> U52(tt, X, Y) U52(tt, X, Y) -> 0(plus(plus(X, Y), 1(z))) U61(tt, A, B) -> U62(tt, A, B) U62(tt, A, B) -> mult(prod(A), prod(B)) U71(tt, A, B) -> U72(tt, A, B) U72(tt, A, B) -> plus(sum(A), sum(B)) mult(z, X) -> z mult(0(X), Y) -> U11(tt, X, Y) mult(1(X), Y) -> U21(tt, X, Y) plus(z, X) -> X plus(0(X), 0(Y)) -> U31(tt, X, Y) plus(0(X), 1(Y)) -> U41(tt, X, Y) plus(1(X), 1(Y)) -> U51(tt, X, Y) prod(empty) -> 1(z) prod(singl(X)) -> X prod(union(A, B)) -> U61(tt, A, B) sum(empty) -> 0(z) sum(singl(X)) -> X sum(union(A, B)) -> U71(tt, A, B) The set E consists of the following equations: mult(x, y) == mult(y, x) plus(x, y) == plus(y, x) union(x, y) == union(y, x) mult(mult(x, y), z') == mult(x, mult(y, z')) plus(plus(x, y), z') == plus(x, plus(y, z')) union(union(x, y), z') == union(x, union(y, z')) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: union(X, empty) -> X union(empty, X) -> X 0(z) -> z U11(tt, X, Y) -> U12(tt, X, Y) U12(tt, X, Y) -> 0(mult(X, Y)) U21(tt, X, Y) -> U22(tt, X, Y) U22(tt, X, Y) -> plus(0(mult(X, Y)), Y) U31(tt, X, Y) -> U32(tt, X, Y) U32(tt, X, Y) -> 0(plus(X, Y)) U41(tt, X, Y) -> U42(tt, X, Y) U42(tt, X, Y) -> 1(plus(X, Y)) U51(tt, X, Y) -> U52(tt, X, Y) U52(tt, X, Y) -> 0(plus(plus(X, Y), 1(z))) U61(tt, A, B) -> U62(tt, A, B) U62(tt, A, B) -> mult(prod(A), prod(B)) U71(tt, A, B) -> U72(tt, A, B) U72(tt, A, B) -> plus(sum(A), sum(B)) mult(z, X) -> z mult(0(X), Y) -> U11(tt, X, Y) mult(1(X), Y) -> U21(tt, X, Y) plus(z, X) -> X plus(0(X), 0(Y)) -> U31(tt, X, Y)
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