details

property	value
status	complete
benchmark	z082.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.53164315224 seconds
cpu usage	6.977229215
max memory	7.58489088E8

stage attributes

key	value
output-size	6488
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4)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: a(c(a(x1))) -> c(a(c(x1))) a(a(b(x1))) -> a(d(b(x1))) a(b(x1)) -> b(a(a(x1))) d(d(x1)) -> a(d(b(x1))) b(b(x1)) -> b(c(x1)) a(d(c(x1))) -> c(a(x1)) b(c(x1)) -> a(a(a(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(c(a(x1))) -> c(a(c(x1))) b(a(a(x1))) -> b(d(a(x1))) b(a(x1)) -> a(a(b(x1))) d(d(x1)) -> b(d(a(x1))) b(b(x1)) -> c(b(x1)) c(d(a(x1))) -> a(c(x1)) c(b(x1)) -> a(a(a(x1))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. The following rules were used to construct the certificate: a(c(a(x1))) -> c(a(c(x1))) b(a(a(x1))) -> b(d(a(x1))) b(a(x1)) -> a(a(b(x1))) d(d(x1)) -> b(d(a(x1))) b(b(x1)) -> c(b(x1)) c(d(a(x1))) -> a(c(x1)) c(b(x1)) -> a(a(a(x1))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173 Node 139 is start node and node 140 is final node. Those nodes are connected through the following edges: * 139 to 141 labelled c_1(0)* 139 to 143 labelled b_1(0)* 139 to 145 labelled a_1(0)* 139 to 146 labelled c_1(0)* 139 to 142 labelled a_1(0), c_1(1)* 139 to 147 labelled a_1(1)* 139 to 156 labelled c_1(1)* 139 to 162 labelled c_1(2)* 140 to 140 labelled #_1(0)* 141 to 142 labelled a_1(0), c_1(1)* 141 to 156 labelled c_1(1)* 142 to 140 labelled c_1(0)* 142 to 149 labelled a_1(1)* 142 to 147 labelled a_1(1)* 142 to 142 labelled c_1(1)* 142 to 158 labelled c_1(2)* 142 to 162 labelled c_1(2)* 142 to 160 labelled c_1(2)* 142 to 164 labelled c_1(2)* 143 to 144 labelled d_1(0)* 144 to 140 labelled a_1(0)* 144 to 142 labelled c_1(1)* 145 to 146 labelled a_1(0)* 145 to 156 labelled c_1(1)* 146 to 140 labelled b_1(0), a_1(0)* 146 to 150 labelled b_1(1)* 146 to 152 labelled a_1(1)* 146 to 153 labelled c_1(1)* 146 to 142 labelled c_1(1)* 146 to 154 labelled a_1(2)* 146 to 164 labelled c_1(2)* 146 to 166 labelled c_1(3)* 147 to 148 labelled a_1(1)* 147 to 158 labelled c_1(2)* 148 to 140 labelled a_1(1)* 148 to 150 labelled a_1(1)* 148 to 142 labelled c_1(1)* 149 to 140 labelled c_1(1)* 149 to 149 labelled a_1(1)* 149 to 147 labelled a_1(1)* 149 to 157 labelled c_1(1)* 149 to 142 labelled c_1(1)* 149 to 158 labelled c_1(2)* 149 to 162 labelled c_1(2)* 149 to 159 labelled c_1(1)* 149 to 163 labelled c_1(1)* 149 to 160 labelled c_1(2)* 149 to 161 labelled c_1(1)* 149 to 164 labelled c_1(2)* 150 to 151 labelled d_1(1)* 151 to 140 labelled a_1(1)* 151 to 142 labelled c_1(1)* 152 to 153 labelled a_1(1)* 152 to 160 labelled c_1(2)* 153 to 140 labelled b_1(1)* 153 to 150 labelled b_1(1)* 153 to 152 labelled a_1(1)* 153 to 153 labelled c_1(1)* 153 to 154 labelled a_1(2)* 153 to 164 labelled c_1(2)* 153 to 166 labelled c_1(3)* 154 to 155 labelled a_1(2)* 154 to 158 labelled c_1(2)* 155 to 140 labelled a_1(2)* 155 to 142 labelled c_1(1)* 155 to 150 labelled a_1(2)* 156 to 157 labelled a_1(1)* 156 to 158 labelled c_1(2)* 157 to 149 labelled c_1(1)* 157 to 147 labelled c_1(1)* 157 to 152 labelled c_1(1)* 157 to 154 labelled c_1(1)* 157 to 165 labelled c_1(1)* 157 to 167 labelled c_1(1)* 158 to 159 labelled a_1(2)* 158 to 158 labelled c_1(2)* 158 to 142 labelled c_1(1)* 158 to 160 labelled c_1(2)* 158 to 168 labelled c_1(3)* 158 to 166 labelled c_1(3)* 159 to 149 labelled c_1(2), a_1(1)* 159 to 147 labelled c_1(2), a_1(1)* 159 to 148 labelled c_1(2)* 159 to 153 labelled c_1(2)* 159 to 140 labelled c_1(2)* 159 to 150 labelled c_1(2)* 159 to 154 labelled a_1(2)* 159 to 163 labelled c_1(2)* 159 to 155 labelled c_1(2)* 159 to 159 labelled a_1(2)* 159 to 142 labelled c_1(1)* 159 to 158 labelled c_1(2)* 159 to 162 labelled c_1(2)* 159 to 166 labelled c_1(3)* 159 to 160 labelled c_1(2)* 159 to 168 labelled c_1(3)* 159 to 164 labelled c_1(2)* 160 to 161 labelled a_1(2)* 160 to 158 labelled c_1(2)* 160 to 170 labelled c_1(3)* 161 to 152 labelled c_1(2)* 161 to 154 labelled c_1(2)* 161 to 165 labelled c_1(2)* 161 to 167 labelled c_1(2)* 162 to 163 labelled a_1(2)* 162 to 158 labelled c_1(2)* 162 to 168 labelled c_1(3)* 162 to 166 labelled c_1(3)* 163 to 159 labelled c_1(2)* 164 to 165 labelled a_1(2)* 165 to 161 labelled c_1(2)* 166 to 167 labelled a_1(3)* 166 to 158 labelled c_1(2)* 166 to 168 labelled c_1(3)* 166 to 166 labelled c_1(3)* 167 to 159 labelled c_1(3)* 168 to 169 labelled a_1(3)* 168 to 170 labelled c_1(3)* 168 to 142 labelled c_1(1)* 168 to 158 labelled c_1(2)* 168 to 166 labelled c_1(3)* 168 to 168 labelled c_1(3)* 168 to 172 labelled c_1(4)* 169 to 154 labelled c_1(3)* 169 to 140 labelled c_1(3)* 169 to 150 labelled c_1(3)* 169 to 149 labelled a_1(1)* 169 to 147 labelled a_1(1)* 169 to 163 labelled c_1(3)* 169 to 161 labelled c_1(3)* 169 to 167 labelled c_1(3)* 169 to 169 labelled c_1(3)* 169 to 159 labelled a_1(2)* 169 to 142 labelled c_1(1)* 169 to 158 labelled c_1(2)* 169 to 162 labelled c_1(2)* 169 to 166 labelled c_1(3)* 169 to 168 labelled c_1(3)* 169 to 164 labelled c_1(2)* 169 to 160 labelled c_1(2)* 169 to 165 labelled c_1(3)* 170 to 171 labelled a_1(3)* 170 to 168 labelled c_1(3)* 171 to 155 labelled c_1(3)* 172 to 173 labelled a_1(4)* 172 to 158 labelled c_1(2)* 172 to 166 labelled c_1(3)* 173 to 167 labelled c_1(4)* 173 to 169 labelled c_1(4) ---------------------------------------- (4) YES popout

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